Matematici pentru economisti, Editia a III-a

52',&$75$1'$),5 ,'8'$FRRUGRQDWRU $8525$%$&,8 52',&$,2$1 6,/9,8%Æ5= 0$7(0$7,&,3(1758(&2120,ù7, HG...

Author: I. Duda (coord.)

20 downloads 707 Views 2MB Size Report

This content was uploaded by our users and we assume good faith they have the permission to share this book. If you own the copyright to this book and it is wrongfully on our website, we offer a simple DMCA procedure to remove your content from our site. Start by pressing the button below!

Report copyright / DMCA form

DOWNLOAD PDF

52',&$75$1'$),5

,'8'$FRRUGRQDWRU

$8525$%$&,8

52',&$,2$1 6,/9,8%Æ5=

0$7(0$7,&,3(1758(&2120,ù7, HGL LDDD

(GLWXUD)XQGD LHL5RPkQLDGH0kLQH (GLWXU DFUHGLWDW GH0LQLVWHUXO(GXFD LHLúL&HUFHW ULL SULQ&RQVLOLXO1D LRQDODO&HUFHW ULLùWLLQ LILFH GLQÌQY PkQWXO6XSHULRU

'HVFULHUHD&,3D%LEOLRWHFLL1D LRQDOHD5RPkQLHL 0DWHPDWLFL SHQWUX HFRQRPLúWL 5RGLFD 7UDQGDILU ,'XGDFRRUG $XURUD%DFLX5RGLFD,RDQ6LOYLX%kU] ± %XFXUHúWL HGL LD D D (GLWXUD )XQGD LHL 5RPkQLD GH 0kLQH SFP %LEOLRJU ,6%1

,7UDQGDILU5RGLFD ,,'XGD,FRRUG ,,,%DFLX$XURUD ,9,RDQ5RGLFD 9%kU] 6LOYLX

5HSURGXFHUHDLQWHJUDO VDXIUDJPHQWDU SULQRULFHIRUP úLSULQRULFHPLMORDFHWHKQLFHHVWHVWULFWLQWHU]LV úLVHSHGHSVHúWHFRQIRUPOHJLL 5 VSXQGHUHDSHQWUXFRQ LQXWXOúLRULJLQDOLWDWHDWH[WXOXL UHYLQHH[FOXVLYDXWRUXOXLDXWRULORU 5HGDFWDUHúLWHKQRUHGDFWDUH6LOYLX%Æ5= &RSHUWD0DULOHQD% /$1 %XQGHWLSDU&ROLWLSDU )RUPDWu (GLWXUD)XQGD LHL5RPkQLDGH0kLQH %XOHYDUGXO7LPLúRDUDQU%XFXUHúWL6HFWRU 7HO)D[ZZZVSLUXKDUHWUR HPDLOFRQWDFW#HGLWXUDURPDQLDGHPDLQHUR

81,9(56,7$7($63,58+$5(7

)$&8/7$7($'(0$7(0$7,& ±,1)250$7,&

52',&$75$1'$),5

,'8'$FRRUGRQDWRU

$8525$%$&,8

52',&$,2$1 6,/9,8%Æ5=

0$7(0$7,&,3(1758(&2120,ù7, HGL LDDD

(',785$)81'$ ,(,520Æ1,$'(0Æ,1( %8&85(ù7,

&835,16

,QWURGXFHUH««««««««««««««««««««««« (OHPHQWHGHDOJHEU OLQLDU ««««««««««««««« 6LVWHPHGHHFXD LLOLQLDUH««««««««««««««« 6LVWHPHGHLQHFXD LLOLQLDUH««««««««««««««« 6SD LLYHFWRULDOH««««««««««««««««««« 6SD LLHXFOLGLHQH««««««««««««««««««« $SOLFD LLOLQLDUH««««««««««««««««««« 9DORULSURSULLúLYHFWRULSURSULLDVRFLD LXQHLDSOLFD LLOLQLDUH«««« )RUPHOLQLDUH)RUPHS WUDWLFH««««««««««««« 5HGXFHUHDXQHLIRUPHS WUDWLFHODIRUPDFDQRQLF «««««« 3URJUDPDUHOLQLDU ««««««««««««««««««« ,QWURGXFHUH««««««««««««««««««««« )RUPDJHQHUDO DSUREOHPHLGHSURJUDPDUHOLQLDU ««««« 6ROX LLOHSUREOHPHLGHSURJUDPDUHOLQLDU ««««««««« 0HWRGDVLPSOH[GHUH]ROYDUHDXQXLSURJUDPOLQLDUVWDQGDUG««« 0HWRGDED]HLDUWLILFLDOH«««««««««««««««« &D]XOvQFDUHVLVWHPXOGHUHVWULF LLFRQ LQHLQHJDOLW L«««« 'XDOLWDWHDvQSURJUDPDUHDOLQLDU «««««««««««« $SOLFD LLvQHFRQRPLH««««««««««««««««« 3UREOHPHGHWUDQVSRUW««««««««««««««««« (OHPHQWHGHDQDOL] PDWHPDWLF ««««««««««««« )XQF LLYHFWRULDOH«««««««««««««««««« /LPLWHLWHUDWH«««««««««««««««««««« &RQWLQXLWDWHDIXQF LLORUYHFWRULDOH«««««««««««« &RQWLQXLWDWHDSDU LDO ««««««««««««««««« 'HULYDWHSDU LDOH««««««««««««««««««« ,QWHUSUHWDUHDHFRQRPLF DGHULYDWHORUSDU LDOH««««««« 'LIHUHQ LDELOLWDWHDIXQF LLORUGHPDLPXOWHYDULDELOH««««« 'HULYDWHSDU LDOHGHRUGLQVXSHULRU«««««««««««« )RUPXODOXL7D\ORU«««««««««««««««««« ([WUHPHOHIXQF LLORUGHPDLPXOWHYDULDELOH«««««««« )XQF LLLPSOLFLWH«««««««««««««««««« ([WUHPHFRQGL LRQDWHOHJDWH ««««««««««««« )XQF LLRPRJHQHGHPDLPXOWHYDULDELOH««««««««« )XQF LLRPRJHQHvQHFRQRPLH««««««««««««« (FXD LLGLIHUHQ LDOH««««««««««««««««« (FXD LLGLIHUHQ LDOHFDUHQXFRQ LQYDULDELOHLQGHSHQGHQWH««« (FXD LLFXYDULDELOHVHSDUDELOH«««««««««««««

(FXD LLRPRJHQH«««««««««««««««««« (FXD LLUHGXFWLELOHODHFXD LLRPRJHQH«««««««««« (FXD LLOLQLDUHGHRUGLQXOvQWkL««««««««««««« 8QHOHDSOLFD LLvQHFRQRPLHDHFXD LLORUGLIHUHQ LDOH«««« 7HRULDSUREDELOLW LORUúLVWDWLVWLF PDWHPDWLF ««««««« &kPSGHHYHQLPHQWH3UREDELOLWDWH«««««««««« &kPSGHHYHQLPHQWH««««««««««««« 3UREDELOLWDWHSHXQFkPSILQLWGHHYHQLPHQWH«««« V FkPSGHSUREDELOLWDWH««««««««««« (YHQLPHQWHLQGHSHQGHQWH3UREDELOLWDWHFRQGL LRQDW « 9DULDELOHDOHDWRDUH&DUDFWHULVWLFLQXPHULFH)XQF LHGH UHSDUWL LH««««««««««««««««««««« 9DULDELOHDOHDWRDUHGLVFUHWH«««««««««« 0RPHQWHOHXQHLYDULDELOHDOHDWRDUHGLVFUHWH««««« 9DULDELOHDOHDWRDUHGHWLSFRQWLQXX«««««««« )XQF LHGHUHSDUWL LH««««««««««««« 0RPHQWHOHXQHLYDULDELOHGHWLSFRQWLQXX««««« )XQF LHFDUDFWHULVWLF ««««««««««««« 5HSDUWL LLSUREDELOLVWLFHFODVLFH«««««««««««« 5HSDUWL LLGHWLSGLVFUHW«««««««««««« 7HRUHPDSDUWLFXODU DH[SHULPHQWHORUUHSHWDWH« 7HRUHPDJHQHUDO DH[SHULPHQWHORUUHSHWDWH«« 5HSDUWL LD3RLVVRQGHSDUDPHWUX O ««««« 6FKHPDSROLQRPLDO ««««««««««« 6FKHPDELOHLQHUHYHQLWH«««««««««« 5HSDUWL LLGHWLSFRQWLQXX««««««««««« 5HSDUWL LDGHGHQVLWDWHXQLIRUP «««««« /HJHDQRUPDO ««««««««««««« 5HSDUWL LDORJQRUPDO «««««««««« 5HSDUWL LDH[SRQHQ LDO QHJDWLY «««««« 5HSDUWL LD F «««««««««««««« 5HSDUWL LD6WXGHQW«««««««««««« 6LVWHPHGHYDULDELOHDOHDWRDUH««««««««««««« 6LVWHPHGHGRX YDULDELOHDOHDWRDUH««««««« &DUDFWHULVWLFLQXPHULFHDOHVLVWHPHORUGHGRX YDULDELOH DOHDWRDUH&RYDULDQ &RHILFLHQWGHFRUHOD LH«««« 7HRULDVHOHF LHL««««««««««««««««««« *HQHUDOLW L«««««««««««««««««« 6HOHF LL««««««««««««««««««« )XQF LDGHUHSDUWL LHGHVHOHF LH««««««««« 9DORULWLSLFHGHVHOHF LH«««««««««««««

7HRULDHVWLPD LHL««««««««««««««««« (VWLPD LLFRQVLVWHQWHFRUHFWHúLDEVROXWFRUHFWH QHGHSODVDWHGHSODVDWH«««««««««««««« )XQF LLGHHVWLPD LHHILFLHQWH0HWRGDYHURVLPLOLW LL PD[LPH«««««««««««««««««« (OHPHQWHGHWHRULDJUDIXULORU«««««««««««««« ,QWURGXFHUH'HILQL LL««««««««««««««««« 0DWULFLDVRFLDWHXQXLJUDI3URSULHW LDOHJUDIXULORU««««« 0DWULFHDFRQH[LXQLORUGLUHFWH««««««««««« 0DWULFHDGUXPXULORU«««««««««««««« 'HWHUPLQDUHDGUXPXULORUKDPLOWRQLHQHvQJUDIXULI U FLUFXLWH««««««««««««««««««« 'HWHUPLQDUHDGUXPXOXLKDPLOWRQLDQvQJUDIFXFLUFXLWH« 'UXPXULGHYDORDUHvQWUXQJUDIDOJRULWPXO %HOOPDQ.DODED«««««««««««««««« )OX[PD[LPvQWURUH HDGHWUDQVSRUW««««««««««« (OHPHQWHGHPDWHPDWLFLILQDQFLDUH«««««««««««« 'REkQGDVLPSO ««««««««««««««««««« 'REkQGDFRPSXV «««««««««««««««««« 2SHUD LXQLGHVFRQW1RWD LLúLGHQXPLUL«««««««««« 3O LHúDORQDWHUHQWH ««««««««««««««««« $QXLW LFRQVWDQWHSRVWLFLSDWH««««««««««« $QXLW LFRQVWDQWHDQWLFLSDWH««««««««««« 3O LHúDORQDWHIUDF LRQDWH«««««««««««« ÌPSUXPXWXUL«««««««««««««««««««« $PRUWL]DUHDXQXLvPSUXPXWSULQDQXLW L FRQVWDQWHSRVWLFLSDWH«««««««««««««« ÌPSUXPXWXULFXDQXLW LUDWH FRQVWDQWHSO WLELOH ODVIkUúLWXODQXOXLSRVWLFLSDW ««««««««««« ÌPSUXPXWXULFXDQXLW LUDWH FRQVWDQWHFXGREkQG SO WLW ODvQFHSXWXODQXOXLDQWLFLSDW «««««««« ÌPSUXPXWXULUDPEXUVDELOHRVLQJXU GDW «««««« ÌPSUXPXWXULFXDPRUWLVPHQWHHJDOH«««««««« (OHPHQWHGHPDWHPDWLFLDFWXDULDOH««««« $VLJXU ULGHSHUVRDQH«««««««««««««« 3UREDELOLWDWHDGHYLD úLGHPRDUWH««««««««« $VLJXUDUHDXQHLVXPHvQFD]GHVXSUDYLH XLUHODvPSOLQLUHD WHUPHQXOXLGHDVLJXUDUH««««««««««««« $QXLW LYLDJHUHSRVWLFLSDWHLPHGLDWH««««««« $QXLW LYLDJHUHDQWLFLSDWHLPHGLDWH«««««««« $QXLW LOLPLWDWHOD Q DQL«««««««««««« $QXLW LYLDJHUHDPkQDWH««««««««««««

$VLJXUDUHDGHSHQVLH«««««««««««««« $VLJXUDUHDGHGHFHV«««««««««««««« $VLJXU ULPL[WH«««««««««««««« 0RGHOHPDWHPDWLFHSHQWUXJHVWLXQHDVWRFXULORU«««««« 1R LXQLJHQHUDOH«««««««««««««««« 0RGHOHGHWHUPLQLVWH««««««««««««««« 0RGHOGHVWRFDUHDXQXLSURGXVFXFHUHUHFRQVWDQW SHULRDG FRQVWDQW GHUHDSURYL]LRQDUHúLI U OLSV GHVWRF 0RGHOGHVWRFDUHDXQXLSURGXVFXFHUHUHFRQVWDQW SHULRDG FRQVWDQW GHUHDSURYL]LRQDUHúLFXSRVLELOLWDWHD OLSVHLGHVWRF««««««««««««««««« 0RGHOGHVWRFDUHDXQXLSURGXVFXFHUHUHFRQVWDQW SHULRDG FRQVWDQW GHUHDSURYL]LRQDUHI U OLSV GHVWRF OXkQGvQFRQVLGHUDUHúLFRVWXOGHDFKL]L LHVDXGH SURGXF LH««««««««««««««««««« 0RGHOGHVWRFDUHDPDLPXOWRUSURGXVH««««««« 0RGHOHSUREDELOLVWH«««««««««««««««« 0RGHOGHVWRFDUHDXQXLSURGXVFXFHUHUHDDOHDWRDUHFX SLHUGHUHvQFD]XOVXUSOXVXOXLGHVWRFFXFKHOWXLHOL VXSOLPHQWDUHvQFD]XOOLSVHLGHVWRFúLFXFRVWGHVWRFDM QHJOLMDELO««««« &D]XOGLVFUHW««««««««««««««« &D]XOFRQWLQXX«««««««««««««« 0RGHOGHVWRFDUHDXQXLSURGXVFXFHUHUHDOHDWRDUHFX FRVWGHVWRFDUHúLFRVWGHSHQDOL]DUHSHQWUXOLSV GHVWRF &D]XOGLVFUHW««««««««««««««« &D]XOFRQWLQXX«««««««««««««« (OHPHQWHGHWHRULDDúWHSW ULL««««««««««««« 6WUXFWXUDGHED] úLFDUDFWHULVWLFLOHXQXLVLVWHPGHDúWHSWDUH« 0 VXUDUHDSHUIRUPDQ HORUVLVWHPXOXLGHDúWHSWDUH5HOD LLGH ED] ««««««««««««««««««««««« /HJLSUREDELOLVWLFHDOHVRVLULORUúLDOHVHUYLFLLORU««« 'HGXFHUHDHFXD LLORUGHVWDUHSHQWUXXQIHQRPHQGHDúWHSWDUHvQ UHJLPVWD LRQDU«««««««««««««««« &D]XO Q ««««««««««««««««« &D]XO Q ! «««««««««««««««««

0RGHOHGHDúWHSWDUH«««««««««««««« 0RGHOFXILUQHOLPLWDW 0 0 ),)2 f f ««

0RGHOFXILUOLPLWDW 0 0 ),)2 1 f «« 0RGXOGHDúWHSWDUHFXVRVLULSRLVVRQLHQHWLPSGHVHUYLUH H[SRQHQ LDOFXVVWD LLLGHQWLFHSRSXOD LHLLQILQLW 0 0 V ),)2 f f «««««««««« 0RGHOXOGHDúWHSWDUHFXVRVLULSRLVVRQLHQHWLPSGH VHUYLUHH[SRQHQ LDOFXRVWD LHSRSXOD LHILQLW 0 0 ),)2 P P ««««««««« 0RGHOGHDúWHSWDUHFXVRVLULSRLVVRQLHQHWLPSGHVFULHUH H[FHS LRQDOFXVVWD LLLGHQWLFHSRSXOD LDILQLW 0 0 V ),)2 P V P «««««««« %LEOLRJUDILH««««««««««««««««««

,1752'8&(5(

3UH]HQWDOXFUDUHHVWHGHVWLQDW VWXGHQ LORUGLQIDFXOW LOH GH SURILO HFRQRPLF GLQ FDGUXO 8QLYHUVLW LL 6SLUX +DUHW úL DFRSHU SURJUDPD FXUVXOXL GH 0DWHPDWLF ILLQG UHGDFWDW SRUQLQGGHODSURJUDPHOHDQDOLWLFH &DUWHDFXSULQGHSUH]HQW ULOHGLQSXQFWGHYHGHUHWHRUHWLF DOH XUP WRDUHORU GRPHQLL HOHPHQWH GH DOJHEU OLQLDU SURJUDPDUH OLQLDU HOHPHQWH GH DQDOL] PDWHPDWLF WHRULD SUREDELOLW LORU úL VWDWLVWLF PDWHPDWLF HOHPHQWH GH WHRULD JUDIXULORU HOHPHQWH GH PDWHPDWLFL ILQDQFLDUH HOHPHQWH GH PDWHPDWLFL DFWXDULDOH PRGHOH PDWHPDWLFH GH WHRULD VWRFXULORU úLHOHPHQWHGHWHRULDDúWHSW ULL ([SXQHUHDPDWHULDOXOXLWHRUHWLFHVWHvQVR LW GHH[HPSOH $XWRULL

(/(0(17('($/*(%5 /,1,$5 6LVWHPHGHHFXD LLOLQLDUH

8QVLVWHPGH P HFXD LLOLQLDUHFX Q QHFXQRVFXWH [ [ [ Q VHVFULH VXEIRUPD

D [ D [ DQ [ Q E °D [ D [ D [ E ° Q Q ® °# °¯D P [ D P [ D PQ [ Q EP XQGH D LM úL EL FX L P úL M Q VXQWFRQVWDQWHUHDOH Q

¦D M

LM

[M

VDXVXEIRUP PDWULFHDO

$;

XQGH

$

§ D ¨ ¨ D ¨ # ¨ ¨D © P

EL L P

D D # DP

E

" DQ · ¸ " DQ ¸ ; % # ¸ ¸ " D PQ ¸¹

§ [ · ¨ ¸ ¨ [ ¸ ¨ # ¸ E ¨ ¸ ¨[ ¸ © Q¹

§ E · ¨ ¸ ¨ E ¸ ¨ # ¸ ¨ ¸ ¨E ¸ © P¹

0DWULFHD $ VH QXPHúWH PDWULFHD FRHILFLHQ LORU E VH QXPHúWH PDWULFHD WHUPHQLORUOLEHULLDU;PDWULFHDQHFXQRVFXWHORU 6WXGLXOVLVWHPHORUFX P HFXD LLúL Q QHFXQRVFXWHSUHVXSXQHGHWHUPLQDUHD XQXLVLVWHPGHYDORULQXPHUH FDUHGDWHQHFXQRVFXWHORUV YHULILFHVLPXOWDQWRDWH HFXD LLOHVLVWHPXOXL 6LVWHPXOGHHFXD LLSHQWUXFDUHVHJ VHúWHXQDVHPHQHDVLVWHPGHQXPHUHVDX PDLPXOWHDVHPHQHDVLVWHPHFDUHV YHULILFHVLPXOWDQWRDWHHFXD LLOHVLVWHPXOXLVH QXPHúWH VLVWHP FRPSDWLELO XQLF GHWHUPLQDW UHVSHFWLY VLVWHP FRPSDWLELO QHGHWHUPLQDW ÌQ FD]XO vQ FDUH QX H[LVW QLFL XQ VLVWHP GH QXPHUH FX DFHDVW SURSULHWDWHVLVWHPXOVHYDQXPLVLVWHPLQFRPSDWLELO 7HRUHPD&URQHNHU&DSHOOL6LVWHPXO HVWHXQVLVWHPFRPSDWLELOGDF a úLQXPDLGDF UDQJXOPDWULFHL $ HVWHHJDOFXUDQJXOPDWULFHLH[WLQVH $ XQGH

a $

§ D ¨ ¨ D ¨ # ¨ ¨D © P

D D # DP

" DQ " DQ % # " D PQ

E · ¸ E ¸ # ¸ ¸ EP ¸¹

a

'DF UDQJ $ UDQJ $ N Q QXP UXO QHFXQRVFXWHORU DWXQFL VLVWHPXO HVWHVLVWHPXQLFGHWHUPLQDW a 'DF UDQJ $ UDQJ $ N Q DWXQFL VLVWHPXO HVWH VLVWHP FRPSDWLELOQHGHWHUPLQDW 6WXGLXOVLVWHPHORUVHSRDWHUHDOL]DúLSULQPHWRGDHOLPLQ ULLVXFFHVLYH0HWRGD OXL*DXVV SHOkQJ DOWHPHWRGHFXQRVFXWHGLQOLFHX 0HWRGDOXL*DXVVFRQVW vQWUDQVIRUP ULHOHPHQWDUHVXFFHVLYHDOHVLVWHPXOXL vQWUXQVLVWHPHFKLYDOHQWFDUHYDHOLPLQDSHUkQGFkWHRYDULDELO GLQWRDWHHFXD LLOH VLVWHPXOXLFXH[FHS LDXQHLVLQJXUHHFXD LLvQFDUHFRHILFLHQWXOYDULDELOHLYDILHJDO FXXQLWDWHD 'DF D z DWXQFLYDULDELOD [ GLQSULPDHFXD LHSRDWHDYHDFRHILFLHQWXO GDF VH vPSDUWH DFHDVW HFXD LH SULQ D (OHPHQWXO D VH YD QXPL SLYRW 3ULPD HFXD LHYDGHYHQL

D D D E [ [ Q [ Q D D D D 3HQWUXDHOLPLQDQHFXQRVFXWD [ GLQHFXD LLOH P HFXD LD VH vQPXO HúWHSHUkQGFX D D D P úLVHVFDGHGLQHFXD LD DSRLGLQHFXD LD [

úDPG6HRE LQHFXD LLOH HFXD LD § D

· § · D ¨¨ D D ¸¸ [ ¨¨ D D ¸¸ [ D D © ¹ © ¹

# HFXD LD P

§ · D ¨¨ D Q Q D ¸¸ [ Q D © ¹

§ · E ¨¨ E D ¸¸ D © ¹

# · § · § D D ¨¨ DP DP ¸¸ [ ¨¨ DP DP ¸¸ [ D D ¹ © ¹ © · § · § DQ E DP ¸¸ [Q ¨¨ EP DP ¸¸ ¨¨ DPQ D D ¹ © ¹ ©

6HRE LQHDVWIHOXQVLVWHPHFKLYDOHQWFXVLVWHPXOLQL LDOvQFDUHQHFXQRVFXWD [ VHDIO GRDUvQSULPDHFXD LHFXFRHILFLHQWXQX

D DQ D E ° [ D [ D [ D [ Q D ° °§ · § · DQ D D ¸¸ [ Q °¨¨ D D ¸¸ [ ¨¨ D Q D D ¹ © ¹ °© ° § · E ° ¨¨ E D ¸¸ ° D ¹ © ® °# ° °§ · § · D D D P ¸¸ [ ¨¨ D PQ Q D P ¸¸ [ Q °¨¨ D P D D ¹ © ¹ °© ° § · E ° ¨¨ EP D P ¸¸ °¯ D © ¹ ÌQ HWDSD XUP WRDUH GDF [ DUH FRHILFLHQWXO QHQXO vQ HFXD LD D GRXD VH YD DOHJHDFHVWDSLYRWúLSULQDFHHDúLPHWRG VHYDXUP ULHOLPLQDUHDQHFXQRVFXWHL [ GLQWRDWHHFXD LLOHFXH[FHS LDHFXD LHLGRLXQGHYDDYHDFRHILFLHQWXOXQX $OJRULWPXOYDFRQWLQXDSkQ FkQGQXYRPPDLSXWHDHOLPLQDGXS SURFHGHXO GHPDLVXVQLFLRYDULDELO 6LVWHPXO HFKLYDOHQWFXVLVWHPXO VHSRDWH FDOFXODúLVFKHPDWLFFXDMXWRUXOPHWRGHLGUHSWXQJKLXOXL

6H VFULX FRHILFLHQ LL WXWXURU QHFXQRVFXWHORU úL WHUPHQLL OLEHUL DL VLVWHPXOXL &DOFXOXO XQXL VLVWHP HFKLYDOHQW VH RE LQ DVWIHO OLQLD vQWkL VH vPSDUWHSULQHOHPHQWXO D z D SLYRWXOVHvQFDGUHD] (OHPHQWHOHFRORDQHL

vQWkL VXQW ]HUR &HOHODOWH HOHPHQWH GLQ FHOHODOWH OLQLL VH FDOFXOHD] IRUPkQG XQ GUHSWXQJKLFHDUHFDGLDJRQDO VHJPHQWXOFHXQHúWHORFXOHOHPHQWXOXLGHFDOFXODW úLSLYRWXO1RXOFRHILFLHQWYDILHJDOFXGLIHUHQ DGLQWUHSURGXVXOFRHILFLHQ LORUGH SH GLDJRQDOD SLYRWXOXL úL SURGXVXO FRHILFLHQ LORU GH SH FHDODOW GLDJRQDO GLIHUHQ DFDUHVHvPSDUWHODSLYRW 6FKHPDWLFRE LQHP

D

D

!

DQ

E

D # D P

D # DP

! % !

E # EP

#

c D c D # D Pc

!

DQ # D PQ DcQ D c Q # c D PQ

# EPc

! % !

Ec Ec

XQGH

Dc M

DLMc

D M

D D DLM D M DL

ELc

SHQWUX M

Q

SHQWUX L P M Q D EL D DL E SHQWUX L P D E Ec D

ÌQPRGVLPLODUvQHWDSHOHXUP WRDUHVHRE LQVLVWHPHHFKLYDOHQWHFXVLVWHPXO LQL LDO ÌQHWDSDD Q DVHRE LQH Q Q ! DP ! DQ EQ Q ! D P ! # # % # # % Q ! D P P !

D QQ

EQ

#

Q

D PQ

#

Q

EP

6ROX LDVLVWHPXOXLVHFLWHúWH

[ ° ®# °[ ¯ Q

EQ DQP [ P DQQ [ Q Q

EP

Q

Q

D P P [ P D PQ [ Q a 'DF P Q úL UDQJ $ UDQJ $ P VLVWHPXO HVWH FRPSDWLELO QHGHWHUPLQDW ([HPSOX6 VHUH]ROYHVLVWHPXO

[ [ [ [ ° ® [ [ [ [ ° [ [ [ [ ¯

6ROX LH)RORVLQGPHWRGDOXL*DXVVSUH]HQWDW PDLVXVRE LQHP

'HRDUHFH vQ XOWLPXO VLVWHP WRDWH HOHPHQWHOH D D E VXQW QXOH DOJRULWPXOQXPDLSRDWHFRQWLQXD6LVWHPXOHVWHFRPSDWLELOQHGHWHUPLQDWGHRDUHFH a UDQJ $ UDQJ $ GHWHUPLQDQWXOPD[LPQHQXOFHVHSRDWHIRUPDHVWHGHRUGLQ 1HFXQRVFXWHSULQFLSDOHVXQW [ úL [ 6ROX LDVLVWHPXOXLHVWH

° [ [ [ °° ® [ [ [ ° [ \ ° °¯ [ \

6LVWHPHGHLQHFXD LLOLQLDUH 8Q VLVWHP GH LQHFXD LL OLQLDUH FX Q QHFXQRVFXWH [ [ [ Q VH VFULH VXE IRUPD

D [ D [ DQ [Q E E ° °D [ D [ D Q [Q E E ® °# °¯DP [ DP [ DPQ [Q E EP

XQGHVHPQXOÄ E µUHSUH]LQW XQXOGLQVHPQHOHÄ d ´VDXÄ t ´6LVWHPXOGHLQHFXD LLFDUH FRQ LQHDWkWLQHFXD LLFXVHPQXOÄ d ´FkWúLÄ t ´SRDWHILDGXVODXQVLVWHPFDUHV FRQ LQ QXPDLXQXOGLQWUHDFHVWHVHPQHSULQvQPXO LUHDXQRULQHFXD LLFX 6HSRDWHRE LQH DúDGDUXQDGLQVLWXD LLOH

VDX

D [ D [ DQ [ Q d E °D [ D [ D [ d E ° Q Q ® °# °¯D P [ D P [ D PQ [ Q d EP

D [ D [ DQ [ Q t E °D [ D [ D [ t E ° Q Q ® °# °¯D P [ D P [ D PQ [ Q t EP

D [ D [ DQ [ Q \ E °D [ D [ D [ \ E ° Q Q ® °# °¯D P [ D P [ D PQ [ Q \ P EP

6WXGLXOVLVWHPHORUGHLQHFXD LL VDX VHUHGXFHODVWXGLXOXQXLVLVWHP GH HFXD LL SULQ DGXQDUHD UHVSHFWLY VF GHUHD OD ILHFDUH HFXD LH D XQHL QHFXQRVFXWH DX[LOLDUHSR]LWLYHFXUROGHHJDOL]DUHúLDQXPH

VDX

D [ D [ DQ [ Q \ E °D [ D [ D [ \ E ° Q Q ® # ° °¯D P [ D P [ D PQ [ Q \ P EP XQGH \ L t SHQWUX L P

9RP QXPL VROX LH D VLVWHPXOXL GH LQHFXD LL UHVSHFWLY XQ VLVWHPGHYDORULFDUHYHULILF VLPXOWDQWRDWHLQHFXD LLOHVLVWHPXOXL 7HRUHP 2ULF UHL VROX LL D VLVWHPXOXL GH LQHFXD LL vL FRUHVSXQGH R VROX LHDVLVWHPXOXLGHHFXD LL VDX úLUHFLSURF 'HPRQVWUD LH Ä ´)LHVLVWHPXOGHLQHFXD LL VFULVVXEIRUP PDWULFHDO $[ d E úL [ RVROX LHDDFHVWXLVLVWHP'HFL $[ d E 6LVWHPXO GH LQHFXD LL VH WUDQVIRUP vQ VLVWHP GH HFXD LL VFULV VXE IRUP PDWULFHDO $[ \ E VDX \ E $[ FX \ t DWXQFL [ \ HVWHVROX LDVLVWHPXOXLGDF

\

E $[ t

Ä ´ )LH [ \ VROX LH SHQWUX VLVWHPXO $WXQFL \ t úL

$[ \

E GH XQGH RE LQHP $[ d E úL GHFL [ VROX LH D VLVWHPXOXL GH

LQHFXD LL ([HPSOX6 VHUH]ROYHVLVWHPXOGHLQHFXD LL

[ [ [ d ° ® [ [ [ d ° [ [ [ d ¯

6ROX LH6LVWHPXOGHLQHFXD LLVHWUDQVIRUP vQWUXQVLVWHPGHHFXD LL

[ [ [ \ ° ® [ [ [ \ ° [ [ [ \ ¯

3ULQPHWRGDHOLPLQ ULLFRPSOHWHRE LQHP [ [ [ \ \

\

E

6ROX LHDVLVWHPXOXLGHHFXD LHHVWH

° [ \ \ ° °[ ° \ \ \ ® ° \ \ \ ° [ ° °¯ \ \ \ t

ÌQFRQVHFLQ VROX LHDVLVWHPXOXLGHLQHFXD LLHVWH

° [ ° ° ® [ ° ° ° [ ¯

6SD LLYHFWRULDOH

)LH 9 RPXO LPHQHYLG GHHOHPHQWHúL . XQFRUSGHVFDODULGHUHJXO . HVWHFRUSXOQXPHUHORUUHDOH \ VDXFRUSXOQXPHUHORUFRPSOH[H ^ 3HPXO LPHD 9 VHGHILQHVFGRX RSHUD LL 2SHUD LD GH DGXQDUH Ä ´ FD OHJH GH FRPSR]L LH LQWHUQ FDUH DVRFLD] ILHF UHLSHUHFKLGHHOHPHQWH [ \ 9 u 9 XQHOHPHQWVXP [ \ 9 2SHUD LD GH vQPXO LUH FX VFDODUL ÄÂ´ FD OHJH GH FRPSR]L LH H[WHUQ FDUH DVRFLD] ILHF UHLSHUHFKLGHHOHPHQWH D [ . u 9 XQHOHPHQW D [ 9 'HILQL LH0XO LPHDQHYLG 9 VHQXPHúWHVSD LXYHFWRULDOVDXVSD LXOLQLDU SHVWHFRUSXO . GDF 9 HVWHJUXSDEHOLDQDGLF YHULILF

\ [ SHQWUX [ \ 9 [ \ ] [ \ ] SHQWUX [ \ ] 9 [ 9 9 HOHPHQW QHXWUX 9 9 DVWIHO vQFkW [ \

[ 9 9 [ [ [ 9 [ HOHPHQW [ [ [ [ 9 úL

RSXV

[ 9 DVWIHO

D[ E[ SHQWUX D E . [ 9 D [ \ D[ D\ SHQWUX D . [ \ 9 D E [ DE [ SHQWUX D E . [ 9 . [ [ SHQWUX [ 9 úL . .

vQFkW

D E [

1RWD LL (OHPHQWHOHXQXLVSD LXYHFWRULDO 9 VHQXPHVFYHFWRUL (OHPHQWHOHFRUSXOXL . VHQXPHVFVFDODUL 'HILQL LH )LH 9 XQ VSD LX YHFWRULDO SHVWH FRUSXO . 8Q YHFWRU Y 9 VH QXPHúWH FRPELQD LH OLQLDU D YHFWRULORU Y Y Y Q 9 GDF H[LVW VFDODUL D D D Q . DVWIHOvQFkW

Y

D Y D Y D Q Y Q

'HILQL LH8QVLVWHPGHYHFWRUL ^Y Y Y Q ` GLQ 9 VHQXPHúWHVLVWHPGH JHQHUDWRUL DL VSD LXOXL YHFWRULDO 9 GDF RULFH YHFWRU Y 9 VH SRDWH VFULH FD R FRPELQD LHOLQLDU DYHFWRULORU Y Y Y Q

'HILQL LH 8Q VLVWHP GH YHFWRUL ^Y Y Y Q ` GLQ 9 VH QXPHúWH VLVWHP OLQLDULQGHSHQGHQWGDF GLQHJDOLWDWHD D Y D Y D Q Y Q UH]XOW VFDODULQXOL D D D Q 'DF H[LVW VFDODULQHQXOLVLVWHPXOGHQXPHúWHVLVWHPOLQLDUGHSHQGHQW 3URSR]L LD 9HFWRULL Y Y Y Q 9 VXQW OLQLDU GHSHQGHQ L GDF úL QXPDLGDF FHOSX LQXQYHFWRUGLQWUHHLHVWHRFRPELQD LHOLQLDU GHFHLODO L 'HPRQVWUD LH Ä ´ )LH Y Y Y Q YHFWRUL OLQLDU GHSHQGHQ L $WXQFL H[LVW VFDODULL

D D D Q QXWR LQXOLDVWIHOvQFkW D Y D Y D Q Y Q )LH D z . DWXQFLSXWHPVFULH D D D Y Y Y Q Y Q D D D FHHDFHDUDW F YHFWRUXO Y VHVFULHFDRFRPELQD LHOLQLDU GHFHLODO LYHFWRUL Ä ´ 3UHVXSXQHP HYHQWXDO UHQXPHURWkQG YHFWRULL F Y VH VFULH FD R FRPELQD LH GH YHFWRULL Y Y Y Q $WXQFL H[LVW VFDODUL D D D Q QX WR L QXOLDVWIHOvQFkW

Y

D Y D Y D Q Y Q

VDX

Y D Y D Y D Q Y Q 9 'HFLYHFWRULL Y Y Y Q VXQWOLQLDUGHSHQGHQ L 'HILQL LH )LH 9 VSD LX YHFWRULDO SHVWH FRUSXO . 8Q VLVWHP GH YHFWRUL % 9 VHQXPHúWHED]DSHVSD LXOYHFWRULDO 9 GDF HVWHIRUPDWGLQWUXQQXP U

PD[LP GH YHFWRUL OLQLDU LQGHSHQGHQ L 1XP UXO YHFWRULORU GLQ ED] GHWHUPLQ GLPHQVLXQHDVSD LXOXL 3URSR]L LD )LH 9 XQ VSD LX YHFWRULDO SHVWH FRUSXO . úL % ^E E EQ ` R ED] D VSD LXOXL 9 DWXQFL RULFH YHFWRU Y 9 VH VFULH vQ PRGXQLFFDRFRPELQD LHOLQLDU DYHFWRULORUED]HL 'HPRQVWUD LH 3UHVXSXQHP F YHFWRUXO Y 9 VH SRDWH H[SULPD vQ GRX PRGXULvQIXQF LHGHYHFWRULLED]HL % úLDQXPH Y D E D E D Q EQ

Y

EE E E E Q EQ

6F ]kQGFHOHGRX UHOD LLRE LQHP

9

D E E D E E D Q E Q EQ

9HFWRULLED]HL E E EQ FRQIRUPGHILQL LHLVXQWOLQLDULQGHSHQGHQ LGHFL WR L VFDODULL FRPELQD LHL VXQW QXOL 'HFL D E D E « D Q E Q ÌQ FRQVHFLQ XQYHFWRUVHVFULHFDRFRPELQD LOLQLDU XQLF GHYHFWRULLED]HL 'HILQL LH&RHILFLHQ LL D D D Q DLUHSUH]HQW ULLYHFWRUXOXL Y 9 vQ ED]D % VHQXPHVFFRRUGRQDWHOHYHFWRUXOXL 9 vQED]D % 6HSRDWHVFULHDWXQFL Y D D D Q 6SD LXOYHFWRULDOUHDO Q GLPHQVLRQDOHVWHPXO LPHD

\Q

úL

\ u \ u u \

½ § [ · ° ° ¨ ¸ [ ¸ ° ° ¨ ® [ [ ¨ ¸ [L \ ¾ SHFDUHVHGHILQHVFRSHUD LLOH # ° ° ¨ ¸ ° ° © [Q ¹ ¯ ¿ § [ · § \ · § [ \ · ¨ ¸ ¨ ¸ ¨ ¸ ¨ [ ¸ ¨ \ ¸ ¨ [ \ ¸ [ \ ¨ ¸¨ ¸ ¨ # # # ¸ ¨ ¸ ¨ ¸ ¨ ¸ ¨[ ¸ ¨\ ¸ ¨[ \ ¸ Q¹ © Q¹ © Q¹ © Q

D[

§ [ · ¨ ¸ ¨[ ¸ D¨ ¸ # ¨ ¸ ¨[ ¸ © Q¹

§ D[ · ¨ ¸ ¨ D[ ¸ ¨ # ¸ ¨ ¸ ¨ D[ ¸ © Q¹

3URSR]L LD6LVWHPXOGHYHFWRULXQLWDUL

E

§· ¨ ¸ ¨¸ ¨ # ¸ E ¨ ¸ ¨¸ © ¹

§· ¨ ¸ ¨¸ ¨ # ¸ « EQ ¨ ¸ ¨¸ © ¹

§ · ¨ ¸ ¨ ¸ ¨ # ¸ ¨ ¸ ¨¸ © ¹

IRUPHD] RED] DVSD LXOXLYHFWRULDO \ Q QXPLW ED]DFDQRQLF 2EVHUYD LHÌQVSD LXO \ Q H[LVW RLQILQLWDWHGHED]H 3URSR]L LD 8Q VLVWHP GH YHFWRUL Y Y Y Q 9 VXQW YHFWRUL OLQLDU LQGHSHQGHQ L GDF UDQJXO PDWULFHL YHFWRULORU HVWH HJDO FX QXP UXO YHFWRULORU 9HFWRULL VXQW OLQLDU GHSHQGHQ L GDF UDQJXO PDWULFHL YHFWRULORU HVWH PDL PLF FD QXP UXOYHFWRULORU

'HPRQVWUD LH)LHYHFWRULL

Y

§ D · ¨ ¸ ¨ # ¸ Y ¨D ¸ © Q ¹

§ D · ¸ ¨ ¨ # ¸ « Y P ¨D ¸ © Q ¹

§ D P · ¸ ¨ ¨ # ¸ ¨D ¸ © PQ ¹

(LVXQWOLQLDUGHSHQGHQ LGDF úLQXPDLGDF H[LVW VFDODUL D D D P QX WR LQXOLDVWIHOvQFkW

§ D · § D · § DP · § · ¨ ¸ ¨ ¸ ¨ ¸ ¨ ¸ D ¨ # ¸ D ¨ # ¸ D P ¨ # ¸ ¨ # ¸ ¨D ¸ ¨D ¸ ¨ D ¸ ¨¸ © Q ¹ © Q ¹ © PQ ¹ © ¹ FHHDFHHVWHHFKLYDOHQWFXVLVWHPXORPRJHQFX P QHFXQRVFXWHúL Q HFXD LL DD D D D PD P ° ®" °D D D D D D Q PQ P ¯ Q

6LVWHPXORPRJHQDGPLWHVROX LLGLIHULWHGHVROX LDEDQDO GDF úLQXPDLGDF P VLVWHPXO HVWH XQLF GHWHUPLQDW úL DGPLWH GRDU VROX LD EDQDO FHHD FH DUDW F YHFWRULL VXQW OLQLDU LQGHSHQGHQ L 0DWULFHD $ HVWHPDWULFHDYHFWRULORU

UDQJ $ P QXP UXO QHFXQRVFXWHORU 'DF UDQJ $

$

§ D ¨ ¨ D ¨ # ¨ ¨D © Q

D D # DQ

" D P · ¸ " DP ¸ % # ¸ ¸ " D PQ ¸¹

&RQVHFLQ DÌQVSD LXOYHFWRULDO \ Q XQVLVWHPGH Q YHFWRUL

Y

§ D · ¨ ¸ ¨ # ¸ Y ¨D ¸ © Q ¹

§ D · ¸ ¨ ¨ # ¸ « Y Q ¨D ¸ © Q ¹

§ D Q · ¨ ¸ ¨ # ¸ ¨D ¸ © QQ ¹

IRUPHD] RED] DVSD LXOXLGDF úLQXPDLGDF GHWHUPLQDQWXOPDWULFHLYHFWRULORU HVWHQHQXO

3URSR]L LD 7UDQVIRUPDUHD FRRUGRQDWHORU XQXL YHFWRU OD VFKLPEDUHDED]HL )LH Y \ Q úL $ ^D D D Q ` úL % ^E E EQ ` GRX ED]HGLQ \ Q 'DF

Y

§ Y · ¨ ¸ ¨ # ¸ ¨Y ¸ © Q¹

D

§ D · ¨ ¸ ¨ # ¸ D ¨D ¸ © Q ¹

§ D · ¸ ¨ ¨ # ¸ « D Q ¨D ¸ © Q ¹

§ D Q · ¨ ¸ ¨ # ¸ ¨D ¸ © QQ ¹

E

§ E · ¨ ¸ ¨ # ¸ E ¨E ¸ © Q ¹

§ E · ¨ ¸ ¨ # ¸ « EQ ¨E ¸ © Q ¹

§ EQ · ¨ ¸ ¨ # ¸ ¨E ¸ © QQ ¹

)LH D D D P FRRUGRQDWHOHYHFWRUXOXL Y vQED]D $ DWXQFL

D D D D D Q D Q

Y VDX XQGH D

D D D P

7

Y

$D

9HFWRULL ED]HL $ SRW IL H[SULPD L OD UkQGXO ORU FD R FRPELQD LH OLQLDU GH YHFWRULLED]HL % GHFL DL O LE O L E O LQ EQ L Q 3HQWUXDFHúWLYHFWRULvQORFXL LvQFRPELQD LDOLQLDU DYHFWRUXOXL Y RE LQHP

Y

VDX

Y

ÌQFRQVHFLQ YRUIL

D O E O E O Q EQ

D Q O QE O Q E O QQ EQ

DO D Q O Q E DOQ D Q O QQ EQ 7 FRRUGRQDWHOH E E E E Q DOHYHFWRUXOXL Y vQED]D % E ° ®" °E ¯ Q

D O D Q O Q

DO Q D Q O QQ

6FULV PDWULFHDOUHOD LDGHYLQH

E

0 D

XQGH

§ O " O Q · ¸ ¨ 0 ¨ # % # ¸ ¸ ¨O © Q " O QQ ¹ 0 VHQXPHúWHPDWULFHDGHWUHFHUHGHODED]D $ ODED]D %

2EVHUYD LL 0DWULFHDGHWUHFHUHGHODRED] ODDOWDHVWHvQWRWGHDXQDPDWULFHQHVLQJXODU 'DF PDWULFHDGHWUHFHUHGHODED]D $ ODED]D % HVWH 0 DWXQFLPDWULFHDGH WUHFHUHGHODED]D % ODED]D $ HVWH 0 )LH YHFWRUXO Y Y Y YQ \ Q Y Y Y Q VXQW FRRUGRQDWHOH

YHFWRUXOXL Y VFULVvQED]DFDQRQLF

Y

( Y XQGH

§ Y · ¨ ¸ ¨ Y ¸ ¨#¸ ¨ ¸ ¨Y ¸ © Q¹

§· § · § · ¨ ¸ ¨ ¸ ¨ ¸ ¨¸ ¨¸ ¨ ¸ Y ¨ ¸ Y ¨ ¸ Y Q ¨ ¸ # # # ¨ ¸ ¨ ¸ ¨ ¸ ¨¸ ¨ ¸ ¨¸ © ¹ © ¹ © ¹

(

§ ¨ ¨ ¨# ¨ ¨ ©

&RRUGRQDWHOH OXL Y vQ ED]D $

Y

#

" " % "

· ¸ ¸ #¸ ¸ ¸¹

^D D D Q ` VXQW D D D Q 7 GHFL

$ D VDX

§ Y · ¨ ¸ ¨#¸ ¨Y ¸ © Q¹

§ D " D Q ·§ D · ¸¨ ¸ ¨ ¨ # % # ¸¨ # ¸ ¸¨ ¸ ¨D © Q " D QQ ¹© D Q ¹ &RRUGRQDWHOHOXL Y vQED]D % YRUIL E E E Q GHFL Y $D VDX E

%E

% E GHXQGH

% $D

ÌQFRQVHFLQ PDWULFHDGHWUHFHUHGHODED]D $ ODED]D % HVWH 0 % $

7 D 7 D 7 úL XQ YHFWRU Y \ H[SULPDWvQUDSRUWFXED]D $ ^D D D ` SULQFRRUGRQDWHOH úL 6 VHH[SULPHFRRUGRQDWHOHYHFWRUXOXL Y vQUDSRUWFXED]D % ^E E E ` 7 7 7 XQGH E E úL E ([HPSOX )LH YHFWRULL D

VXQW

6ROX LH 0DWULFHOH GH WUHFHUH GH OD ED]D $ UHVSHFWLY % OD ED]D FDQRQLF

§ · § · ¸ ¸ ¨ ¨ $ ¨ ¸ úL % ¨ ¸ ¨ ¸ ¨ ¸ ¹ ¹ © © &RRUGRQDWHOHYHFWRUXOXL Y vQUDSRUWFXED]D % VXQWFRQIRUPREVHUYD LHLGH

PDLVXVUHOD LHL

§ E · ¨ ¸ ¨E ¸ ¨E ¸ © ¹

§ · § ¨ ¸ ¨ ¨ ¸ ¨ ¨ ¸ ¨ © ¹ © § ¨ ¨ ¨ ©

·§ · ¸¨ ¸ ¸¨ ¸ ¸¹¨© ¸¹ ·§ ·§ · ¸¨ ¸¨ ¸ ¸¨ ¸¨ ¸ ¸¹¨© ¸¹¨© ¸¹

§ · ¨ ¸ ¨ ¸ ¨ ¸ © ¹

6SD LLHXFOLGLHQH 'HILQL LH )LH 9 VSD LX YHFWRULDO SHVWH FRUSXO GH VFDODUL . 2 DSOLFD LH I 9 u 9 o \ QRWDW I [ \ [ \ VDX I [ \ [ \ VHQXPHúWHSURGXV

VFDODUGDF VDWLVIDFH [ [ \ [ \ [ \ [ [ \ 9

\ [ [ \ 9

[ \

D [ \

[ [ t SHQWUX [ t

D [ \ [ \ 9 D .

'HILQL LH 8Q VSD LX YHFWRULDO ( SHVWH FRUSXO . SH FDUH VD GHILQLW XQ SURGXVVFDODUVHQXPHúWHVSD LXHXFOLGLDQ ([HPSOX 'DF VSD LX YHFWRULDO 9 HVWH Q GLPHQVLRQDO SHVWH FRUSXO GH VFDODUL . úLSURGXVXOVFDODURIXQF LH I \ Q u \ Q o \ HVWHGHILQLWSULQ

[ \

[ \ [ \ [ Q \ Q

VHREVHUY FXXúXULQ F VHYHULILF FHOHSDWUXSURSULHW LGHGHILQL LH 'HILQL LHÌQWUXQVSD LXHXFOLGLDQUHDOVDXFRPSOH[GRLYHFWRUL [ \ ( VH QXPHVFYHFWRULRUWRJRQDOLGDF SURGXVXOORFVFDODUHVWHQXOGHFL [ \

'HILQL LH )LH ( VSD LX HXFOLGLDQ 8Q VLVWHP [ [ [ Q ( VH QXPHúWH VLVWHP RUWRJRQDO GH YHFWRUL GDF ILHFDUH YHFWRU [L HVWH RUWRJRQDO SH WR L FHLODO L

SHQWUXRULFH L z M L M

YHFWRUL'HFL [L [ M

Q

3URSR]L LDÌQRULFHVSD LXHXFOLGLDQ Q GLPHQVLRQDOSHVWHFRUSXO . H[LVW FHO SX LQ R ED] RUWRJRQDO FDUH VH SRDWH GHWHUPLQD FX SURFHGHXO OXL *UDPP6FKPLGW 6HSOHDF GHODRED] RDUHFDUHDVSD LXOXL ( % ^E E EQ ` úLVHYRU FRQVWUXLYHFWRULL

D

E

D

E O D

"" D Q EQ O Q D O Q D O Q Q D Q

6FDODULL O LM VH YRU GHWHUPLQD SXQkQG FRQGL LD FD RULFDUH GRL GLQ YHFWRUL

D D D Q V ILHRUWRJRQDOL

6HRE LQH O LM

D D

O

D D

O

D D

O

EL D M DMDM

E D D D E D D D E D D D

([HPSOX6 VHFRQVWUXLDVF RED] RUWRJRQDO DVSD LXOXLHXFOLGLDQ \

§· §· §· ¨ ¸ ¨ ¸ ¨ ¸ 6ROX LH)LHYHFWRULL E ¨ ¸ E ¨ ¸ E ¨ ¸ ¨¸ ¨ ¸ ¨ ¸ © ¹ © ¹ © ¹ $FHúWLWUHLYHFWRULDYkQGPDWULFHD $ FX UDQJ $ IRUPHD] RED] DVSD LXOXL

\

6HYRUFRQVWUXLYHFWRULL

D

D

D

§· ¨ ¸ ¨ ¸ ¨¸ © ¹

E

§· ¨ ¸ E O D ¨ ¸ ¨ ¸ © ¹ §· § · § · ¨ ¸ ¨ ¸ ¨ ¸ ¨ ¸ ¨ ¸ ¨ ¸ ¨ ¸ ¨ ¸ ¨ ¸ © ¹ © ¹ © ¹

§· ¨ ¸ ¨¸ ¨¸ © ¹

E OD O D

§· ¨ ¸ ¨ ¸ ¨ ¸ © ¹

§· ¨ ¸ ¨¸ ¨¸ © ¹

· ¸ © ¹ § · § · ¨ ¸ ¨ ¸ © ¹ © ¹

¨§

§ · ¨ ¸ ¨ ¸ ¨ ¸ © ¹

§· §· § · § · ¸ ¨ ¸ ¨ ¸ ¨ ¸ ¨ ¨ ¸ ¨ ¸ ¨ ¸ ¨ ¸ ¨ ¸ ¨¸ ¨ ¸ ¨ ¸ © ¹ © ¹ © ¹ © ¹ 9HFWRULL D D D IRUPHD] RED] RUWRJRQDO DVSD LXOXL \ GHRDUHFHVXQW WUHLYHFWRULOLQLDULQGHSHQGHQ LúLRUWRJRQDOLGRLFkWHGRL 'HILQL LH)LH 9 VSD LXYHFWRULDOSHVWHFRUSXO . 2IXQF LH I 9 o \

QRWDW I [

[ VHQXPHúWHQRUPDYHFWRUXOXL [ [ 9 GDF YHULILF

[ t [ 9 D [

D [ [ 9 D .

[ \ d [ \ [ \ 9

2EVHUYD LH1RUPDXQXLYHFWRUSHXQVSD LXHXFOLGLDQVHSRDWHGHILQLvQPDL PXOWHIHOXUL1RLYRPIRORVLQRUPDGHILQLW FXDMXWRUXOSURGXVXOXLVFDODU

[

[ [

'HILQL LH8QVSD LXYHFWRULDOSHFDUHVDGHILQLWRQRUP VHYDQXPLVSD LX YHFWRULDOQRUPDW 3URSR]L LDÌQRULFHVSD LXYHFWRULDOQRUPDWH[LVW RED] RUWRQRUPDW DGLF RED] RUWRJRQDO vQFDUHQRUPDILHF UXLYHFWRUHVWHHJDO FXXQLWDWHD )LHRED] RUWRJRQDO $ ^D D D Q ` FRQVWUXLW SULQSURFHGHXO*UDPP 6FKPLGW 6HYDFRQVWUXLRED] RUWRQRUPDW GLQED]D $ SULQvPS U LUHDILHF UXLYHFWRU ODQRUPDVD6HRE LQHED]D

D

F

D

F

D « F Q D

DQ DQ

([HPSOX6 VHGHWHUPLQHRED] RUWRQRUPDW DVSD LXOXL \ 5H]ROYDUH9RPSOHFDFXED]DRUWRJRQDO

D

§· ¨ ¸ ¨ ¸ D ¨ ¸ © ¹

9RPQRUPDILHFDUHYHFWRU

F

D D

F

D D

F

D D

§ · ¸ ¨ ¨ ¸ D ¨ ¸ ¹ ©

§ · ¸ ¨ ¨ ¸ ¨ ¸ ¹ ©

§ · ¨ ¸ ¨ ¸ ¨¨ ¸¸ © ¹ § · §¨ ·¸ ¸ ¨ ¨ ¸ ¨ ¸ ¨ ¸ ¸ ¨ © ¹ ¨© ¸¹ § · §¨ ·¸ ¸ ¨ ¸ ¨ ¸ ¨ ¨ ¨ ¸ ¸¹ ¨© ¸¹ © §· ¨ ¸ ¨¸ ¨ ¸ © ¹

9HFWRULL F F F IRUPHD] RED] RUWRQRUPDW DVSD LXOXL \ $SOLFD LLOLQLDUH 'HILQL LH)LH 9 9 c GRX VSD LLYHFWRULDOHSHVWHDFHODúLFRUSGHVFDODUL . GH GLPHQVLXQL Q UHVSHFWLY P 2 DSOLFD LH 7 9 o 9 c VH QXPHúWH DSOLFD LH WUDQVIRUPDUHVDXRSHUDWRU OLQLDU GDF HVWHDGLWLY úLRPRJHQ GHFLYHULILF 7 [ \ 7 [ 7 \ [ \ 9 7 D[

D7 [ [ 9 D .

7HRUHPD2DSOLFD LH 7 9 o 9 c HVWHDSOLFD LHOLQLDU GDF úLQXPDL GDF 7 D[ E\ D7 [ E7 \ [ \ 9 D E . 'HPRQVWUD LH Ä ´ 7 DSOLFD LHOLQLDU 9RPFDOFXODFXDMXWRUXOSURSULHW LORUGHGHILQL LH YDORDUHD 7 D[ E\ 7 D[ 7 E\ D7 [ E7 \ Ä ´3UHVXSXQHPF UHOD LD 7 D[ E \

$WXQFLHDHVWHYHULILFDW úLSHQWUXVFDODULL D

D7 [ E7 \ HVWHYHULILFDW E . FHHDFHFRQGXFHODHJDOLWDWHD

FkWúLSHQWUXVFDODUXO E . FHHDFHFRQGXFHODHJDOLWDWHD 2EVHUYD LH 7HRUHPD SRDWH IL IRORVLW FD GHILQL LH SHQWUX DSOLFD LD OLQLDU 7HRUHPD )LH 9 9 c GRX VSD LL YHFWRULDOH SHVWH DFHODúL FRUS GH VFDODUL . % ^D D D Q ` R ED] D VSD LXOXL YHFWRULDO 9 úL

%c

^E E EQ ` R ED]

D VSD LXOXL YHFWRULDO 9 c DWXQFL H[LVW R DSOLFD LH

OLQLDU 7 9 o 9 c FXSURSULHWDWHD 7 D N EN SHQWUX N ^ Q` 'HPRQVWUD LH)LH Y 9 7 9 o 9 c RDSOLFD LH

7 Y EE E E E Q EQ

YRPGHPRQVWUDF DSOLFD LDDVWIHOGHILQLW HVWHOLQLDU )LH Y Y GRLYHFWRULRDUHFDUHGLQ 9 FDUHVHSRWH[SULPDvQIXQF LHGHED]D % DVWIHO Y D D D D DQ D Q

Y 9RPFDOFXOD

DY EY

D D D D D Q D Q

DD D D Q D Q ED D D Q D Q

DD ED D DD Q ED Q D Q DD ED E DD Q ED Q EQ 7 DY EY DD E DQ EQ ED E D Q EQ D7 Y E7 Y

'HFL DSOLFkQG WHRUHPD DSOLFD LD 7 GHILQLW PDL VXV HVWH R DSOLFD LH OLQLDU 3HQWUX RULFH YHFWRU D N % FRRUGRQDWHOH VDOH vQ ED]D % VXQW

n úLGHFLSULQGHILQL LH N

7 D N E EN EN EN EQ

EN

ÌQFRQVHFLQ H[LVW RDSOLFD LHOLQLDU FDUHYHULILF 7 D N EN 7HRUHPD0DWULFHDDVRFLDW XQHLDSOLFD LLOLQLDUH )LHDSOLFD LDOLQLDU 7 9 o 9 c 9 9 c VSD LLYHFWRULDOHSHVWHXQFRUS . ^D D Q ` R ED] D VSD LXOXL YHFWRULDO 9 úL % c ^E EQ ` R ED] D

%

VSD LXOXL YHFWRULDO 9 c )LH DL XQ YHFWRU RDUHFDUH GLQ % DWXQFL 7 DL HVWH XQ YHFWRU DO VSD LXOXL 9 c úL SRDWH IL UHSUH]HQWDW vQ PRG XQLF vQ IXQF LH GH YHFWRULL ED]HL % c 7 DL D LE D L E D LQ EQ

0DWULFHDIRUPDW GLQFRRUGRQDWHOHYHFWRULORU 7 D 7 D 7 D Q vQED]D

% c VH YD QXPL PDWULFH DVRFLDW DSOLFD LHL OLQLDUH 7 vQ UDSRUW FX SHUHFKHD GH ED]H ^% % c`

0 % %c 7 6

([HPSOX

VH

7 \ o \ 7 [ [

%

§ D ¨ ¨ D ¨ # ¨ ¨D © Q

6ROX LH

" D P · ¸ " D P ¸ % # ¸ ¸ " D PQ ¸¹

GHWHUPLQH

PDWULFH

DVRFLDW DSOLFD LHL OLQLDUH [ [ [ [ [ vQUDSRUWFXSHUHFKHDGHED]H

^D D ` D

§· ¨¨ ¸¸ D ©¹

úL

%c

D D # D Q

^E E E ` E

§· ¨ ¸ ¨¸ E ¨¸ © ¹

§ · ¨¨ ¸¸ ©¹

§· ¨ ¸ ¨ ¸ E ¨ ¸ © ¹

§· ¨ ¸ ¨ ¸ ¨¸ © ¹

7 D 7 7 D 7

&RRUGRQDWHOH DFHVWRU GRL YHFWRUL vQ IXQF LH GH ED]D % c VXQW úL UHVSHFWLY 'HFL PDWULFHD DVRFLDW SHUHFKLL GH ED]HHVWH

0 % %c 7

· § ¸ ¨ ¨ ¸ ¨ ¸ ¹ ©

9DORULSURSULLúLYHFWRULSURSULLDVRFLD L XQHLDSOLFD LLOLQLDUH 'HILQL LH)LH 9 XQVSD LXYHFWRULDO Q GLPHQVLRQDOSHVWHFRUSXOGHVFDODUL . úL 7 9 o 9 RDSOLFD LHOLQLDU 8QVFDODU O . VHQXPHúWHYDORDUHSURSULH SHQWUXDSOLFD LDOLQLDU 7 GDF H[LVW FHOSX LQXQYHFWRUQHQXO Y 9 DVWIHOvQFkW 7 Y OY 9HFWRUXOQHQXO Y 9 FDUHYHULILF UHOD LD VHQXPHúWHYHFWRUSURSULX SHQWUXDSOLFD LDOLQLDU 7 DVRFLDWYDORULLSURSULL O 'HWHUPLQDUHD YDORULORU úL YHFWRULORU SURSULL SHQWUX R DSOLFD LH OLQLDU )LH 7 9 o 9 c DSOLFD LHOLQLDU FXPDWULFHDDSOLFD LHL $7 GHILQLW vQ

vQED]D % VDX

^D D Q `5HOD LD VHPDLVFULH 7 Y OY $7

O( Q Y

9

XQGH

$7

§ D " DQ · ¸ ¨ ¨ # % # ¸ ( Q ¸ ¨D © Q " D QQ ¹

5HOD LD FRQGXFHODVLVWHPXO

§ " · ¸ ¨ ¨ # % # ¸ úL Y ¨ " ¸ ¹ ©

§ Y · ¨ ¸ ¨ # ¸ ¨Y ¸ © Q¹

D O Y D Y D QY Q °D Y D O Y D Y ° Q Q ® °"" °¯DQ Y D Q Y D QQ O Y Q ÌQFRQVHFLQ FRRUGRQDWHOHYHFWRUXOXLSURSULX Y QHQXOVXQWVROX LLOHVLVWHPXOXL

RPRJHQ 6ROX LLOHVLVWHPXOXLRPRJHQ QXVXQWWRDWHQXOHQXPDLGDF GHWHUPLQDQWXOVLVWHPXOXLHVWHQXO 'HWHUPLQDQWXOVLVWHPXOXL

3O

D O D D D O # # DQ DQ

" D Q " DQ % # " D QQ O

VHQXPHúWHSROLQRPXOFDUDFWHULVWLFDVRFLDWDSOLFD LHLOLQLDUH 7 (FXD LD 3O VHQXPHúWHHFXD LHFDUDFWHULVWLF DDSOLFD LHL 7 'HFLVHYHULILF WHRUHPD 7HRUHPD)LH 7 9 o 9 O . HVWHRYDORDUHSURSULHDDSOLFD LHL OLQLDUH 7 GDF úLQXPDLGDF HVWHU G FLQ DHFXD LHLFDUDFWHULVWLFH

2EVHUYD LL 3ROLQRPXOFDUDFWHULVWLFúLGHFLHFXD LDFDUDFWHULVWLF QXGHSLQGHGHED]DDOHDV 9HFWRULL SURSULL DVRFLD L DSOLFD LHL OLQLDUH 7 9 o 9 SHQWUX YDORULOH SURSULL GHWHUPLQDWH VH RE LQ vQORFXLQG YDORULOH SURSULL vQ VLVWHPXO úL UH]ROYkQG VLVWHPXO 6ROX LLOH VLVWHPXOXL YRU IL FRRUGRQDWHOH YHFWRULORU SURSULL DVRFLD L DSOLFD LHL 7 vQUDSRUWFXED]D % )LHF UHL YDORUL SURSULL O vL FRUHVSXQG R LQILQLWDWH GH YHFWRUL SURSULL 6LVWHPXO RPRJHQ HVWHFRPSDWLELOQHGHWHUPLQDWF FL 3O 0XO LPHDVROX LLORU IRUPHD] XQVXEVSD LXQXPLWVXEVSD LXSURSULXDWDúDWYDORULLSURSULLUHVSHFWLYH 6HQRWHD] ( O Y Y 9 ? ^` 7 Y OY

^

`

8QYHFWRUSURSULX Y SRDWHILDVRFLDWFDYHFWRUSURSULXXQHLVLQJXUHYDORULSURSULL DVRFLDW DSOLFD LHL OLQLDUH 7 2EVHUYD LD VH GHPRQVWUHD] SUHVXSXQkQG FD SHQWUX Y YHFWRU SURSULX DO OXL 7 H[LVW GRX YDORUL SURSULL DGLF 7 Y OY úL

7 Y EY Y z 9 $WXQFL OY EY VDX O E Y O E O E úLGHFLSUHVXQHUHDHVWHIDOV

ÌQ FRQVHFLQ

([HPSOX 6 VH GHWHUPLQH YDORULOH úL YHFWRULL SURSULL DVRFLD L DSOLFD LHL OLQLDUH 7 \ o \ FX 7 Y Y Y Y Y Y 6ROX LH0DWULFHDDSOLFD LHLHVWH

$7 3HQWUXHFXD LDFDUDFWHULVWLF DYHP

3O

O O

§ · ¨¨ ¸¸ © ¹

9HFWRULLSURSULLDVRFLD LYDORULLSURSULL O ED]DFDQRQLF GDWHGHVLVWHPXOGHHFXD LL

FXVROX LD D

O ® ¯O

O

O D D ® ¯D O D D D N \

DXFRRUGRQDWHOHvQUDSRUWFX

D D ® ¯D D

6XEVSD LXYHFWRULORUSURSULXDLOXL O HVWH (O

YY

9HFWRULLSURSULLDVRFLD LYDORULLSURSULL O ED]DFDQRQLF GDWHGHVROX LLOHVLVWHPXOXL

N N N \

DXFRRUGRQDWHOHvQUDSRUWFX

O Y Y Y Y ® ® O Y Y Y Y ¯ ¯ FXVROX LDQHGHWHUPLQDW Y Y K FX K \ 6XEVSD LXOSURSULX (O

YY

K K K \

7HRUHPD 'DF Y Y Y S VXQW YHFWRUL SURSULL DL DSOLFD LHL OLQLDUH

7 9 o 9 DVRFLD L YDORULORU SURSULL GLVWLQFWH O O S DWXQFL HL VXQW OLQLDUL LQGHSHQGHQ L 'HPRQVWUD LDWHRUHPHLVHIDFHSUHVXSXQkQGF YHFWRULLDUILGHSHQGHQ LGHFL DUYHULILFD D Y D Y D S Y S 9 FX D L z

9HFWRULL SURSULL DL DSOLFD LHL OLQLDUH 7 YHULILF 7 Y

7 Y S O S Y S

&DOFXO P

D 7 Y D S 7 Y S

7 DY D S Y S

D O Y D S O S Y S

9

O Y «

'DF GLQ VF GHP vQPXO LWFX O VHRE LQH

D O Y D S O S Y S O D Y D Y D S Y S 9

VDX

O O D Y O S O D S Y S

9

&XPYDORULOHSURSULL O O S VXQWGLVWLQFWHGDF YHFWRULL Y Y Y S DUIL LQGHSHQGHQ L DP RE LQH D

DS

FHHD FH DU FRQWUD]LFH SUHVXSXQHUHD

I FXW 5H]XOW F YHFWRULLSURSULLVXQWOLQLDULQGHSHQGHQ L 7HRUHPD )LH 9 VSD LX YHFWRULDO GH GLPHQVLXQH Q 7 9 o 9 R DSOLFD LH OLQLDU úL O O O Q YDORUL SURSULL GLVWLQFWH SHQWUX 7 $WXQFL H[LVW R ED] % SHQWUX 9 DVWIHOvQFkWPDWULFHDDVRFLDW DSOLFD LHLOLQLDUH 7 V DLE IRUP GLDJRQDO FXHOHPHQWHOHGLDJRQDOHLSULQFLSDOHHJDOHFXYDORULOHSURSULL 'HPRQVWUD LDWHRUHPHLSOHDF GHODWHRUHPDF FLYHFWRULLSURSULLDVRFLD L YDORULORU SURSULL GLVWLQFWH O O O Q VXQW Y Y Y Q OLQLDU LQGHSHQGHQ L 9HFWRULL Y Y Y Q IRUPHD] RED] DVSD LXOXL 9 F FLQXP UXOORUHVWHPD[LPDO 0DWULFHD DSOLFD LHL OLQLDUH 7 7 YL O L YL L

^% %`HVWH

$7

§ O ¨ ¨ ¨ # ¨ ¨ ©

O #

Q vQ UDSRUW FX SHUHFKHD GH ED]H

" · ¸ " ¸ % # ¸ ¸ " O Q ¸¹

7HRUHPD )LH 9 VSD LX YHFWRULDO GH GLPHQVLXQH Q 7 9 o 9 R DSOLFD LHOLQLDU FDUHDUHXQSROLQRPFDUDFWHULVWLF P P P 3O O O O O O O S S

FX P P P S

Q $WXQFLH[LVW RED] % DVSD LXOXLYHFWRULDO 9 DVWIHO

vQFkWPDWULFHDDVRFLDW DSOLFD LHLOLQLDUH 7 vQUDSRUWFXSHUHFKHDGHED]H ^% %` V DLE IRUP GLDJRQDO GDF úL QXPDL GDF GLPHQVLXQHD ILHF UXL VXEVSD LX SURSULX ( OL FRUHVSXQ] WRU YDORULL SURSULL O L HVWH HJDO FX PL RUGLQXO GH PXOWLSOLFLWDWHDOYDORULLSURSULLUHVSHFWLYH

$7

GLDJ O O O S O S

P

PS

%D]D % HVWH IRUPDW GLQ YHFWRUL SURSULL DSDU LQkQG VXEVSD LLORU SURSULL FRUHVSXQ] WRDUH ([HPSOX)LH 7 \ o \ GDW SULQ 7 Y Y Y Y Y Y Y Y Y 6 VH VWXGLH]H GDF H[LVW R ED] D VSD LXOXL YHFWRULDO \ vQ UDSRUW FX FDUH PDWULFHDDVRFLDW DSOLFD LHLOLQLDUH 7 V DLE IRUP GLDJRQDO 6ROX LH0DWULFHDWUDQVIRUP ULLHVWH

§ · ¸ ¨ ¨ ¸ ¨ ¸ ¹ ©

$7 3ROLQRPXOFDUDFWHULVWLFHVWH

3O

O

O O

O O

GHFLHFXD LDFDUDFWHULVWLF O O DUH O YDORDUHSURSULHGHRUGLQ GHPXOWLSOLFLWDWHGRLU G FLQ GXEO úL O YDORDUHSURSULHGLVWLQFW 9HFWRULLSURSULLDVRFLD LYDORULLSURSULL O VXQWVROX LLOHVLVWHPXOXL

Y Y Y ° ®Y Y Y ° ¯Y Y

'HFL (O

[[

Y Y Y Y Y ° ° ®Y Y ®Y Y °Y Y °Y \ ¯ ¯

N N N N \

D F UHL GLPHQVLXQH HVWH ÌQ

FRQIRUPLWDWHFXWHRUHPDQXH[LVW RED] DVSD LXOXLYHFWRULDO \ vQUDSRUWFX FDUHPDWULFHDDVRFLDW DSOLFD LHL 7 V DLE IRUP GLDJRQDO

([HPSOX )LH 7 \ o \ R DSOLFD LH OLQLDU D F UHL PDWULFH DVRFLDW vQ UDSRUWFXED]DFDQRQLF HVWH

§ · ¸ ¨ ¨ ¸ ¨ ¸ ¹ ©

$7

6 VH VWXGLH]H GDF H[LVW R ED] D VSD LXOXL YHFWRULDO \ vQ UDSRUW FX FDUH PDWULFHDDVRFLDW DSOLFD LHLOLQLDUH 7 V DLE IRUP GLDJRQDO 6ROX LH(FXD LDFDUDFWHULVWLF DVRFLDW HVWH

O 9DORULOHSURSULLVXQW O

O O

O O

O

O

9HFWRULL SURSULL DVRFLD L YDORULL O O

HFXD LL

GHFL (O

Y ° ® Y Y ° ¯Y Y

YY

VXQW VROX LLOH VLVWHPXOXL GH

Y Y \ ° ° ®Y Y ®Y Y °Y Y °Y \ ¯ ¯

N K K N K \

'LPHQVLXQHD VXEVSD LXOXL SURSULX ( O HVWH GRL úL N K \ FkW HVWH úL RUGLQXOGHPXOWLSOLFLWDWHDYDORULLSURSULL O 9HFWRULL SURSULL FRUHVSXQ] WRUL YDORULL SURSULL O VLVWHPXOXL

GHFL ( O

VXQW VROX LLOH

Y Y Y ° ° ° ® Y Y ®Y Y ®Y Y ° °Y Y °Y \ ¯ ¯ ¯Y Y ^Y Y S S S 5`DF UHLGLPHQVLXQHHVWH

0DWULFHD $7 VHWUDQVIRUP vQ

vQWURED] %

§ · ¸ ¨ $7c ¨ ¸ ¨ ¸ ¹ © ^E E E `XQGH E E (O úL E (O

FDGHH[HPSOX

§· ¨ ¸ ¨ ¸ E ¨ ¸ © ¹

^E E E ` E

%

§ · ¨ ¸ ¨ ¸ E ¨¸ © ¹

§ · ¨ ¸ ¨ ¸ ¨ ¸ © ¹

)RUPHOLQLDUH)RUPHS WUDWLFH 'HILQL LH )LH 9 VSD LX YHFWRULDO SHVWH FRUSXO \ GH GLPHQVLXQH Q 2 DSOLFD LH I 9 o \ HVWHRIRUP WUDQVIRUPDUHVDXRSHUDWRU OLQLDU GHFkWHVWH DGLWLY úLRPRJHQ I [ \ I [ I \ [ \ 9

I O[ OI [ [ 9 O \

2EVHUYD LH

$FHDVW DSOLFD LH DWDúHD] ILHF UXL YHFWRU [ [ [Q 9 VFULVvQWURED] DVSD LXOXLXQXLQXP UUHDO I [ \

[

'HILQL LH )LH 9 VSD LX YHFWRULDO SHVWH FRUSXO \ GH GLPHQVLXQH Q 2 DSOLFD LH I 9 u 9 o \ HVWH R IRUP ELOLQLDU GDF HVWH OLQLDU vQ UDSRUW FX DPEHOHDUJXPHQWH I D[ E[ \ DI [ \ EI [ \ [ [ \ 9

I [ D\ E\ DI [ \ EI [ \ [ \ \ 9

D E \

6FULHUHDXQHLIRUPHELOLQLDUHVXEIRUP PDWULFLDO )LHVSD LXOYHFWRULDO 9 úLRED] % ^E EQ ` $WXQFLYHFWRULL [ \ 9 VH SRWVFULH [ [E [ Q EQ

\

\E \ Q EQ

$SOLFD LD I 9 u 9 o \ VHVFULH

I [ \

I [E [ Q EQ \E \ Q EQ Q

Q

Q

L M

L

M

L

M

Q

¦¦ [ \ I E E ¦¦ [ \ D L M

L

M

LM

VDX

I [ \

§ D " DQ ·§ \ · ¸¨ ¸ ¨ [ [Q ¨ # % # ¸¨ # ¸ ¸¨ ¸ ¨D © Q " D QQ ¹© \ Q ¹

[ 7 $\

2EVHUYD LH 2 IRUP ELOLQLDU HVWH GHWHUPLQDW GDF VH FXQRDúWH PDWULFHD IRUPHL $

([HPSOX

I [ \

)LH

R

IRUP

ELOLQLDU

I \ u \ o \

[ \ [ \ [ \ 9HFWRULL [ úL \ VXQWH[SULPD LvQED]DFDQRQLF

&DUH HVWH PDWULFHD IRUPHL ELOLQLDU vQ ED]D FDQRQLF " &DUH HVWH PDWULFHD IRUPHL ELOLQLDUHvQED]D %

§ · ¨¨ ¸¸ E © ¹

^E E ` E

6ROX LH

I [ \

§ D © D

[ [ ¨¨

§· ¨¨ ¸¸ " ©¹

D ·§ \ · ¸¨ ¸ D ¸¹¨© \ ¸¹ § \ · ¸¸ \ © ¹

[D [ D [D [ D ¨¨

[ \ D [ \ D [ \ D [ \ D $FHDVW IRUP RLGHQWLILF PFXIRUPDELOLQLDU GDW I [ \ [ \ [ \ [ \ 6HRE LQHPDWULFHDIRUPHLvQED]DFDQRQLF

§ · ¨¨ ¸¸ © ¹ &HLGRLYHFWRUL [ úL \ VFULúLvQED]D % ^E E `GHYLQ $I

§[ · % D ¨¨ ¸¸ © [ ¹ §\ · \ % E ¨¨ ¸¸ © \ ¹

[

§ ¨¨ © § ¨¨ ©

·§ D · ¸¨ ¸ ¸¹¨© D ¸¹ ·§ E · ¸¨ ¸ ¸¹¨© E ¸¹

ÌQFRQVHFLQ IRUPDELOLQLDU GHYLQH

§ D D · ¨¨ ¸¸ © D D ¹ § E E · ¨¨ ¸¸ E E ¹ ©

§ · § E E · ¸ ¸¨ © ¹© E E ¹ DE DE D E D E 6HRE LQHPDWULFHDIRUPHLELOLQLDUHvQED]D % § · ¸¸ $ I ¨¨ © ¹ I [ \

D D D D ¨

'HILQL LH 2 IRUP ELOLQLDU VH QXPHúWH IRUPD ELOLQLDU VLPHWULF GDF PDWULFHD IRUPHL HVWH R PDWULFH VLPHWULF DGLF PDWULFHD $ HVWH HJDO FX WUDQVSXVDVD $ I $7I

'HILQL LH)LHXQVSD LXYHFWRULDO 9 SHVWHFRUSXOUHDO \ GHGLPHQVLXQHD Q 2 DSOLFD LH J 9 o \ HVWH R IRUP S WUDWLF GDF H[LVW R DSOLFD LH ELOLQLDU

VLPHWULF I 9 u 9 o \ DVWIHOvQFkW J [ 2EVHUYD LH

I [ [

§ D " DQ ·§ [ · ¨ ¸¨ ¸ [ [Q ¨ # % # ¸¨ # ¸ ¨D ¸¨ ¸ © Q " D QQ ¹© [ Q ¹

7

[ $[ Q

I [ [ [ 9

Q

¦¦ D L M

LM

[L [ M

XQGH $ PDWULFHDVLPHWULF DGLF D LM

D ML

([HPSOH )LH I \ u \ o \ RIRUP ELOLQLDU VLPHWULF

I [ \ [ \ [ \ [ \ [ \

&DUHHVWHPDWULFHDIRUPHLELOLQLDUH"&DUHHVWHIRUPDS WUDWLF " 6ROX LH

$ $ VLPHWULF GHRDUHFH D

)RUPDS WUDWLF HVWH

J [

D

§ · ¨¨ ¸¸ © ¹

·§ [ · ¸¸¨¨ ¸¸ © ¹© [ ¹ §[ · [ [ [ [ ¨¨ ¸¸ © [ ¹

[ [ §¨¨

I [ [

[ [ [ [ [ [

[ [ [ [

)LH J \ o \ RIRUP S WUDWLF

J [

[ [ [ [ [ [ [

6 VHVFULHPDWULFHDIRUPHLS WUDWLFH 6ROX LH

$ $ PDWULFHVLPHWULF

· § ¸ ¨ ¸ ¨ ¨ ¸¹ ©

'HILQL LL 2IRUP S WUDWLF J 9 o \ HVWHSR]LWLYGHILQLW GDF WR LPLQRULLPDWULFHL VLPHWULFH $ VXQWVWULFWSR]LWLYL0LQRULLVXQW

'

D D

D '

D « ' Q D

D " DQ

# % # D Q " D QQ

2IRUP S WUDWLF J 9 o \ HVWHVHPLSR]LWLYGHILQLW GDF PLQRULLVXQWQH QHJDWLYL ' L t L

Q 2 IRUP S WUDWLF J 9 o \ HVWH QHJDWLY GHILQLW GDF PLQRULL LPSDUL ' ' VXQWVWULFWQHJDWLYLúLFHLSDUL ' ' VXQWVWULFWSR]LWLYL 2 IRUP S WUDWLF HVWH VHPLQHJDWLY GHILQLW GDF ' d ' d úL

' t ' t 2 IRUP S WUDWLF SHQWUX FDUH QX VXQW vQGHSOLQLWH QLFL XQD GLQ FRQGL LLOH DQWHULRDUHHVWHRIRUP S WUDWLF QHGHILQLW ([HPSOH6 VHVWDELOHDVF QDWXUDIRUPHORUS WUDWLFH J [ [ [ [ [ [ [ [

J [

J [ [ [ [ [ J [ [ [ [ [

[ [ [ [ [ [ [ [

6ROX LH

$

§ · ¸ ¨ ¨ ¸ ' ¨ ¸¹ ©

! '

! '

! GHFL J [

HVWHRIRUP S WUDWLF SR]LWLYGHILQLW

$

§ · ¨¨ ¸¸ ' © ¹

! '

DVWIHO F J [ HVWH R IRUP

S WUDWLF VHPLSR]LWLYGHILQLW

$

§ · ¨¨ ¸¸ ' © ¹

'

! GHFL J [ HVWH R

IRUP S WUDWLF QHJDWLYGHILQLW

'

· § ¸ ¨ $ ¨ ' ! ' ¸ ¸ ¨ ¹ © DVWIHSF J [ HVWHRIRUP S WUDWLF QHGHILQLW

'HILQL LH )LH J 9 o \ R IRUP S WUDWLF ÌQWUR ED] % D VSD LXOXL 9 IRUPD S WUDWLF J DUH R IRUP FDQRQLF GDF PDWULFHD IRUPHL HVWH R PDWULFH GLDJRQDO DGLF J \ E \ E \ EU \U XQGH U UDQJ $ Q 5HGXFHUHDXQHLIRUPHS WUDWLFHODRIRUP FDQRQLF 0HWRGD-DFREL )LHRIRUP S WUDWLF J 9 o \ J [ [ 7 $[ $ PDWULFHVLPHWULF 'DF WR L PLQRULL PDWULFHL $ VXQW QHQXOL DWXQFL H[LVW R ED] % D VSD LXOXL 9 DVWIHO vQFkWIRUPDS WUDWLF V VHWUDQVIRUPHvQIRUP FDQRQLF

' ' \ \ Q \ Q 'Q ' ' \ \ Q UHSUH]LQW FRRUGRQDWHOHYHFWRUXOXL [ vQED]D % J\

0HWRGDYDORULORUSURSULL $FHDVW PHWRG GHWHUPLQ YDORULOH SURSULL FX DMXWRUXO HFXD LHL FDUDFWHULVWLFH DWDúDW PDWULFHL IRUPHL 'DF DFHDVW PDWULFH SRDWH IL WUDQVIRUPDW vQWUR PDWULFH GLDJRQDO >vQGHSOLQHúWHFRQGL LLOHWHRUHPHL@DWXQFLVHSRDWHGHWHUPLQDRED] vQFDUHVHSRDWHVFULHIRUPDFDQRQLF 0HWRGD*DXVV $FHDVW PHWRG IRUPHD] S WUDWHSHUIHFWHFkQGFRQ LQHFHOSX LQXQ DLL z

J [

([HPSOXO

6

VH

WUDQVIRUPH

IRUPD

S WUDWLF

J \ o \

[ [ [ [ [ [ vQWURIRUP FDQRQLF 6ROX LH0DWULFHDIRUPHLHVWH

$ FXPLQRULL

'

'

§ · ¸ ¨ ¨ ¸ ¨ ¸ ¹ © '

0HWRGD-DFRELQXVHSRDWHDSOLFDGHRDUHFHDYHPPLQRULQXOL

9RP vQFHUFD PHWRGD YHFWRULORU SURSULL VFULLQG HFXD LD FDUDFWHULVWLF GLQ PDWULFHD $

3O

O

O O

O O

YDORULSURSULLGLVWLQFWH 6XEVSD LXOSURSULXDOYDORULLSURSULL O

DVWIHOF

O ° ®O °O ¯

VHRE LQHGLQVLVWHPXO

O [ [ [ [ [ [ [ ° ° ° ® [ O [ ® [ [ ® [ [ ° ° [ [ °[ \ ¯ ¯ ¯ [ O [ (O

[[

N N N N \

3ULQWUXQFDOFXOVLPLODUVHRE LQH

(O úL

(O

K K K K \

[[

[[

W W W W \

ÌQFRQVHFLQ PDWULFHD $ VHSRDWHVFULHFDRPDWULFHGLDJRQDO

$

§ · ¸ ¨ ¨ ¸ ¨ ¸ ¹ © \ \

FDUHFRQGXFHODIRUPDFDQRQLF J \ %D]D vQ FDUH VD I FXW WUDQVIRUPDUHD VH RE LQH GLQ WUHL YHFWRUL FDUH DSDU LQ FHORUWUHLVXEVSD LLDOHYHFWRULORUSURSULLFDGHH[HPSOX

%

° ®E ° ¯

§· ¨ ¸ ¨ ¸ E ¨ ¸ © ¹

§ · ¨ ¸ ¨ ¸ E ¨ ¸ © ¹

§ ·½ ¨ ¸° ¨ ¸ ¾ ¨ ¸ ° © ¹¿

([HPSOXO6 VHVFULHRIRUP FDQRQLF DIRUPHLS WUDWLFH J [ [ [ [ [ [ [ [ [ [ 6ROX LH0DWULFHDIRUPHLHVWH

$

§ · ¸ ¨ ¨ ¸ ¨ ¸ ¹ ©

FXPLQRULL

'

'

$WXQFL

J \

'

\ \ \

/DDFHDVW IRUP S WUDWLF VHSRDWHIRORVLúLPHWRGDOXL*DXVV

> [ [ [ @ [ [ [ [ [ [ [ [ (OHPHQWXO D z 6HYDIRUPDXQS WUDWSHUIHFWFXFHLWUHLWHUPHQLFH J [

FRQ LQSH [ > [ [ [ [ [ @ 3HQWUXUHVWXOWHUPHQLORUVHFDXW IRUPDXQXLQRXS WUDWSHUIHFWFXWHUPHQLFH FRQ LQSH [

J [

> [ [ [ @ [ [ [

6XEVWLWXLQG

> [ [ [ @ ª« [ [ º» [ ¬ ¼

RE LQHPIRUPDFDQRQLF

\ ° ° ® \ ° °¯ \

[ [ [ [ [ [

\ \ \ 2EVHUYD LH 'DF WR L FRHILFLHQ LL DLL XQHL IRUPH S WUDWLFH J [ VXQW J\

QXOLDWXQFLQXVHSRDWHDSOLFDQLFLRPHWRG GHPDLvQDLQWHÌQDFHDVW VLWXD LHVHYD IDFHvQWkLRWUDQVIRUPDUHGHIRUPD

[L ° ®[ M ° ¯ [N

\L \ M

\L \ M

\ N N z L M

([HPSOX6 VHUHGXF IRUPDS WUDWLF J \ o \

J [

[ [ [ [ [ [

ODRIRUP FDQRQLF 6ROX LH0DWULFHDIRUPHLHVWH

9RPIDFHWUDQVIRUPDUHD

§ · ¸ ¨ ¸ ¨ ¨ ¸¹ © [ ° ® [ °[ ¯

\ \ \ \ \

ÌQDFHVWHFRQGL LLIRUPDS WUDWLF GHYLQH

J\

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

FXPDWULFHD

$

· § ¸ ¨ ¸ ¨ ¨ ¸ ¹ ©

0LQRULLSULQPHWRGD-DFRELVXQW ' ' ' úLDVWIHO

J ]

] ] ]

352*5$0$5(/,1,$5 ,QWURGXFHUH

ÌQ SUH]HQW R VHULH GH DFWLYLW L HFRQRPLFH úL VRFLDOH FRPSOH[H FRQGXF OD UH]ROYDUHDXQRUSUREOHPHGHRSWLPL]DUH$VWIHOSUREOHPHGLQGRPHQLXOSODQLILF ULL SURGXF LHLGHSODQLILFDUHDLQYHVWL LLORUSUREOHPHGHWUDQVSRUWSUREOHPHGHGLHW HWFFRQGXFODSUREOHPHGHRSWLPL]DUHDOHF URUVROX LLRSWLPHWUHEXLHGHWHUPLQDWH 0RGHODUHD ORU PDWHPDWLF D SHUPLV XWLOL]DUHD DSDUDWXOXL PDWHPDWLF IXUQL]DW GH DOJHEUD OLQLDU SHQWUX GHWHUPLQDUHD VROX LLORU RSWLPH 'H H[HPSOX PRGHODUHD vQ XQHOHSUREOHPHHFRQRPLFHSRDWHILI FXW DVWIHOQRWkQGFX [L L Q QLYHOHOH OD FDUH WUHEXLH V VH GHVI úRDUH Q DFWLYLW L úL SULQ I [ [ Q IXQF LD RELHFWLY GH HILFLHQ VH FHUH V VH GHWHUPLQH YDORULOH YDULDELOHORU [L L vQFkWIXQF LDRELHFWLYV LDYDORDUHDPD[LP PLQLP >PD[ PLQ @ I [ [Q FXFRQGL LLOH I M [ [ Q t d M d P

Q DúD

QXPLWHúLUHVWULF LLOHSUREOHPHL 'DF IXQF LLOH I úL I M M P VXQWIXQF LRQDOHOLQLDUHSUREOHPDHVWH GHSURJUDPDUHOLQLDU ,DW FkWHYDH[HPSOH ([HPSOXO3UREOHP GHSODQLILFDUHDSURGXF LHL 2 vQWUHSULQGHUH LQGXVWULDO GLVSXQH GH PDWHULLOH SULPH 0 0 Q GLQ FDUH IDEULF SURGXVHOH 3 3P 'LQWUR WRQ GH PDWHULH SULP 0 L L SURGXF DLM XQLW L GLQ SURGXVXO 3M M

Q VH

P DLM VH QXPHVF úL FRQVXPXUL

VSHFLILFH /XQDUvQWUHSULQGHUHDWUHEXLHV SURGXF E M M

P XQLW LGLQILHFDUH

SURGXV 3M 'DF SUH XOXQHLWRQHGLQPDWHULDSULP 0 L HVWH FL L

Q V

VH vQWRFPHDVF XQ SODQ GH FRQVXP OXQDU DO PDWHULLORU SULPH DVWIHO vQFkW SHQWUX UHDOL]DUHDSURGXF LHLSODQLILFDWHFKHOWXLHOLOHV ILHPLQLPH )LH [L FDQWLWDWHD GLQ PDWHULD SULP 0 L XWLOL]DW vQ SURFHVXO GH SURGXF LH

DLM [ M UHSUH]LQW FDQWLWDWHD GH PDWHULH SULP GLQ UHVXUVD 0 L XWLOL]DW SHQWUX SURGXFHUHD FDQWLW LL GH SURGXV 3M LDU FDQWLWDWHD WRWDO GLQ UHVXUVD 0 L QHFHVDU SHQWUXSURGXF LDWRWDO IRUPDW GLQSURGXVHOH 3 3Q HVWH

D M [ D M [ D QM [ Q

LQkQG VHDPD GH IDSWXO F OXQDU vQWUHSULQGHUHD WUHEXLH V SURGXF FHO SX LQ E M XQLW LGLQILHFDUHSURGXV 3M

D M [ D M [ D QM [ Q t E M M

P

'HFLPRGHOXOPDWHPDWLFDOSUREOHPHLHVWH Q

¦D L

LM

[L t E M M

P

[ t L Q

Q

>PLQ @ I ¦ FL [L

L

&RQGL LLOH VXQW UHVWULF LLOH SUREOHPHL VXQW FRQGL LL GH QHQHJDWLYLWDWHLDU I HVWHIXQF LDRELHFWLYVDXIXQF LDGHHILFLHQ ([HPSOXO2SUREOHP GHXWLOL]DUHRSWLP DXQRUUHVXUVH ÌQFRQGL LLOHH[HPSOXOXLGLQPDWHULLOHSULPH 5 5Q FDUHVXQWOLPLWDWHGH FDQWLW LOH E EQ VHIDEULF SURGXVHOH 3 3P 6HFXQRVFFRQVXPXULOHVSHFLILFH

DLM t úL EHQHILFLLOH XQLWDUH F M M

P F M HVWH VXPD UHDOL]DW SULQ

YDORULILFDUHD XQHL XQLW L GLQ SURGXVXO 3M vQ XQLW L E QHúWL 6H FHUH V VH GHWHUPLQH FDQWLW LOH [ M GLQ ILHFDUH SURGXV 3M FDUH WUHEXLH UHDOL]DWH DVWIHO vQFkW EHQHILFLXOV ILHPD[LP 0RGHOXOPDWHPDWLFDOSUREOHPHLHVWH P

¦D M

LM

[ M d EL L Q

[ M t M

P

P

>PD[@ I ¦ F M [ M

M

&RQGL LLOH UH]XOW GLQIDSWXOF QXSXWHPFRQVXPDGLQILHFDUHUHVXUV PDL PXOWGHFkWFDQWLWDWHDGHFDUHGLVSXQHPLDU

P

¦F M

M

[ M UHSUH]LQW vQFDV ULOHWRWDOH

6HSRWGDúLDOWHH[HPSOHGHSUREOHPHGHSURJUDPDUHOLQLDU SHFDUHOHYRP WUDWDvQFDGUXODFHVWXLFDSLWRO

)RUPDJHQHUDO DSUREOHPHLGHSURJUDPDUHOLQLDU )RUPDJHQHUDO DXQHLSUREOHPHGHSURJUDPDUHOLQLDU HVWH Q

¦D L Q

¦D L Q

¦D L

LM

[L d E M M

N

LM

[L t E M M

N O

LM

[L

E M M

O P

[L t [L t « [L S t [L S d [L S d « [LU d

&HOHODOWHYDULDELOHQXDXVHPQXOVSHFLILFDW Q

>PD[ PLQ @ I ¦ FL [L

L

$ UH]ROYD R DVWIHO GH SUREOHP vQVHDPQ D GHWHUPLQD YDORULOH QHQHJDWLYH DOH YDULDELOHORU [L FDUH VDWLVIDF FRQGL LLOH GHFL D GHWHUPLQD QLYHOXULOH [L OD FDUH VH GHVI úRDU DQXPLWH DFWLYLW L úL FDUH RSWLPL]HD] IXQF LD RELHFWLY I VDXIXQF LHGHHILFLHQ 2 SUREOHP GH SURJUDPDUH OLQLDU SRDWH IL IRUPXODW úL PDWULFHDO GDF WRDWH LQHFXD LLOHVLVWHPXOXLGHUHVWULF LLDXDFHODúLVHQVFRQGL LHFDUHSRDWHILXúRUvQGHSOLQLW vQPXO LQGFX LQHFXD LLOH VDX W 'H H[HPSOX QRWkQG FX $ DLM L P E E EP & F F Q úL

M Q

[ [Q SUREOHPDGLQH[HPSOXOVHVFULH W

;

$; d E ; t >PLQ @ I

&;

)RUPDVWDQGDUGDXQHLSUREOHPHGHSURJUDPDUHOLQLDU HVWH $; E ; t >PD[ PLQ @ I &; 2ULFH SUREOHP GH SURJUDPDUH OLQLDU SRDWH IL DGXV OD IRUPD VWDQGDUG úL DQXPH 7RDWHLQHFXD LLOHGLQVLVWHPXOGHUHVWULF LLSRWILWUDQVIRUPDWHvQHJDOLW LDGXQkQG VDXVF ]kQGGXS FD] RVHULHGHYDULDELOHQHQHJDWLYHQXPLWHYDULDELOHHFDUWVDXGH FRPSHQVDUHÌQDFHVWIHOGLQPDWULFHD $ DLM UH]XOW PDWULFHD $ RE LQXW GLQ $

ODFDUHVDXDG XJDW O YHFWRULFRORDQ FXWRDWHHOHPHQWHOHQXOHFXH[FHS LDHOHPHQWXOXL

VLWXDWSHOLQLD M FDUHHVWH SHQWUXLQHFXD LLOH d VDX SHQWUXLQHFXD LLOH t LDU

[ [Q W GHYLQH ; RE LQXWGLQ ; SULQDG XJDUHDD O FRPSRQHQWH

YHFWRUXO ;

QHQHJDWLYH [ Q [ Q O úL FDUH UHSUH]LQW DFWLYLW L ILFWLYH $QDORJ & GHYLQH

&

F FQ DG XJkQGOD & O FRPSRQHQWHQXOH

9DULDELOHOH QHQHJDWLYH [L [L S U PkQ DFHOHDúL LDU vQ ORFXO YDULDELOHORU

QHJDWLYH [L

S

[LU YRPLQWURGXFHQRLYDULDELOHQHQHJDWLYHSULQVXEVWLWX LLOH

ZN 9DULDELOHOH [L

U

[ N N

L S LU

[LQ FDUH QX DX VHPQXO VSHFLILFDW VH SRW vQORFXL ILFWLY FX

GLIHUHQ DDGRX YDULDELOHSUHVXSXVHQHQHJDWLYHúLDQXPH [ N X N Y N X N t Y N t N LU LQ $FHVWHPRGLILF ULFRQGXFODIRUPDH[WLQV DSUREOHPHLGHSURJUDPDUHOLQLDU

$ ;

E

; t

>PD[ PLQ @ I

& ;

FDUHHVWHIRUPDVWDQGDUG ([HPSOX6 VHDGXF ODIRUPDVWDQGDUGSUREOHPDGHSURJUDPDUHOLQLDU

[ [ [ [ [ ° [ [ [ [ [ d ° ® [ [ t ° [ [ [ [ °¯ [ [ [ [ [ [ t [ t [ t [ d [ d [ [ [ I U UHVWULF LLGHVHPQ >PD[@ I [ [ [ [ [ [

3HQWUX[úL[FDUHVXQWQHJDWLYHIDFHPVXEVWLWX LLOH Z [ Z [ LDUYDULDELOHOH [ [ [ FDUHQXDXUHVWULF LLGHVHPQVHYRUvQORFXLFX

[

X Y [

X Y [

&XDFHVWHvQORFXLULVLVWHPXOGHUHVWULF LLGHYLQH

úL

X Y

[ [ Z X Y X Y ° [ [ Z X Y X Y d ° ® ° [ [ Z X Y X Y Z t °¯ [ [ Z X Y X Y Z t

I

[ [ Z X Y X Y Z

H úLRE LQHP 3HQWUXIRUPDVWDQGDUGDG XJ PYDULDELOHOHHFDUW [H [H [

[ [ Z X Y X Y ° H ° [ [ Z X Y X Y [ ® H ° [ [ Z X Y X Y Z [ ° [ [ Z X Y X Y Z [ H ¯ [ t [ t Z t X t Y t X t Y t X t Y t Z t [H t [H t [H t >PD[@ I [ [ Z X Y X Y Z

'H PHQ LRQDW F vQ RULFH FHULQ GH RSWLPL]DUH PD[LPXO úL PLQLPXO VH SRW vQORFXLUHFLSURFDQXPH >PD[@ I [ > PLQ @ I [

>PLQ @ I [ > PD[@ I [

6ROX LLOHSUREOHPHLGHSURJUDPDUHOLQLDU ÌQFRQWLQXDUHYRPFRQVLGHUDSUREOHPDVWDQGDUG6 GHSURJUDPDUHOLQLDU 3HQWUX FRPSDWLELOLWDWHDVLVWHPXOXL FRQVLGHU PF UDQJ $ UDQJ $ E úL UDQJ $ P FHHDFHLPSOLF P d Q 'HILQL LH1XPLPVROX LDSRVLELO VDXUHDOL]DELO DSUREOHPHL6 XQYHFWRU W [ [ [ Q GLQVSD LXOVROX LLORUFDUHVDWLVIDFH úL 0XO LPHD VROX LLORU SRVLELOH HVWH R VXEPXO LPH D VSD LXOXL YHFWRULDO Q GLPHQVLRQDO DO VROX LLORU HD SRDWH IL YLG UHGXV OD XQ SXQFW LQILQLW GDU P UJLQLW LQILQLW úL QHP UJLQLW DúD FXP UH]XOW GLQ H[HPSOHOH SH FDUH OH YRP DQDOL]D 6HGHPRQVWUHD] F PXO LPHDVROX LLORUSRVLELOHHVWHRPXO LPHFRQYH[ 'HILQL LH2VROX LHSRVLELO VDXUHDOL]DELO ; VHQXPHúWHVROX LHGHED] VDX SURJUDP GH ED] GDF DUH FHO PXOW P FRPSRQHQWH VWULFW SR]LWLYH [L [LU U d P úL GDF YHFWRULL FRORDQ DL DLU FRUHVSXQ] WRU

FRRUGRQDWHORUQHQXOHDOHYHFWRUXOXL ; VXQWOLQLDULQGHSHQGHQ L 'DF VROX LDGHED] DUHH[DFW P FRPSRQHQWHQHQXOHHDHVWHQHGHJHQHUDW vQ FD] FRQWUDU GDF FRQ LQH PDL SX LQ GH P FRPSRQHQWH QHQXOH HD HVWH GHJHQHUDW 'HILQL LH6HQXPHúWHVROX LHRSWLP DSUREOHPHL6 RVROX LHSRVLELO FDUH VDWLVIDFHFHULQ DGHRSWLP

([HPSOX)LHSURJUDPXO6

[ [ [ [ ® ¯ [ [ [ [ [L t L 0DWULFHD $

DUHUDQJXO W

9HFWRUXO ;

§ · ¨ ¸ HVWH R VROX LH SRVLELO GHRDUHFH VDWLVIDFH © ¹

FRQGL LLOH úL W 9HFWRUXO ; UHSUH]LQW R VROX LH GH ED] QHGHJHQHUDW GHRDUHFHQXP UXOFRPSRQHQWHORUQHQXOHHVWH

D

§· ¨¨ ¸¸ VXQWOLQLDULQGHSHQGHQ L © ¹

UDQJ $ úLYHFWRULL D

§· ¨¨ ¸¸ úL © ¹

W

§ · 9HFWRUXO ; ¨ ¸ QX HVWH R VROX LH GH ED] GHúL HVWH R VROX LH © ¹ SRVLELO GHRDUHFH YHFWRULL FRORDQ GLQ PDWULFHD $ FRUHVSXQ] WRUL FRPSRQHQWHORU §· § · ¸¸ VXQWOLQLDUGHSHQGHQ L QHQXOH D ¨ ¸ úL D ¨¨ © ¹ © ¹

9RP GD vQ FRQWLQXDUH FkWHYD WHRUHPH SULYLQG VROX LLOH XQXL SURJUDP OLQLDU SHQWUXGHPRQVWUDUHDORUVHSRWFRQVXOWD>@>@>@HWF 7HRUHPD ÌQWUH VROX LLOH SRVLELOH DOH XQHL SUREOHPH GH SURJUDPDUH OLQLDU úLVROX LLOHSRVLELOHDOHSUREOHPHLH[WLQVHH[LVW RFRUHVSRQGHQ ELXQLYRF 7HRUHPD ÌQWUH VROX LLOH RSWLPH DOH XQHL SUREOHPH GH SURJUDPDUH OLQLDU úLFHOHDOHSUREOHPHLH[WLQVHH[LVW RFRUHVSRQGHQ ELXQLYRF 6SD LXOYHFWRULDO Q GLPHQVLRQDODOWXWXURUVROX LLORU ; VHQXPHúWHVSD LXO VROX LLORULDUPXO LPHDVROX LLORUSRVLELOHIRUPHD] XQVXEVSD LX + DODFHVWXLD(D SRDWHILYLG UHGXV ODXQSXQFWLQILQLW GDUP UJLQLW VDXLQILQLW úLQHP UJLQLW DúDFXPYDUH]XOWDGLQH[HPSOHOHSHFDUHOHYRPGD 7HRUHPD 'DF SHQWUX XQ SURJUDP OLQLDU + z DWXQFL H[LVW FHO SX LQRVROX LHGHED] 'LQ FHOH H[SXVH SkQ DFXP UH]XOW F SHQWUX UH]ROYDUHD XQHL SUREOHPH GH SURJUDPDUHOLQLDU HVWHQHFHVDUúLVXILFLHQWV SXWHPGHVFRSHULvQPXO LPHDVROX LLORUGH ED] SHDFHOHDFDUHRSWLPL]HD] IXQF LDRELHFWLYÌQFD]XOvQFDUHvQSUREOHP LQWHUYLQ GRX VDX WUHL YDULDELOH VROX LD SXWHD IL GHWHUPLQDW SULQ PHWRGH HOHPHQWDUH úL DQXPH PHWRGDJUDILF úLPHWRGDDOJHEULF ÌQFHOHODOWHFD]XULRLQVSHFWDUHFRPSOHW DPXO LPLL

WXWXURU VROX LLORU GH ED] DU SUHVXSXQH XQ YROXP PDUH GH FDOFXOH úL R VHULH GH GH]DYDQWDMHFDvQFD]XOSUREOHPHORUFXVROX LHLQILQLW 2 PHWRG FDUH QH G U VSXQVXUL SUHFLVH úL FRQFOXGHQWH úL FDUH QHFHVLW XQ YROXP UHODWLY PLF GH FDOFXOH HVWH PHWRGD VLPSOH[ FDUH SHUPLWH GHWHUPLQDUHD VROX LHLRSWLPHSRUQLQGGHODRVROX LHGHED] GXS XQQXP UILQLWGHLWHUDWH 0HWRGDVLPSOH[GHUH]ROYDUHDXQXLSURJUDPOLQLDUVWDQGDUG )LHSURJUDPXOVWDQGDUG $; E ; t 6 >PD[@ I &;

FXQRWD LLOHGLQSDUDJUDIXO'DF YHFWRULLFRORDQ DLPDWULFHL $ DL DL DLP

P

IRUPHD] R ED] vQ \ DWXQFL [L [L [LP VH QXPHVF FRRUGRQDWH ED]LFH

YDULDELOH GH ED] 0DWULFHD $ SRDWH IL GHVFRPSXV vQ GRX VXEPDWULFH % IRUPDW GLQYHFWRULL DL DL DLP úL ( IRUPDW FXFHOHODOWHFRORDQHGHFL

$ úLDQDORJ

& ;

LDUIRUPDVWDQGDUGVHVFULH

% _ ( ; % ; (

W

%_(

& % & ( ; % ; ( W

E

; % t ; ( t

>PD[@ I & % & ( ; % ; ( W

) FkQGFDOFXOHOHUH]XOW

%; % (; ( E ; % t ; ( t >PD[@ I & % ; % & ( ; (

2VROX LHDVLVWHPXOXL HVWH

; % % E % (; ( /XkQGDLFL ; ( RE LQHPRVROX LHGHED] SHQWUX úLDQXPH ; % % E 'DF ; % t VSXQHPF ED]D % DL DL DLP HVWHSULPDODGPLVLELO 'DF YHFWRUXO D M

\ L M \ L M \ LP M M

UDSRUWFXED]D % LDU & (

Q DUH DFHVWH FRPSRQHQWH vQ

FL FL FLP DWXQFL

[M

¦F \ L

L,

LM

^L L LP ` M -

,

^ Q` ? , 'LVSXQkQGGHRED] SULPDODGPLVLELO VHvQWRFPHúWHWDEHOXOVLPSOH[vQFDUH WUHFHP D VROX LD ; % % E

FX -

E & (

FL FL FLP & % ; % ¦ FL a [L YDORDUHD IXQF LHL RELHFWLY FRUHVSXQ] WRDUH VROX LHL GH

F I %

L,

ED] G % D M

W

\ L M \ L M \ LP M FDUH UHSUH]LQW FRRUGRQDWHOH YHFWRULORU D M

d M d Q vQ ED]D % GDF % HVWH ED]D FDQRQLF \ LM VXQW FRHILFLHQ LL GLQ VLVWHPXOGHUHVWULF LLGDW

¦F \

H VHFDOFXOHD] I M

L

L,

LM

F M ¦ FL \ LM ° L, ® °¯

I VHFDOFXOHD] GLIHUHQ HOH F M I M

M, M,

8QDVWIHOGHWDEHOVLPSOH[DUDW GHFLVXEIRUPD F P F F ! FL ! F P

& % % ; % D D ! F D a [ ! F D a [ ! # # # # # % FL DL a [L !

FM I M

!

FQ

D P

!

DQ

!

\P

!

\Q

!

\ P

!

\ Q

#

% !

# \ LQ

#

\ P P

% !

# \ PQ

I P

!

IQ

I % I I ! I L F F

!

DL ! D P

# # # # # # % # FP DP a [P ! IM

% # ! % # ! ! IP

FL I

!

FP

\ L P

F P I P ! F Q I Q

ÌQFRQWLQXDUHVHDSOLF WHVWXOGHRSWLPDOLWDWHDOVROX LHL ; % ED]DWSHXUP WRDUHOH WHRUHPHSHFDUHOHG PI U GHPRQVWUD LH

7HRUHPD 'DF

F M I M d SHQWUX WR L M - SUREOHPD GH

SURJUDPDUHOLQLDU DUHRSWLPILQLWúL I RSW 7HRUHPD'DF SHQWUXXQLQGLFH

I % M - SHQWUXFDUH F M I M ! WRDWH

FRPSRQHQWHOH \ MN d SURJUDPXODUHRSWLPLQILQLW $YHPXUP WRDUHOHFD]XUL 'DF WR L F M I M d M - DWXQFL ; % HVWHVROX LDRSWLP úL I RSW

I %

'DF H[LVW FHOSX LQRGLIHUHQ F M I M ! DWXQFLVROX LDQXHVWHRSWLP ÌQ DFHVWFD]H[LVW XUP WRDUHOHSRVLELOLW L D ILH O - DúDvQFkW FO I M ! úLGDF WR L \ LM d L , SUREOHPDQX DUHRSWLPILQLW E ILH O - FX FO I O ! úL H[LVW FHO SX LQ XQ \ LM ! DWXQFL VROX LD SRDWHILvPEXQ W LW 6H WUHFH OD SULPD LWHUD LH úL VH GHWHUPLQ YHFWRUXO FDUH LQWU vQ ED] úL YHFWRUXOFDUHLHVHGLQED] ,QGLFHOH N DOYHFWRUXOXLFDUHLQWU vQED] QHHVWHGDW GH F N I N PD[ F M I M F M I M ! LDULQGLFHOH K DOYHFWRUXOXLFDUHLHVHGLQED] HVWHGDWGH

a [K \ NK

½ a [ PLQ ® L L , \ LN ! ¾ ¿ ¯ \ LN ÌQDFHVWPRGYHFWRUXOXL D K vLLDORFXOYHFWRUXO D N vQED]

6HVWDELOHúWHHOHPHQWXOSLYRW \ NK VHUHFDOFXOHD] WRDWHHOHPHQWHOHWDEORXOXL VLPSOH[úLVHRE LQHRQRX VROX LHGHED] 'DF DFHDVW VROX LHQXHVWHRSWLP VH WUHFHODLWHUD LDXUP WRDUH&DUH]XOWDWDOILHF UHLLWHUD LLVHRE LQHRQRX VROX LHGH ED] úLvQED]DWHRUHPHORUHQXQ DWHDQWHULRUvQILQDORE LQHPVROX LDRSWLP VDXQH FRQYLQJHPF QXDYHPRSWLPILQLW 2EVHUYD LH5HDPLQWLPUHJXOLOHGHFDOFXO HOHPHQWHOHGHSHOLQLDSLYRWXOXLVHvPSDUWODSLYRW HOHPHQWHOH GH SH FRORDQD SLYRWXOXL GHYLQ QXOH FX H[FHS LD SLYRWXOXL FDUH GHYLQH FHOHODOWHHOHPHQWHVHFDOFXOHD] GXS ÄUHJXODGUHSWXQJKLXOXL´6HGHWHUPLQ YDORDUHD XQXL GHWHUPLQDQW GH RUGLQ GRL XQGH SH GLDJRQDOD SULQFLSDO DYHP SLYRWXO úL HOHPHQWXO FH WUHEXLH UHFDOFXODW LDU FHOHODOWH HOHPHQWH VH J VHVF SH OLQLD úL FRORDQD SLYRWXOXL LQWHUVHFWDWH FX OLQLD úL FRORDQD HOHPHQWXOXL GH FDOFXODW5H]XOWDWXOVHvPSDUWHODSLYRW

([HPSOX6 VHUH]ROYHSUREOHPDGHSURJUDPDUHOLQLDU

[ [ [ [ ® [ ¯ [ [ [L t L >PD[@ I [ [ [ [ UDQJ $

6ROX LH $

D

9HFWRULL D

§ · ¨¨ ¸¸ IRUPHD] RED] 9DULDELOHOHED]LFHVXQW [ úL [ GHFL , ©¹

§· ¨¨ ¸¸ úL ©¹

^`

$OF WXLPWDEHOXOVLPSOH[

FM

&%

%

;%

D

D

D

D

IM

D

FM I M

&HD PDL PDUH GLIHUHQ SR]LWLY HVWH F I

D

D

úL DYHP \ L ! GHFL

VROX LDSRDWHILvPEXQ W LW ÌQED] YDLQWUDYHFWRUXO D 3HQWUXDYHGHDFHYHFWRU LHVHGLQED] FDOFXO P

[ ½ ½ PLQ ® L ¾ PLQ ® ¾ ¯ ¿ ¯ \ L ¿ GHFLGLQED] LHVHYHFWRUXO D 3LYRWXOHVWH

7DEHOXOVLPSOH[GLQLWHUD LDXUP WRDUHHVWH

FM

&% IM

% D D

FM I M

;%

D

D

D

D

D

0DLDYHPRGLIHUHQ F M I M SR]LWLY GHFLvQED] LQWU YHFWRUXO D úLLHVH YHFWRUXO D GHRDUHFHSHFRORDQDOXL D DYHPRVLQJXU FRRUGRQDW SR]LWLY SLYRWXOHVWH 7DEORXOVLPSOH[vQLWHUD LDXUP WRDUHHVWH FM

&%

% D D

IM

D

;%

D

D

D

D

FM I M

$YHP GRX GLIHUHQ H F M I M SR]LWLYH GDU SH FRORDQHOH ORU HOHPHQWHOH \ L WUDQVIRUPDWHVXQWQHJDWLYHGHFLSUREOHPDQXDUHRSWLPILQLW ([HPSOX6 VHUH]ROYHSUREOHPDGHSURJUDPDUHOLQLDU

[ [ [ [ ° [ ® [ [ [ ° [ [ [ [ ¯

[L t L >PD[@ I [ [ [ [ [

UDQJ $

6ROX LH $

9HFWRULL D D D

IRUPHD] RED] 7DEORXOVLPSOH[HVWHXUP WRUXO FM

;%

D

D

D

D

D

% D

D

D

IM

D

&%

FM I M

$YHP

½ PLQ ® ¾ ¯ ¿

F I ! GHFL LQWU vQ ED] YHFWRUXO D 'LQ [ GHFL LHVH GLQ ED] YHFWRUXO D 3LYRWXO HVWH \ \

8UP WRUXOWDEHOHVWH FM

&%

IM

D

D

D

D

% D

;%

D

D

D D

FM I I

7RDWH GLIHUHQ HOH F M I M VXQW QHJDWLYH VDX QXOH GHFL I RSW

úL HVWH

[ [ [ úL [ W § · 6ROX LD RSWLP HVWH ; ¨ ¸ úL HVWH QHGHJHQHUDW QXP UXO GH © ¹ FRPSRQHQWHSR]LWLYHDOHYHFWRUXOXLVROX LH ; HJDOFXQXP UXOUHVWULF LLORU

UHDOL]DW SHQWUX YDORULOH [

[

0HWRGDED]HLDUWLILFLDOH ÌQ SUREOHPHOH VWXGLDWH DQWHULRU PDWULFHD VLVWHPXOXL GH UHVWULF LL FRQ LQHD YHFWRULXQLWDULFDUHDOF WXLDXRED] XQLWDU FHHDFHXúXUDGHWHUPLQDUHDXQHLVROX LL LQL LDOH GH ED] 'DF DFHDVW ED] XQLWDU QX H[LVW UHFXUJHP OD PHWRGD ED]HL DUWLILFLDOH SULQ LQWURGXFHUHD YDULDELOHORU [ DN t SHQWUX D DYHD R ED] SULPDO DGPLVLELO úLVHUH]ROY SUREOHPDGHSURJUDPDUHOLQLDU $; ,; D E ; t [ D t >PD[@ I &; O; D

FX O XQQXP UUHDODUELWUDUVWULFWSR]LWLYSHQWUX PLQ I VHDGDXJ O; D 2ULFH VROX LH SRVLELO D SUREOHPHL LQL LDOH HVWH R VROX LH SRVLELO D SURJUDPXOXL H[WLQV SHQWUX FDUH YDORULOH WXWXURU YDULDELOHORU DUWLILFLDOH VXQW QXOH úL UHFLSURF RULFH VROX LH SRVLELO D SURJUDPXOXL H[WLQV vQ FDUH WRDWH YDULDELOHOH DUWLILFLDOHVXQWQXOHHVWHRVROX LHDSURJUDPXOXLLQL LDOGXS vQO WXUDUHDDFHVWRUD

$VHPHQHDVROX LLVHUHDOL]HD] SHQWUX >PLQ @O; D 2DVWIHOGHSUREOHP VHUH]ROY SULQPHWRGDFHORUGRX ID]H )D]D, ÌQDFHDVW ID] VHUH]ROY SUREOHPD $; ,; D E ; t [ D t >PLQ @ I ; D /DVIkUúLWSXWHPDYHDXUP WRDUHOHVLWXD LL >PLQ @ I GHFL WRDWH YDULDELOHOH DUWLILFLDOH VXQW QXOH úL QLFL R YDULDELO DUWLILFLDO QXHVWHED]LF ID GHVROX LDRSWLP ÌQDFHVWFD] GLVSXQHP GH R VROX LH GH ED] D SURJUDPXOXL H[WLQV GLQ FDUH SULQ vQO WXUDUHD YDULDELOHORU DUWLILFLDOH VH RE LQH R VROX LH GH ED] D SURJUDPXOXLLQL LDOúLVHWUHFHODID]DD,,D >PLQ @ I úLFHOSX LQRYDULDELO DUWLILFLDO HVWHED]LF (DWUHEXLH HOLPLQDW DVWIHO GDF SH OLQLD YDULDELOHL DUWLILFLDOH H[LVW HOHPHQWH QHQXOH UDQJ $ P DOHJHP XQXO GLQWUH DFHVWHD GUHSW SLYRW úL IDFHP vQF RLWHUD LHSHQWUXDRHOLPLQDGLQED] GDF SH OLQLD YDULDELOHL DUWLILFLDOH QX DYHP HOHPHQWH QHQXOH UDQJ $ P R YRP QHJOLMD VXSULPkQGR GLQ WDEHO 6H WUHFH OD ID]DD,,D >PLQ @ I ! SUREOHPDLQL LDO QXDUHVROX LHGHED] )D]D,, ÌQDFHDVW ID] vQFD]XO VHHOLPLQ GLQXOWLPXOWDEHOVLPSOH[FRORDQHOH YDULDELOHORU DUWLILFLDOH úL VH FRQWLQX DOJRULWPXO LQWURGXFkQG FRHILFLHQ LL IXQF LHLRELHFWLY I &; ([HPSOX6 VHUH]ROYHSURJUDPXOOLQLDU

[ [ [ ° [ [ [ ® °[ [ [ ¯

[L t d L d >PD[@ I [ [ [ [ 6ROX LH

$

1X GLVSXQHP GH R ED] FDQRQLF GHFL YRP DG XJD VLVWHPXOXL GH UHVWULF LL YDULDELOH DUWLILFLDOH [D [ D D úL YRP UH]ROYD SUREOHPD SULQ PHWRGD FHORU GRX ID]H

)D]D, 5H]ROY PSURJUDPXOOLQLDU

[ [ [ [D ° D ® [ [ [ D ° D ¯ [ [ [ D [L t d L d [ ND t d N d

>PLQ @ I

[D [D [D

$YHPRSUREOHP GHPLQLP7DEORXULOHVLPSOH[VXQW FM

&% % ; % D D

D

D

D

D D D D

D IM

FM I M

FM

& % % ; % D

D

D

D

D

IM

FM I M

D

D D D

D

FM

& % % ; % D D D D D IM FM I M

FM

D

D D D

& % % ; % D D D D D D IM FM I M

D

D

D

D D

$PHOLPLQDWGLQED] WRDWHYDULDELOHOHDUWLILFLDOHúL I RSW

7UHFHPODID]D

XUP WRDUH )D]D,, 5HOX P WDEHOXO VLPSOH[ GH XQGH DP U PDV GDU FX F M FRHILFLHQ LL IXQF LHL RELHFWLY I úL I U FRORDQHOH YHFWRULORU D D D $YHP SHQWUX SUREOHPD GH PD[LPWDEHOXO

FM

&%

% ; % D

D

D

D

D

IM

FM I M

D

D

D

D

FM

&%

IM

% D D

;%

D

D

D

FM I M

PD[ I

úLHVWHUHDOL]DW GHYHFWRUXO $

W

úLHVWHGHJHQHUDW

([HPSOX6 VHUH]ROYHSURJUDPXOOLQLDU

[ [ [ ° [ ® [ [ ° [ [ [ ¯

[L t d L d >PD[@ I [ [ [ [ 6ROX LH

$

ÌQ $ DYHPXQYHFWRUFRORDQ XQLWDU D D

W GHFLDG

XJ PVLVWHPXOXL

GHUHVWULF LLQXPDLGRX YDULDELOHDUWLILFLDOH [ ODSULPDHFXD LHúL [ D ODXOWLPD úLUH]ROY PSUREOHPDSULQFHOHGRX ID]H

)D]D, 5H]ROY PSURJUDPXOOLQLDU

[ [ [ [D ° ® [ [ [ ° D ¯ [ [ [ [

[L t d L d [D t [D t

>PLQ @ I

[D [D

$YHPWDEHOXOVLPSOH[ FM

% ; % D D D D

D

D

& % % ; % D D D D IM FM I M

&% IM

FM I M

D D

D

D

D

D

D

D

FM

FM

&% %

D

D

IM

;% D D D

FM I M )D]D,,

FM

&%

IM

QHGHJHQHUDW

D

D D

D

% D

;%

D

D

D

D

D D

FM I M 5H]XOW >PD[ @ I

úLHVWHUHDOL]DWGHYHFWRUXO ;

W

§ · ¨ ¸ VROX LH © ¹

&D]XOvQFDUHVLVWHPXOGHUHVWULF LLFRQ LQHLQHJDOLW L $PY ]XWvQSDUDJUDIXOF RULFHSURJUDPOLQLDUSRDWHILDGXVODIRUPD VWDQGDUG SULQ DG XJDUHD SHQWUX LQHJDOLW L GH WLSXO d VDX VF GHUHD SHQWUX LQHJDOLW LGHWLSXO t DXQRUYDULDELOHHFDUWGHFRPSHQVDUH FDUHSRWILLQWHUSUHWDWH HFRQRPLFFDUHSUH]HQWkQGDFWLYLW LILFWLYHSHFDUHvQWUHSULQGHUHDQXOHHIHFWXHD] úLF URUDvQIXQF LDGHHILFLHQ OHYRUFRUHVSXQGHEHQHILFLLQXOH3UREOHPDH[WLQV VHUH]ROY SULQPHWRGDVLPSOH[VWXGLDW DQWHULRU

([HPSOX 6 VH DGXF OD IRUPD VWDQGDUG úL V VH UH]ROYH SUREOHPD GH SURJUDPDUHOLQLDU

[ [ [ d ° ® [ [ [ d °[ [ [ d ¯ [L t d L d >PD[@ I [ [ [

6ROX LH3UREOHPDH[WLQV HVWH

[ [ [ [ ° ® [ [ [ [ °[ [ [ [ ¯

[L t d L d >PD[@ I [ [ [ [ [ [ $YHPXUP WRUXOWDEHOVLPSOH[ FM

&% IM

IM

D

D

D

D

D

D

D

D

D

D

% ; % D D D D D

FM I M $YHP I RSW

D

FM

&%

% ;% D D

FM I M

SHQWUX ;

W 6ROX LDHVWHGHJHQHUDW

([HPSOX6 VHDGXF ODIRUPDVWDQGDUGúLV VHUH]ROYHSURJUDPXOOLQLDU

[ [ [ ° ® [ [ [ [ d ° [ [ [ [ t ¯ [ t [ t [ d [ QXDUHVHPQVSHFLILFDW >PD[@ I [ [ [ [

6ROX LH)DFHPVXEVWLWX LLOH

3URJUDPXOGHYLQH

[

[ \ \ t X Y FX X t Y t

[ [ \ ° ® [ [ \ X Y d ° [ [ \ X Y t ¯ [ t [ t \ t X t Y t >PD[@ I [ [ \ X Y

5HVWULF LLOHFRQ LQúLLQHFXD LLGHFLODLQHFXD LDDGRXDDG XJ PYDULDELODHFDUW \ t LDUvQXOWLPDVF GHPYDULDELODHFDUW \ t DVWIHOF SURJUDPXOGHYLQH

[ [ \ ° ® [ [ \ X Y \ ° [ [ \ X Y \ ¯ [ t [ t \ t X t Y t \ t \ t >PD[@ I [ [ \ X Y \ \ $YHP

$

D D D D D D

D UDQJ $

[

\

[

\

X

Y \

1X DYHP R ED] FDQRQLF vQ $ YHFWRUXO D

W

HVWH XQLWDU

&RPSOHW PRED] FXDMXWRUXOYDULDELOHORUDUWLILFLDOH \ D DG XJDWSULPHLHFXD LLúL

\D DG XJDW XOWLPHL HFXD LL GLQ 3UREOHPD VH UH]ROY SULQ PHWRGD FHORU GRX ID]H

)D]D, $YHPGHUH]ROYDWSURJUDPXOOLQLDU

[ [ \ \ D ° ® [ [ \ X Y \ ° D ¯ [ [ \ X Y \ \

[ t [ t \ t X t Y t \ t \ t \ D t \D t

>PLQ @ I

\ D \ D

7DEHOXOVLPSOH[YDIL FM

D D D D D D D D D

&% % ; % D D D IM FM I M

FM

& % % ; % D D D D D D D D D

D D IM FM I M D

FM

& % % ; % D D D D D D D D D IM FM I M

$PRE LQXW > PLQ @ I

D

D

D

úLGLQED] DPHOLPLQDWWRDWHYDULDELOHOHDUWLILFLDOH

)D]D,, 5HOX P XOWLPD SDUWH D WDEHOXOXL VLPSOH[ I U XOWLPHOH GRX FRORDQH úL FX FRHILFLHQ LL F M DLIXQF LHL I 9RPDYHD

FM

& % % ; % D D D D D

D

IM FM I M

D

D D D

FM

&% % ; %

D

D D

D

D

D

IM

FM I M I RSW

úLHVWHUHDOL]DWGH ;

D D D D

6ROX LDHVWHGHJHQHUDW W

'XDOLWDWHDvQSURJUDPDUHDOLQLDU 3UREOHPD GXDOLW LL vQ SURJUDPDUHD OLQLDU SUH]LQW XQ LQWHUHV GHRVHELW GLQ SXQFW GH YHGHUH PDWHPDWLF FkW úL HFRQRPLF ÌQ SDUDJUDIHOH DQWHULRDUH DP I FXW LSRWH]DFD UDQJ $ P SkQ ODPHWRGDED]HLDUWLILFLDOHU PkQkQGWRWXúLUHVWULF LD P t Q FDUHQXYDPDLILQHFHVDU vQDERUGDUHDSUREOHPHLGXDOH 3HQWUX IRUPDUHD XQXL SURJUDP GXDO WUHEXLH V LQHP VHDPD GH XUP WRDUHOH UHJXOL ILHF UHLYDULDELOHQHQHJDWLYHQHSR]LWLYH GLQSURJUDPXOSULPDOvLFRUHVSXQGHvQ SURJUDPXOGXDORLQHFXD LH t d XQHLYDULDELOHI U VHPQVSHFLILFDWGLQSURJUDPXOSULPDOvLFRUHVSXQGHvQGXDO RHFXD LH FRHILFLHQ LLIXQF LHLRELHFWLYGLQSUREOHPDSULPDO VXQWRSXúLLWHUPHQLORUOLEHUL GLQVLVWHPXOGHUHVWULF LLDOSUREOHPHLGXDOH WHUPHQLL OLEHUL DL UHVWULF LLORU GLQ SUREOHPD SULPDO VXQW RSXúLL FRHILFLHQ LORU IXQF LHLRELHFWLYGLQSUREOHPDGXDO ILHF UHLUHVWULF LLGHIRUPD t d VDX GLQSURJUDPXOSULPDOvLFRUHVSXQGHvQ FHOGXDORYDULDELO QHQHJDWLY QHSR]LWLY VDXRDUHFDUH PDWULFHD FRHILFLHQ LORU GLQ VLVWHPXO GH UHVWULF LL GLQ SURJUDPXO GXDO HVWH WUDQVSXV PDWULFLLFRHILFLHQ LORUGLQSURJUDPXOSULPDO 8WLOL]kQGQRWD LLOHYHFWRULDOHDYHPXUP WRDUHOHIRUPHGHSURJUDPHGXDOH 'DF SURJUDPXOSULPDOHVWH $; d E ; t 3 >PD[@ I &;

DWXQFLSURJUDPXOGXDOYDIL

'

<$ t & < t >PLQ @J <E

ÌQSUREOHPD 3 SXWHPGDXUP WRDUHOHLQWHUSUHW ULHOHPHQWHORU

[L SRDWH IL YHFWRUXO SUH XULORU XQLWDUH DOH EXQXULORU UH]XOWDWH GLQGHVI úXUDUHD

DFWLYLW LORU YHFWRUXO E ±FHUHUHDGHSURGXVHVDXGLVSRQLELOXOGHPDWHULLSULPH F M ± FRVWXO ILHF UHL DFWLYLW L VDX EHQHILFLXO UHDOL]DW GLQ GHVI úXUDUHD

DFWLYLW LL YDORDUHDWRWDO DEXQXULORUFUHDWH E M V ILHPD[LP 3XWHPLQWHUSUHWDSUREOHPDGXDO ' DVWIHO

[L V UHSUH]LQWHQLYHOXOODFDUHVHGHVI úRDU DFWLYLW LOHIHQRPHQXOXLHFRQRPLF

UHVSHFWLY E M ±FHUHUHDGHSURGXVHVDXGLVSRQLELOXOGHPDWHULLSULPH

F M ±FRVWXOILHF UHLDFWLYLW LVDXEHQHILFLXOUHDOL]DWGLQGHVI úXUDUHDDFWLYLW LL

UHVSHFWLYH V VH GHWHUPLQH QLYHOXO ILHF UHL DFWLYLW L [L DúD vQFkW V ILH vQGHSOLQLWH VDX GHS úLWHFHUHULOH E M LDUFRVWXOWRWDODODFWLYLW LORUGHVI úXUDWHV ILHPLQLP

'DF SURJUDPXOSULPDO 3 HVWHGDWVXEIRUPDVWDQGDUG $; E ; t 3 >PD[@ I &; GXDOXOYDIL <$ t & < RDUHFDUH ' >PLQ @J <E 'HREVHUYDWF GXDOXOQXDUHIRUPDVWDQGDUG ÌQWUHFXSOXULOHGHSUREOHPHGXDOHH[LVW RVWUkQV LQWHUGHSHQGHQ DVROX LLORU ORU9RPGDvQFRQWLQXDUHFkWHYDUH]XOWDWHI U GHPRQVWUD LH /HPD 'DF ; úL < FRQVWLWXLH VROX LL SRVLELOH SHQWUX FXSOXO GH SURJUDPH 3 ' DYHPLQHJDOLWDWHD &; d <E 3HQWUXXQFXSOXGHSURJUDPHOLQLDUHGXDOHWHRUHPDGHH[LVWHQ QHDVLJXU GH XUP WRDUHOHSRVLELOLW L

7HRUHPD GH H[LVWHQ 3HQWUX XQ FXSOX GH SURJUDPH OLQLDUH GXDOH DYHPDOWHUQDWLYHOHXUP WRDUH D QLFLXQXOGLQSURJUDPHQXDGPLWHVROX LLSRVLELOH E XQSURJUDPDUHRSWLPILQLWLDUFHO ODOWQXDGPLWHVROX LLSRVLELOH F DPEHOHSURJUDPHDGPLWVROX LLRSWLPHILQLWH 7HRUHPD IXQGDPHQWDO D GXDOLW LL 3HQWUX XQ FXSOX GH SURJUDPH GXDOH FRQGL LD QHFHVDU úL VXILFLHQW SHQWUX FD VROX LD UHDOL]DELO GH ED] ; D SURJUDPXOXL SULPDO 3 V ILH RSWLP HVWH V H[LVWH R VROX LHUHDOL]DELO GHED] < DSURJUDPXOXLGXDO ' DúDvQFkWV DYHP &; <E 3HED]DWHRUHPHLGXDOLW LLVHSRDWHGDúLXUP WRUXOUH]XOWDW 7HRUHPD3HQWUXXQFXSOXGHSURJUDPHOLDQLDUHGXDOH 3 ' FRQGL LD QHFHVDU úLVXILFLHQW FDVROX LLOHSRVLELOH ; úL < V ILHRSWLPHHVWH < E $; & <$ ; 'LQUHOD LLOH UH]XOW XUP WRDUHOH GDF VROX LDRSWLP ; < DSUREOHPHLSULPDOHGXDOH VDWLVIDFHUHVWULF LD M d M d P L d L d Q GLQ VLVWHPXO UHVSHFWLY FX LQHJDOLWDWH VWULFW DWXQFL FRPSRQHQWD \ M [L D VROX LHL SURJUDPXOXL GXDO

SULPDO HVWHQXO GDF FRPSRQHQWD [L ! d L d Q \ M ! d M d P D VROX LHL RSWLPH D

SURJUDPXOXL SULPDO GXDO DWXQFL VROX LD RSWLP < ; D GXDOXOXL SULPDO VDWLVIDFHFXHJDOLWDWHUHVWULF LD M L DOXL UHVSH[WLY 6H SRDWH GHPRQVWUD SH ED]D UH]XOWDWHORU DQWHULRDUH F R VROX LH SRVLELO D GXDOHLHVWH < & % % XQGH & % % UHSUH]LQW SURGXVXOGLQWUHYHFWRUXO & % IRUPDWGHFRHILFLHQ LLED]LFL úL LQYHUVD PDWULFLL GH ED] GLQ XOWLPXO WDEORX VLPSOH[ FDUH DSDUH SH FRORDQHOH FRUHVSXQ] WRDUHYHFWRULORUXQLWDULGLQSULPXOWDEORX6HDUDW F HVWHFKLDU VROX LDRSWLP 'DF SULQWUHYDULDELOHOHED]LFHDOHWDEHOXOXLVLPSOH[RSWLPDODSDUúL YDULDELOHHFDUWGHFRPSHQVDUH GHH[HPSOX [ N ! DWXQFL \ N ([HPSOX6 VHUH]ROYHSURJUDPXOOLQLDU

[ [ t ® ¯ [ [ t

[ t [ t >PLQ @ I [ [

'XDOXOV XHVWH

\ \ d ® ¯ \ \ d \ t \ t >PD[@J \ \

7DEHOXO VLPSOH[ DO GXDOXOXL DGXV OD IRUPD VWDQGDUG SULQ DG XJDUHD YDULDELOHORUHFDUW \ úL \ HVWH

FM

&% JM

D

D

D

D

D

D

%

<%

D

D

JM

FM J M FM

JM FM J M

<% D D

%

D

&%

&%

<%

FM

% D

FM J M

D D

D

D

D

D

§ · ¨ ¸ © ¹ 6ROX LDRSWLP DSULPDOHLGXDODGXDOHL HVWH I RSW úLVHFLWHúWHSHXOWLPDOLQLH

6ROX LDRSWLP HVWH J RSW

SHQWUX <

D WDEHOXOXL VLPSOH[ OXkQG FX VHPQ VFKLPEDW YDORULOH GH SH XOWLPHOH GRX FRORDQH W FRUHVSXQ] WRDUHYHFWRULORUXQLWDULGHFL ; ([HPSOX6 VHUH]ROYHSURJUDPXOOLQLDU

'XDOXOV XHVWH

[ [ t ° [ [ t ° ® t [ [ ° °¯ [ t [ t [ t >PLQ @ I [ [

\ \ \ \ d ® ¯ \ \ \ d

\ t \ t >PD[@J \ \ \ \ $G XJkQG OD SULPD LQHFXD LH YDULDELOD HFDUW \ t LDU OD D GRXD \ t RE LQHPXQSURJUDPVWDQGDUGDOF UXLWDEHOVLPSOH[HVWH FM

&% % D

<%

D

D

D

D

D

D

D

JM FM J M

FM

<% D D D D D JM &% %

FM J M

FM

D

D

D

<% D D D D D D D D JM FM J M $P RE LQXW J RSW 3H XOWLPD OLQLH DYHP FRPSRQHQWHOH FX VHPQ VFKLPEDW DOH SUREOHPHL SULPDOH úL DQXPH SHQWUX [ [ úL RE LQHP I RSW &% %

3HQWUX DOWH PHWRGH GH UH]ROYDUH D SHUHFKLL GH SURJUDPH GXDOH VH SRDWH FRQVXOWDOLWHUDWXUDGHVSHFLDOLWDWHPHQ LRQDW ODELEOLRJUDILH

$SOLFD LLvQHFRQRPLH ([HPSOX)LHSUREOHPDGHODQVDUHDSURGXF LHL 3URGXVH

3 3

0DWHULLSULPH

0 0

ÌQFDV UL XQLWDUH

D E

F G D

'LVSRQLELO &RVWXULXQLW LGH 3 PDWHULL DFKL]L LHPDWHULL SULPH SULPH

&RVWXULGH SURGXF LH

3HQDOLW LSHQWUX PDWHULDSULP QHIRORVLW

&DSLWDOGLVSRQLELO SHQWUXDFKL]L LRQDUHDGH PDWHULLSULPH

6HFHUH 8QSODQGHSURGXF LHFXvQFDV ULWRWDOHPD[LPHvQFRQGL LLOHXWLOL] ULLPDWHULLORU SULPHGLVSRQLELOH 8Q SODQ GH SURGXF LH FRUHVSXQ] WRU XQHL FDQWLW L WRWDOH PLQLPH GH PDWHULL SULPHU PDVHQHIRORVLWH 8Q SODQ GH SURGXF LH GH IRORVLUH D PDWHULLORU SULPH GLVSRQLELOH SHQWUX FDUH SHQDOL]DUHDWRWDO SHQWUXPDWHULLOHQHIRORVLWHV ILHPLQLP 8QSODQGHSURGXF LHvQFRQGL LLOHvQFDUHPDWHULDSULP VHFXPS U SURGXF LD WRWDO IL]LF HVWHGHFHOSX LQ EXF LSURGXVHúLEHQHILFLXOWRWDOPD[LP 6ROX LH )LH [ [ [ FDQWLW LOH IDEULFDWH &RQVXPXO GH PDWHULL SULPH SH XQLWDWHD GH SURGXV HVWH GH LDU FRVWXULOH GH PDWHULH SULP FRQVXPDW SH XQLWDWHD GH SURGXV VXQW u u SHQWUX SULPXO SURGXV úL DQDORJ SHQWUX FHOHODOWH GRX u u úL UHVSHFWLY u u $YHPGHUH]ROYDWSUREOHPDGHSURJUDPDUHOLQLDU

[ [ [ d ® ¯[ [ [ d

[ t [ t [ t >PD[@ I [ [ [

7DEHOXOVLPSOH[HVWHGXS FHDGXFHPSURJUDPXOODIRUPDVWDQGDUG

FM

;%

D

D

D

D

D

D

D IM

FM I M

D

D

D

D

D

&% % ; %

D

D

D

IM

D D D

&% %

FM

&% % ; % D D

IM

FM I M

FM

FM I M 3HQWUX [

[

[

D

RE LQHP I RSW

9DULDELOHOH GH

FRPSHQVDUH LQWURGXVH [ úL [ VXQW HJDOH FX ]HUR FHHD FH FRQILUP IDSWXO F PDWHULDSULP GLVSRQLELO VHFRQVXP LQWHJUDO 'DF QHDUILLQWHUHVDWXQSODQGHSURGXF LHFXFRVWWRWDOGHSURGXF LHPLQLP DYHPGHUH]ROYDWSUREOHPDGHSURJUDPDUHOLQLDU >PLQ @ I [ [ [ vQFRQGL LLOH

3HQWUXXQSODQGHSURGXF LHFXXQEHQHILFLXWRWDOPD[LPvQDFHOHDúLFRQGL LL VHYDUH]ROYDSUREOHPDGHSURJUDPDUHOLQLDU >PD[@ I [ [ [ FXUHVWULF LLOH E LQkQGVHDPDGHFDQWLWDWHDGHPDWHULLSULPHFRQVXPDW

J

vQVHDPQ F QXVDFRQVXPDW

[ [ [

J

J

'HFLDYHPGHUH]ROYDWSUREOHPDGHSURJUDPDUHOLQLDU >PD[@J [ [ [ VDX >PLQ @J [ [ [ FXDFHOHDúLUHVWULF LL F 'DF ILUPD SO WHúWH vQDLQWH GH D GHPDUD SURGXF LD SHQDOLW LOH SHQWUX PDWHULD SULP GH FDUH GLVSXQH vQ YDORDUH GH u u GXS UHDOL]DUHD SODQXOXL ILUPHL L VH UHVWLWXLH SHQDOLW LOH SHQWUX PDWHULLOH SULPH FRQVXPDWH3HQDOLW LOHSHQWUXPDWHULDSULP FRQVXPDW SHQWUXSURGXVXO 3 VXQW u u DQDORJ SHQWUX FHOHODOWH GRX u u u u )LUPDDUHGHFLGHSULPLW RYDORDUHGH [ [ [ $YHPGHGHWHUPLQDW

>PD[@ I

[ [ [

FXUHVWULF LLOH G 6HYDUH]ROYDSURJUDPXOOLQLDU

>PD[@ I [ [ [

FXUHVWULF LLOH

[ [ [ d ® ¯ [ [ [ t [L t L

,9

([HPSOXO 2 SUREOHP GH LQYHVWL LH 2 vQWUHSULQGHUH GLVSXQH GH XQLW LE QHúWLGLQFDUHWUHEXLHV LQYHVWHDVF RSDUWHvQDFWLYLW LOH $ $ $ vQ WUHLHWDSHÌQSULPDHWDS vúLSURSXQHV LQYHVWHDVF vQDFWLYLW LOH $ $ QXPDL PXOWGH XEÌQHWDSDDDLQYHVWHúWHPD[LP XEvQ $ úL $ ÌQXOWLPDHWDS LQYHVWHúWHFHOSX LQ XEvQFHOHWUHLDFWLYLW L%HQHILFLLOHRE LQXWHSULQLQYHVWL LL VXQW vQ $ GH vQ $ GH vQ $ GH &kWWUHEXLHV LQYHVWHDVF vQ WRWDOvQILHFDUHDFWLYLWDWHDVWIHOvQFkWEHQHILFLXOV ILHPD[LP

6ROX LH$YHPSURJUDPXOOLQLDU

[ [ d ° ® [ [ d °[ [ [ d ¯ [ [ [ t >PD[@ I [ [ [

XQGH [L HVWHVXPDLQYHVWLW vQXEvQDFWLYLWDWHD $L 'LQXOWLPDSDUWHDWDEORXOXLVLPSOH[ FM

& % % ; % D D D D D D D IM FM I M

UH]XOW I RSW

SHQWUX [

[

D

D

[

6XPDU PDV QHLQYHVWLW HVWH

GH XE 3UREOHPHGHWUDQVSRUW 3UREOHPHOH GH WUDQVSRUW VXQW R IRUP SDUWLFXODU D SUREOHPHORU GH SURJUDPDUH OLQLDU SHQWUX FDUH PHWRGD VLPSOH[ SRDWH IL DGDSWDW FRQGL LLORU SDUWLFXODUH DYkQG FD UH]XOWDW XQ SURFHGHX GH UH]ROYDUH vQ SULQFLSLX LGHQWLF FHOXL XWLOL]DW vQ FD]XO JHQHUDO 3ULPHOH UH]XOWDWH DX IRVW RE LQXWH GH +LWFKFRFN .DQWRURYLFLúL.RRSPDQVúLXOWHULRUGH'DQW]LJÌQSUDFWLF RDVHPHQHDSUREOHP SRDWH IL vQWkOQLW GH H[HPSOX VXE IRUPD XUP WRDUH XQ DQXPLW SURGXV VH DIO vQ FDQWLW LOH D D D P vQ SXQFWHOH $ $ $P QXPLWH úL VXUVH (O WUHEXLH WUDQVSRUWDW vQ SXQFWHOH % % %Q QXPLWH GHVWLQD LL vQ FDQWLW LOH E E EQ XUP ULQG PLQLPL]DUHD FKHOWXLHOLORU GH WUDQVSRUW FXQRVFkQG SUH XULOH XQLWDUH GH WUDQVSRUW FLM GHODVXUVD L F WUHGHVWLQD LD M

)RUPXODUHDPDWHPDWLF DSUREOHPHLHVWH Q

¦[ M

LM

d DL L P

LM

t E M M

P

¦[ L

Q

[LM t L P M P

Q

Q

>PLQ @ I ¦¦ FLM [LM L M

DL t L P E M t M Q FLM t L Q M P

Q

L

M

P

¦ DL t ¦ E M XQGHDPQRWDWSULQ [LM FDQWLW LOHWUDQVSRUWDWHGHODVXUVD L F WUHGHVWLQD LD M 5HOD LLOH VXQWLPSXVHGHIDSWXOF WRWDOXOWUDQVSRUWDWGHODILHFDUHVXUV V QX GHS úHDVF FDQWLWDWHDH[LVWHQW FRQGL LLOH LPSXQVDWLVIDFHUHDFHUHULLLDU DSDU QDWXUDOHvQFRQWH[WXOFRQFUHWDOSUREOHPHL 3ULQ WUDQVIRUP UL HOHPHQWDUH DFHVW WLS GH SUREOHP SRDWH IL DGXV OD IRUPD HFKLOLEUDW Q

¦[ M

LM

DL L P

LM

E M M

P

¦[ L

Q

[LM t L P M P

Q

Q

>PLQ @ I ¦¦ FLM [LM L M

DL t L P E M t M Q FLM t L Q M P

¦ D ¦E L

P

Q

L

M

M

XOWLPD HJDOLWDWH ¶ VH SRDWH UHDOL]D SULQ LQWURGXFHUHD XQHL GHVWLQD LL ILFWLYH F UHLDV LILHGHVWLQDWVXUSOXVXOGHSURGXVH[LVWHQWSHDQVDPEOXOVXUVHORU 'DWHOHSUREOHPHLVHSUH]LQW VXEIRUPDXQXLWDEHO % % ! % M ! %Q 'LVSRQLELO

$

F

F ! F M !

FQ

D

$

F F ! F M !

FQ

D

# $L

# FL

% !

# FLQ

# DL

# $P

# # % # % F P F P ! F PM !

# F PQ

# DP

EQ

E

1HFHVDU

# % FL !

# FLM

EM

!

E

!

3URSR]L LD 2ULFH SUREOHP GH WUDQVSRUW DUH WRWGHDXQD R VROX LH UHDOL]DELO GHIRUPD [LM 'HPRQVWUD LH [LM Q

¦ [LM M

P

¦ [LM L

DL E M

V DL E M V Q

¦ M

P

¦ L

V

P

¦ DL L

Q

¦E M

M

VDWLVIDFUHVWULF LLOH úL

DL E M V DL E M

DL V EM

V

V

Q

¦E M

M

DL L P

L

E M M

P

¦D L

Q

úLFRQGL LLOHGHQHQHJDWLYLWDWH ÌQ JHQHUDO DFHDVW VROX LH QX HVWH RSWLP GDU LQkQG VHDPD GH IDSWXO F XQ SURJUDP OLQLDU VDX QX DUH VROX LL SRVLELOH VDX DGPLWH VROX LL SRVLELOH FX RSWLP LQILQLWVDXDUHVROX LHRSWLP ILQLW úL LQkQGVHDPDGHSURSR]L LDDQWHULRDU UH]XOW F RULFHSUREOHP GHWUDQVSRUWDGPLWHRVROX LHRSWLP ILQLW GHRDUHFH [LM d PLQ DL E M

úLGHFLVLWXD LDRSWLPXOXLLQILQLWVHH[FOXGH 3URSR]L LD 5DQJXO PDWULFLL $ D FRHILFLHQ LORU UHVWULF LLORU OLQLDUH ¶ ¶ HVWH P Q 5H]XOW F R VROX LH UHDOL]DELO GH ED] vQWURSUREOHP GHWUDQVSRUWDUHFHO PXOW P Q FRPSRQHQWH QHQXOH HD HVWH QHGHJHQHUDW GDF DUH H[DFW P Q FRPSRQHQWH QHQXOH úL GHJHQHUDW GDF DUH PDL SX LQ GH P Q FRPSRQHQWHQHQXOH

)RUPDPDWULFHDO DSUREOHPHLGHWUDQVSRUW 7 HVWH

$;

7

G

; t >PLQ @ I XQGH $ HVWHPDWULFHDGHRUGLQ P Q u PQ

$

&;

!

# (Q

# (Q

! % # ! ! (Q

XQGH HVWHYHFWRUXOOLQLH FX Q FRPSRQHQWH YHFWRUXOQXO FX Q FRPSRQHQWH ( Q PDWULFHD XQLWDWH GH RUGLQ Q G YHFWRUXO FRORDQ GH FRPSRQHQWH D D D P E E EQ ; YHFWRUXO FRORDQ GH FRPSRQHQWH

[ [ [Q [ P [ P [ PQ 3HQWUX UH]ROYDUHD SUREOHPHORU GH WUDQVSRUW FD úL vQ FD]XO SUREOHPHORU JHQHUDOHGHSURJUDPDUHOLQLDU DOJRULWPXOGHUH]ROYDUHDUHGRX HWDSH D DIODUHDXQHLVROX LLLQL LDOHUHDOL]DELOHGHED] E vPEXQ W LUHDVROX LHLLQL LDOHSkQ ODRE LQHUHDVROX LHLRSWLPH 9RP GD vQ FRQWLQXDUH GRX SURFHGHH GH RE LQHUH D XQHL VROX LL LQL LDOH UHDOL]DELOHGHED] 0HWRGDGLDJRQDOHLPHWRGDFRO XOXLQRUGYHVW &DQWLW LOH GLVSRQLELOH D D P úL FHUHULOH FRUHVSXQ] WRDUH E EQ VH GLVSXQ SH ODWXULOH XQXL WDEHO LDU FHOXOHOH GLQ LQWHULRUXO WDEHOXOXL VH UH]HUY SHQWUX QHFXQRVFXWHOH [LM L P M Q FDUHWUHEXLHGHWHUPLQDWH

D D # DL

# DP

E

E

!

EM

!

EQ

V

&RPSRQHQWHOHED]LFH [LM DOHVROX LHLVHGHWHUPLQ SHUkQGvQFHSkQGFX [ úLDQXPH 6HDOHJH [

PLQ D E úLYRUILFRQVLGHUDWHQHED]LFHGHFLYRUILHJDOLFX ]HUR WRDWH YDULDELOHOH GH SH DFHLDúL OLQLH VDX FRORDQ FX [ FRQIRUP

XUP WRDUHORUVLWXD LL D GDF D E DWXQFL [

D úL [ M

M

Q

E GDF D ! E DWXQFL [

E úL [L L P F GDF D E DWXQFL [ D E úL OD DOHJHUH [ VDX [ WRDWH FHOHODOWH FRPSRQHQWH GH SH OLQLD úL FRORDQD ILLQG FRQVLGHUDWH QHED]LFH Dc

GHFLQXOH &RQFRPLWHQW VH PRGLILF úL YDORULOH OXL D VDX E vQORFXLQGXVH FX

D [ úL Ec

E [

ÌQSDVXOXUP WRUSURFHGHXOVHUHSHW SHQWUXFHOXOHOHU PDVHQHFRPSOHWDWHúL VHWHUPLQ GXS P Q SDúLvQILHFDUHSDVFRPSOHWkQGROLQLHVLWXD LDD VDXR FRORDQ VLWXD LDE VDXROLQLHúLRFRORDQ VLWXD LDF 'H UHJXO FRPSRQHQWHOH ED]LFH QX VH WUHF vQ WDEHO FL VH KDúXUHD] F VX D UHVSHFWLY ([HPSOX D D D E E E

E

D D D 3DVXO,

3DVXO,,

[

E

E

E

E

V

PLQ D E E

DP KDúXUDW FHOXOHOH FRUHVSXQ] WRDUH YDULDELOHORU QHED]LFH SHQWUX [ [ 6H UHFDOFXOHD] D FDUH GHYLQH Dc [ PLQ Dc E Dc úL KDúXU P FHOXOHOH FRUHVSXQ] WRDUH YDULDELOHORU QHED]LFH SHQWUX [ [ 6H UHFDOFXOHD] E FDUH GHYLQH Ec

3DVXO,,, 3DVXO,9

[ PLQ D Ec Ec úL KDúXU P FHOXOD FRUHVSXQ] WRDUH OXL [ FDUHHQXO5HFDOFXO P D FDUHGHYLQH D c [ PLQ D c E D c KDúXU P FHOXOD OXL [ FDUH H QXO úL UHFDOFXO P E Ec [ PLQ D Ec Ec úLHVWHHYLGHQWF [

3DVXO9 LQkQGVHDPDGHFRVWXULOHWUHFXWHvQFRO XULOHGHVXVDOHFHOXOHORUDYHPSHQWUX I YDORDUHD I $P RE LQXW R VROX LH GH ED] QHGHJHQHUDW [

[

[

[

[

[

[

[ [ [

[

[

0HWRGDFRVWXULORUPLQLPH 3HQWUX GHWHUPLQDUHD VROX LHL GH ED] VH LDX vQ FRQVLGHUDUH FRVWXULOH FDUH QH LQGLF RUGLQHDGHDOHJHUHDFRPSRQHQWHORUvQILHFDUHSDV ÌQSULPXOSDVVHGHWHUPLQ FRPSRQHQWD [ NK SHQWUXFDUH F NK PLQ FLM úLVHLD

PLQ D N EK FX FHOH WUHL DOWHUQDWLYH FD OD PHWRGD GLDJRQDOHL 6H UHSHW

[ NK

SURFHGHXOXUP ULQGFRVWXULOHPLQLPHSHQWUXFHOXOHOHQHFRPSOHWDWH ([HPSOX5HOX PGDWHOHGLQH[HPSOXO 3DVXO, 3H SULPD OLQLH D WDEORXOXL FHO PDL PLF FRVW HVWH F

GHFL OX P

PLQ D E E VH KDúXUHD] UHVWXO GH FHOXOH GLQ FRORDQDOXL E úLVHUHFDOFXOHD] D FDUHGHYLQH Dc [

E

D D D 3DVXO,,

E E

F XW P PLQ FLM

F

[

E

PLQ D E D

FHOXOHOHOLQLHLGRL5HFDOFXO P E FDUHGHYLQH Ec 3DVXO,,,

PLQ FLM

F GHFL [

OXL E úLDYHP Dcc

PLQ Dc E E

úL KDúXU P

+DúXU P FRORDQD

Dc

3DVXO,9

[

PLQ FLM

F F

F [

PLQ Dc Ec Ec úL Ec GHYLQH

Ecc Ec (VWHHYLGHQWDFXPF [ úL [ $YHP I SHQWUX [ [ [ [ [ [ [ [ [ [ [

0HWRGD FRVWXULOH PLQLPH G vQ JHQHUDO R VROX LH LQL LDO GH ED] PDL EXQ GHFkWPHWRGDGLDJRQDOHLUHDOL]kQGRYDORDUHDFKHOWXLHOLORUGHWUDQVSRUWPDLPLF $FHVW OXFUX HVWH XWLO GHRDUHFH QXP UXO LWHUD LLORU QHFHVDUH SHQWUX DWLQJHUHD RSWLPXOXLYDILPDLPLF 3HQWUXGHWHUPLQDUHDVROX LHLRSWLPHDXQHLSUREOHPHGHWUDQVSRUWVHXWLOL]HD] DOJRULWPXO ED]DW SH DGRSWDUHD PHWRGHL VLPSOH[ OD FRQGL LLOH SDUWLFXODUH DOH SUREOHPHLGHWUDQVSRUW 'HWHUPLQDUHDVROX LHLRSWLPH )LHF UHL YDULDELOH [ NO vL FRUHVSXQGH vQ $ XQ YHFWRU FRORDQ

P Q GLPHQVLRQDO D NO

'DF GLVSXQHPGHRED] % IRUPDW GLQ Q P YHFWRULYHFWRULL D NO VXQW OLQLDULQGHSHQGHQ L2ULFHYHFWRUQHED]LFVHVFULHvQDFHDVW ED] DLM [ NOLM D NO D %

¦ LM

LM NO

FX [ HJDOLFX VDX 3UREOHPD GH WUDQVSRUW HVWH XQ SURJUDP OLQLDU GH PLQLP GHFL R VROX LH HVWH RSWLP GDF WR L FLM ] LM t DGLF

FLM F % ] LM t L P M

Q

DYkQG DLFL VXPD DOJHEULF D FRVWXOXL FLM FX R SDUWH GLQ FRVWXULOH DVRFLDWH FRPSRQHQWHORUED]LFHDOHVROX LHL'DF FRQGL LLOH QXVXQWvQGHSOLQLWHVROX LD SRDWH IL vPEXQ W LW SULQ PRGLILFDUHD ED]HL LQWURGXFkQG XQ YHFWRU QHED]LF D LM úL DQXPHSHDFHODSHQWUXFDUHGLIHUHQ D FLM ] LM HVWHPLQLP $FHDVW PRGLILFDUHVH IDFH DWULEXLQG FRPSRQHQWHL QRL R YDORDUH QHQXO T D F UHL P ULPH VH YD GHWHUPLQD SURYRFkQG XQ WUDQVSRUW DO OXL T vQ FLFOXO FRPSRQHQWHORU [ NO FRUHVSXQ] WRDUH FRHILFLHQ LORU QHQXOL GLQ VF ]kQG úL DGXQkQG VXFFHVLY DFHDVW YDORDUH GLQ FRPSRQHQWHOH ED]LFH DúD IHO vQFkW VXPD WRWDO V U PkQ LQYDULDQW QRXD VROX LH U PkQkQGRVROX LHSRVLELO FXFRPSRQHQWH t 3URFHGHXOVHUHSHW SkQ ODYHULILFDUHDWHVWXOXLGHRSWLPDOLWDWH 0HFDQLVPXOGHFDOFXOvOYRPH[SOLFLWDSHH[HPSOXOXUP WRU 5HOX P H[HPSOXO DYkQG FRVWXULOH vQVFULVH vQ FRO XO GLQ GUHDSWD DO ILHF UHLF VX HúL LQHPVHDPDGHIDSWXOF SULQPHWRGDGLDJRQDOHLDPGHWHUPLQDW

SHQWUX IXQF LD RELHFWLY YDORDUHD I GHFL SRUQLP FX VROX LD GH ED] GHWHUPLQDW OD 3HQWUXYHULILFDUHDRSWLPDOLW LLVROX LHLDVRFLHPILHF UHLFHOXOHOLEHUHXQFLFOX FDUH vQFHSH úL VH WHUPLQ vQ FHOXOD UHVSHFWLY úL DOH F UHL QRGXUL VXQW vQ PRG REOLJDWRULX FHOXOH FRUHVSXQ] WRDUH FRPSRQHQWHORU ED]LFH 9RP DOF WXL XQ WDEORX DMXW WRUvQFDUHYRPWUHFHvQFHOXOHOHFRUHVSXQ] WRDUHOXL [LM YDORULOH G LM FLM [LM HJDOH FX VXPD FRVWXULORU FX VHPQ DOWHUQDW FDUH DSDU vQ FLFOXO L M vQFHSkQG FX

FLM $YHP

G úLDQDORJ G

G F F F F F F F F F F G F F F F G G G

&HDPDLPLF GLIHUHQ QHJDWLY HVWH G

GHFLYRPLQWURGXFHvQED]

YHFWRUXO D

ÌQFLFOXOFRUHVSXQ] WRUFHOXOHL SXQHPvQFHOXOD YDORDUHD T LDUOD FHOHODOWH FRPSRQHQWH ED]LFH DG XJ P úL VF GHP T SkQ OD HFKLOLEUDUHD VXPHL WRWDOHúLDQXPH

T m T p n T o T

&HDPDLPDUHYDORDUHDOXL T DúDvQFkWWRDWHFHOHODOWHYDORULV ILHQHQHJDWLYH HVWH T 'HFLWDEORXOSUREOHPHLYDIL 1RXDVROX LHDSUREOHPHLGHWUDQVSRUWHVWH I 6ROX LDQXHVWHRSWLP GHRDUHFHDSOLFkQGWHVWXOGHRSWLPDOLWDWHDYHP G G G G G G $YHP G GHFL

VROX LD QX HVWH RSWLP 5HSHWkQG UD LRQDPHQWXO GDF SXQHP T vQ F VX D DYHPFLFOXO

T o T n p T m T

FX T

6ROX LDSUREOHPHLYDIL

FX I

7HVWXOGHRSWLPDOLWDWHQHG 7RDWH YDORULOH G LM t GHFL UHOD LD I HVWH RSWLP SHQWUX [

[

[

[

[

[

WRDWHFHOHODOWHYDORULILLQGQXOH

(/(0(17('($1$/,= 0$7(0$7,& )XQF LLYHFWRULDOH 6H VSXQH F I HVWH R IXQF LH YHFWRULDO GH YDULDELO YHFWRULDO GDF

I ( o \ P XQGH ( \ Q úL I RIXQF LHRDUHFDUH 'DW IXQF LDYHFWRULDO I ( o \ P VHYRUFRQVLGHUDXUP WRDUHOHIXQF LLUHDOH IL ( o \ L P XQGH I L [

\ L LDU I [

\ \P \ P

I I P

6HDGRSW QRWD LD I

)XQF LLOH I I P VHQXPHVFFRPSRQHQWHOHUHDOHDOHOXL I ÌQPRGFDQRQLF VHLQWURGXFRSHUD LLOHFXIXQF LLYHFWRULDOH I J [ I [ J [ [ (

IJ [ OI [

I [ J [ [( OI [ [ ( O \ P 0XO LPHDIXQF LLORUYHFWRULDOH I ( o \ IRUPHD] XQVSD LXYHFWRULDO

'H DVHPHQHD VH LQWURGXFH SURGXVXO VFDODU úL QRUPD SHQWUX DFHVWH IXQF LL YHFWRULDOH I J [ I [ J [ [(

I [

'DF I

I [

[(

I I P úL J J J P DWXQFL IJ

[

DGLF

IJ

I [ J [ P

¦IJ L

'HDVHPHQHD

I

I I

L

L

P

¦ I [ J [ L

L

L

SURGXVXOVFDODU P

¦I L

L

QRUPD

)LHPXO LPLOH ( \ Q ) \ P úLIXQF LLOH I ( o ) J ) o \ S 6H

J D I ( o \ S [( J I [

FRQVLGHU IXQF LDFRPSXV K

K [

7HRUHPD ÌQ FRQGL LLOH GH PDL VXV GDF

J

J J úL K K K DWXQFL

S

úL

K [

S

J I [ « K S [

K[ [ Q

I

I I P

J S I [

J I [ [ Q I P [ [ Q

'HILQL LH )XQF LD I ( o \ P HVWH P UJLQLW GDF PXO LPHD I ( HVWH P UJLQLW 7HRUHPD )XQF LD I ( o \ P HVWH P UJLQLW GDF úL QXPDL GDF

H[LVW XQQXP U 0 t DVWIHOvQFkW I [ d 0 SHQWUXRULFH [ ( 7HRUHPD)XQF LD I

I I P HVWHP

UJLQLW GDF úLQXPDLGDF

IXQF LLOH I I P VXQWP UJLQLWH 'HILQL LDOLPLWHLXQHLIXQF LLUHDOHVHH[WLQGHúLSHQWUXIXQF LLYHFWRULDOH )LH PXO LPHD ( \ Q [ XQ SXQFW GH DFXPXODUH SHQWUX ( úL IXQF LD YHFWRULDO I ( o \ P 'HILQL LH 8Q YHFWRU O \ P HVWH OLPLWD IXQF LHL I vQ SXQFWXO [ GDF SHQWUXRULFHYHFLQ WDWH 8 DOXL O vQ \ P H[LVW RYHFLQ WDWH 9 DOXL [ vQ \ Q

DVWIHOvQFkWRULFDUHDUIL [ 9 ( [ z [ DWXQFL I [ 8 6HVFULH [o [ O OLP I [ VDX I [ o O FkQG [ o [ VDX I [ o O [ o [

3URSR]L LLOHXUP WRDUHGDXGHILQL LLHFKLYDOHQWHDOHOLPLWHL'HPRQVWUD LDORU VHIDFHODIHOFDúLvQFD]XOIXQF LLORUUHDOHGHRVLQJXU YDULDELO 3URSR]L LD OLP I [ O GDF úL QXPDL GDF SHQWUX RULFH úLU [ o [

[ N o [ [ N ( [ N z [ DWXQFL I [ N o O 3URSR]L LD OLP I [ O GDF úL QXPDL GDF SHQWUX RULFH QXP U [ o [

H ! H[LVW XQ QXP U GH ! DVWIHO vQFkW RULFDUH DU IL [ z [ GLQ ( FX

[ [ GH DWXQFL I [ O H 3URSR]L LD OLP I [ [ o [

O GDF úL QXPDL GDF SHQWUX RULFH QXP U

H ! H[LVW R YHFLQ WDWH 9 D OXL [ 9 GHSLQGH GH H DVWIHO vQFkW FRQGL LLOH

[ 9 ( úL [ z [ LPSOLF I [ O H

3URSR]L LD OLP I [

O GDF úLQXPDLGDF SHQWUXRULFHYHFLQ WDWH

[ o [

8 DOXL O H[LVW XQQXP U G ! G GHSLQGH 8 DVWIHOvQFkWFRQGL LLOH [ ( [ z [ úL [ [ G LPSOLF I [ 8 'DF [ S

[

S

[ S [ QS úL D

D D D Q FRQGL LD

[S o D S

[ S FRQYHUJH SXQFWXDO HVWH HFKLYDOHQW FX [ S o D [ S o D « S S

[ QS o D Q S

'HDFHHDvQORFGH OLP I [ OLPLWDVHPDLQRWHD] úLDVWIHO [o D

OLP I [ [ Q

[ o D #

[Q o D Q

$VWIHO SHQWUX R IXQF LH GH GRX YDULDELOH I [ \ OLPLWD VD vQ SXQFWXO

[ \ VHVFULH

OLP I [ \

[ o [

\ o \

6HVSXQHF DFHDVWDHVWHOLPLWDIXQF LHL I FkQG [ úL \ WLQGLQGHSHQGHQWGDU VLPXOWDQ F WUH [ úLUHVSHFWLY \ ÌQDFHVWFD]SURSR]L LDVHSRDWHWUDQVFULH DVWIHO OLP I [ \ O GDF úLQXPDLGDF SHQWUXRULFH H H[LVW XQQXP U [ o [ \ o \

GH ! DVWIHO vQFkW RULFDUH DU IL [ [ GH úL \ \ GH DWXQFL

[ \ z [ \ I [ \ O H

GLQ ( FX

6HGHILQHúWHOLPLWDIXQF LHL I ( \ Q o \ P UHODWLYODRPXO LPH $ ( vQWUXQ SXQFW GH DFXPXODUH D OXL $ OD IHO FD úL SHQWUX IXQF LL UHDOH GH R VLQJXU YDULDELO 8QYHFWRU O \ P HVWHOLPLWDIXQF LHL I vQSXQFWXO D UHODWLYODVXEPXO LPHD

$ GDF SHQWUX RULFH úLU [ S o D [ S $ [ S z D DYHP I [ S o O 6H

QRWHD]

O

OLP I [ [oD [ $

'DF OLP I [ H[LVW DWXQFL úL OLP I [ H[LVW úL FHOH GRX OLPLWH VXQW [oD [$

[o D

HJDOH'DF vQV H[LVW OLP I [ QXUH]XOW QHDS UDWF H[LVW OLP I [ [oD [$

[o D

ÌQSDUWLFXODUGDF $ HVWHLQWHUVHF LDPXO LPLL ( FXRGUHDSW FDUHWUHFHSULQ D DWXQFL OLP I [ VHQXPHúWHOLPLWDIXQF LHL I GXS RGLUHF LH [oD [$

'H H[HPSOX vQ FD]XO XQHL IXQF LL I [ \ GH GRX YDULDELOH UHDOH GDF

K [ OLPLWDVHVFULH

HFXD LDGUHSWHLHVWH \

I [ \ 6H]LFHF DFHDVWD

OLP

[ o [

\ o \ \ K [

HVWH OLPLWD IXQF LHL I FkQG [ úL \ WLQG VLPXOWDQ GDU GHSHQGHQW SH GUHDSWD

K [ UHVSHFWLYF WUH [ úL \ ÌQIDSWDFHDVWDHVWHROLPLW DIXQF LHLFRPSXVH GHRVLQJXU YDULDELO I [ K [ OLP I [ \ OLP I [ K [ \

[ o [ \ o \

[ o [

7RDWH SURSULHW LOH OLPLWHORU GH IXQF LL UHDOH FDUH QX LPSOLF UHOD LD GH RUGLQH úL SURGXVXO VH S VWUHD] úL SHQWUX IXQF LLOH YHFWRULDOH úL GHPRQVWUD LLOH VXQWDFHOHDúL /LPLWDXQHLIXQF LLYHFWRULDOHvQWUXQSXQFWGDF H[LVW HVWHXQLF 'DF OLP I [ O DWXQFL OLP I [ O [ o [

OLP I [ [ o [

[ o [

O GDF úL QXPDL GDF OLP I [ O DGLF GDF úL QXPDL

GDF OLP I [ O [ o [

[ o [

'DF OLP I [ z DWXQFL H[LVW R YHFLQ WDWH 9 D OXL [ DVWIHO vQFkW [ o [

I [ z RULFDUHDUIL [ z [ GLQ 9 ( )XQF LD I DUHOLPLWDvQ [ H GDF H[LVW RYHFLQ WDWH 9 DOXL [ DVWIHO vQFkW RULFDUH DU IL [ c [ cc 9 ( [ c z [ [ cc z [ DWXQFL I [ c I [ cc H

&ULWHULX)LH I ( o \ P úL K ( o \ GDF OLP K [ [ o [

úLGDF H[LVW XQ

YHFWRU O \ P úL R YHFLQ WDWH 9 D OXL [ DVWIHO vQFkW I [ O d K [ SHQWUXRULFH [ z [ GLQ 9 ( DWXQFL OLP I [ [ o [

O

'DF I ( o \ P úL J ( o \ P DX OLPLWH vQ [ DWXQFL IXQF LLOH

I J IJ ( o \ P DXOLPLW vQ [ úL OLP > I [ J [ @

[ o [

OLP I [ OLP J [

[ o [

[ o [

OLP > I [ J [ @ §¨ OLP I [ ·¸§¨ OLP J [ ·¸ [ o [ © [ o [ ¹© [o [ ¹

'DF

I ( o \ P úL M ( o \ DX OLPLW vQ [ DWXQFL IXQF LD

M I ( o \ P DUHOLPLW vQ [ úL OLP M [ I [ §¨ OLP M [ ·¸§¨ OLP I [ ·¸ © [ o [ ¹© [ o [ ¹ ÌQSDUWLFXODUSHQWUX M [ D VHGHGXFH OLP DI [ D OLP I [ [ o [

[ o [

[ o [

3URSR]L LD )LH IXQF LD I ( \ Q o \ P úL I I I P ( o \

I I I P $WXQFL [OLP I [ o[

FRPSRQHQWHOHVDOHUHDOH I GDF OLP I L [ [ o [

OL L P XQGH O

O GDF úLQXPDL

O O O P 5 P

/LPLWHLWHUDWH )LH I [ [ [ Q RIXQF LHYHFWRULDO GH Q YDULDELOH I ( \ Q o \ Q 'LQ DFHDVW IXQF LH VH SRDWH RE LQH IXQF LD YHFWRULDO GH R VLQJXU YDULDELO úL DQXPHIXQF LLOHVDOHSDU LDOH

I [ o I [ [ [ Q

I [ o I [ [ [ Q # I Q [ Q o I [ [ [ Q

6HSRWFRQVLGHUDDWXQFLOLPLWHOHDFHVWRUIXQF LLGHRVLQJXU YDULDELO OLP I L [L OLP I [ [ [ Q [L o DL

[L o DL

GDF DL HVWH SXQFW GH DFXPXODUH DO PXO LPLL (L

[L [L \ [ [ [Q (

/LPLWDIXQF LHL I L HVWHXQQXP UFDUHGHSLQGHGHFHOHODOWH Q YDULDELOHUHDOHGLIHULWHGH

[L 6HSRWFRQVLGHUDDSRL

OLP OLP I [ [ Q L z M

[ M o D M [L o DL

$FHDVW OLPLW HVWH XQ QXP U FDUH GHSLQGH GH FHOHODOWH Q YDULDELOH GLIHULWHGH [L úL [ M 6HSRDWHFRQVLGHUDOLPLWDLWHUDW DDFHVWHLIXQF LLvQUDSRUWFX WRDWHYDULDELOHOHSHUkQG$FHDVW OLPLW HVWHXQQXP UFDUHQXPDLGHSLQGHGHQLFL XQDGLQYDULDELOH$FHDVWDVHQXPHúWHOLPLWDLWHUDW DIXQF LHL I

'H H[HPSOX SHQWUX IXQF LLOH GH GRX YDULDELOH I [ \ VH SRW FRQVLGHUD

OLPLWH LWHUDWH OLP OLP I [ \ úL OLP OLP I [ \ 6H VSXQH F DFHVWHD VXQW [ o [ \ o \

\ o \ [ o [

OLPLWHOH IXQF LHL I [ \ FkQG [ úL \ WLQG VXFFHVLY UHVSHFWLY F WUH [ úL \ /HJ WXUDGLQWUHOLPLWHúLOLPLWHOHLWHUDWHHVWHGDW GH 3URSR]L LD'DF H[LVW OLPLWDIXQF LHLvQWUXQSXQFWúLXQDGLQOLPLWHOH LWHUDWHvQDFHVWSXQFWDWXQFLDFHVWHOLPLWHVXQWHJDOH &RQWLQXLWDWHDIXQF LLORUYHFWRULDOH 'HILQL LD FRQWLQXLW LL IXQF LLORU UHDOH GH R VLQJXU YDULDELO VH H[WLQGH úL SHQWUXIXQF LLYHFWRULDOH 'HILQL LH )LH IXQF LD I ( \ Q o \ P úL XQ SXQFW [ ( )XQF LD I HVWH FRQWLQX vQ [ GDF SHQWUX RULFH YHFLQ WDWH 8 D OXL I [ H[LVW R

YHFLQ WDWH 9 DOXL [ DVWIHOvQFkWRULFDUHDUIL [ 9 ( DWXQFL I [ 8 8UP WRDUHOHSURSR]L LLGDXGHILQL LLHFKLYDOHQWHDOHFRQWLQXLW LL 3URSR]L LD)XQF LD I HVWHFRQWLQX vQSXQFWXO [ GDF úLQXPDLGDF

o [ [ S ( DWXQFL I [ S o I [ SHQWUXRULFHúLU [ S S S

3URSR]L LD )XQF LD I HVWHFRQWLQX vQ [ GDF úLQXPDLGDF SHQWUX

RULFHQXP U H ! H[LVW XQQXP U GH ! DVWIHOvQFkWRULFDUHDUIL [ ( FX

[ [ GH DWXQFL I [ I [ H

3URSR]L LD )XQF LD I HVWHFRQWLQX vQ [ GDF úLQXPDLGDF SHQWUX RULFHQXP U H ! H[LVW RYHFLQ WDWH 9 DOXL [ 9 GHSLQGHGH H DVWIHOvQFkW RULFDUHDUIL [ ( 9 V DYHP I [ I [ H

3URSR]L LD)XQF LD I HVWHFRQWLQX vQSXQFWXO [ GDF úLQXPDLGDF

SHQWUXRULFHYHFLQ WDWH 8 DOXL I [ H[LVW XQQXP U G ! FDUHGHSLQGHGH

8 DVWIHOvQFkWRULFDUHDUIL [ ( FX [ [ G V DYHP I [ 8

3URSR]L LD)XQF LD I HVWHFRQWLQX vQSXQFWXO [ GDF úLQXPDLGDF

OLP I [ I [

[ o [

6HVSXQHF IXQF LD I HVWHFRQWLQX SHPXO LPHD ( GDF HVWHFRQWLQX vQ ILHFDUHSXQFWGLQ ( 3URSULHW LOHIXQF LLORUUHDOHFRQWLQXHFDUHQXLPSOLF UHOD LDGHRUGLQHU PkQ YDULDELOHúLSHQWUXIXQF LLOHYHFWRULDOHFRQWLQXH 'DF IXQF LD I HVWH FRQWLQX vQ SXQFWXO [ VDX SH ( DWXQFL IXQF LD

I [ HVWHFRQWLQX vQ [ UHVSHFWLYSH (

3URSR]L LD )XQF LD YHFWRULDO I ( \ Q o \ P HVWH FRQWLQX vQWUXQ SXQFW [ ( GDF úL QXPDL GDF ILHFDUH GLQ FRPSRQHQWHOH VDOH UHDOH

I I I P ( o \ VXQWFRQWLQXHvQ [ 3URSR]L LDUH]XOW GLQLQHJDOLW LOH

P

I L [ I L [ d I L [ I L [ d ¦ I L [ I L [ L

DSOLFkQGGHH[HPSOXGHILQL LDFRQWLQXLW LLFX H úL G &RQWLQXLWDWHDSDU LDO 'HILQL LH)LHIXQF LD I ( \ Q o \ Q úL D

D D D Q XQSXQFWGLQ

( 6H FRQVLGHU IXQF LD SDU LDO GH R I L [L o I D DL [L DL D Q GHILQLW

(L

^[

L

VLQJXU SH

YDULDELO PXO LPHD

[L 5 D DL [L DL D Q (` 'DF IXQF LD SDU LDO I HVWH

FRQWLQX vQ SXQFWXO DL ( VH VSXQH F IXQF LD I HVWH FRQWLQX SDU LDO vQ

D D D Q $ VSXQH F IXQF LD I [ [ Q HVWH FRQWLQX SDU LDO vQ UDSRUW FX [L vQ SXQFWXO D vQVHDPQ F SHQWUX RULFH QXP U H ! H[LVW XQ QXP U GH ! DVWIHOvQFkWRULFDUHDUIL [L (L FX [L DL GH V DYHP I L [L I L DL H UDSRUWFXYDUWLDELOD [L vQSXQFWXO D

DGLF

I D DL [L DL D Q I D DL DL DL D Q H

'DF IXQF LD I HVWHFRQWLQX vQSXQFWXO D D D D Q VHVSXQHDGHVHD F HVWHFRQWLQX vQDFHVWSXQFWvQUDSRUWFXDQVDPEOXOYDULDELOHORUSHQWUXDGHRVHEL GHFRQWLQXLWDWHDSDU LDO vQUDSRUWFXFkWHRYDULDELO 2EVHUYD LH'DF IXQF LD I HVWHFRQWLQX vQWUXQSXQFWvQUDSRUWFXILHFDUH YDULDELO vQ SDUWH QX UH]XOW F HD HVWH FRQWLQX vQ DFHVW SXQFW vQ UDSRUW FX DQVDPEOXOYDULDELOHORU

'HULYDWHSDU LDOH )LH I R IXQF LH UHDO GH GRX YDULDELOH GHILQLW SH R PXO LPH ( \ úL

[ \ XQSXQFWLQWHULRUOXL (

'HILQL LH)XQF LD I DUHvQSXQFWXO [ \ GHULYDW SDU LDO vQUDSRUWFX YDULDELOD [ GDF H[LVW úLHVWHILQLW

I [ \ I [ \ [ o [ [ [ /LPLWDVHQXPHúWHGHULYDWDSDU LDO vQUDSRUWFX [ DOXL I vQ [ \ úLVH OLP

QRWHD]

wI [ \ w[ wI [ \

I [c [ \ $VHP Q WRUVHGHILQHúWH

w\

' [ I [ \

6HVSXQHF I DUHGHULYDW SDU LDO vQUDSRUWFX [ SH ( GDF HDDUHGHULYDW

SDU LDO vQ UDSRUW FX [ vQ ILHFDUH SXQFW [ \ $ ÌQ DFHVW FD] IXQF LD

wI [ \ wI ( o \ GHILQLW GH [ \ o VHQXPHúWHGHULYDWDSDU LDO DOXL I w[ w[ wI wI SH ( $QDORJVHGHILQHúWH ( o \ 1RWD LH I [c ' [ I w\ w[ 3UDFWLFGHULYDWD I [c VHFDOFXOHD] FRQVLGHUkQGSH \ FRQVWDQWúLGHULYkQGFD R IXQF LH GH R VLQJXU YDULDELO [ 'HULYDWD SDU LDO vQ UDSRUW FX \ VH RE LQH FRQVLGHUkQGSH [ FRQVWDQWúLGHULYkQGFDSHRIXQF LHGH \ 3URSR]L LD 'DF GHULYDWD SDU LDO I [c UHVSHFWLY I \c H[LVW vQ

[ \ DWXQFL

UHVSHFWLY \

I HVWH FRQWLQX vQ [ UHVSHF\LY \ vQ UDSRUW FX [

'HPRQVWUD LH)XQF LD M [

I [ \ GHRVLQJXU YDULDELO HVWHGHULYDELO

vQ [ GHFLFRQWLQX

3URSR]L LD )LH [ \ XQ SXQFW LQWHULRU DO OXL ( 'DF GHULYDWHOH

SDU LDOH I [c úL I \c H[LVW SH R YHFLQ WDWH 9 D OXL [ \ DWXQFL SHQWUX RULFH

SXQFW [ \ 9 H[LVW XQQXP U [ FXSULQVvQWUH [ úL [ úLXQQXP U K FXSULQV vQWUH \ úL \ DVWIHOvQFkW

I [ \ I [ \

I [c [ \ [ [ I \c [ K \ \

'HPRQVWUD LH6HDOHJHXQSXQFWDUELWUDU [ \ 9 úLVHPHQ LQHIL[$WXQFL

I [ \ I [ \ I [ \ I [ \ I [ \ I [ \

6HQRWHD] MW I W \ W \ 9 úL \ W RVLQJXU YDULDELO M úL \ VXQWGHULYDELOHúL

McW

I [ W [ W 9 )XQF LLOHGH

I [c W \ \ cW

I \c [ W $SOLFkQGWHRUHPDFUHúWHULORUILQLWHSHQWUX M úL \ DWXQFL M[ M [ Mc[ [ [ [ d [ d [ \ \ \ \ \ cK \ \ \ d K d \

DGLF

I [ \ I [ \ I [ \ I [ \

$WXQFLSULQDGXQDUHDUHOD LLORU

I [ \ I [ \

I [c [ \ [ [ I \c [ K \ \

I [c [ \ [ [ I \c [ K \ \

2EVHUYD LH$FHDVW HJDOLWDWHVHQXPHúWHIRUPXODOXL/DJUDQJHSHQWUXIXQF LL GHGRX YDULDELOH 3URSR]L LD)LH [ \ XQSXQFWLQWHULRUDOOXL ( 'DF IXQF LD I DGPLWH GHULYDWH SDU LDOH P UJLQLWH vQWUR YHFLQ WDWH 9 D OXL [ \ DWXQFL HD HVWHFRQWLQX vQ [ \ vQUDSRUWFXDQVDPEOXOYDULDELOHORU

&RURODU'DF I [c úL I \c H[LVW SHRYHFLQ WDWHDOXL [ \ úLVXQW

FRQWLQXHvQ [ \ DWXQFLIXQF LD I HVWHFRQWLQX vQ [ \

'HPRQVWUD LH'DF I [c úL I \c VXQWFRQWLQXHvQ [ \ H[LVW RYHFLQ WDWH

9 DOXL [ \ SHFDUHDFHVWHIXQF LLVXQWP UJLQLWH &RURODU 'DF GHULYDWHOH SDU LDOH I [c úL I \c H[LVW SH ( úL VXQW FRQWLQXHVDXVXQWP UJLQLWHDWXQFLIXQF LD I HVWHFRQWLQX SH ( ,QWHUSUHWDUHDHFRQRPLF DGHULYDWHORUSDU LDOH 'HULYDWD SDU LDO vQ UDSRUW FX YDULDELOD [L LQGLF YDULD LD IXQF LHL I OD R YDULD LH FUHúWHUH VDX GHVFUHúWHUH IRDUWH PLF '[L D YDULDELOHL [L ÌQ FD]XO

I [ [ Q XQGH [ [ Q VXQW IDFWRULL XWLOL]D L vQ SURFHVXO GH SURGXF LH GHULYDWHOH SDU LDOH I [c P VRDU HILFLHQ D XWLOL] ULL XQHL

IXQF LLORU GH SURGXF LH \

L

XQLW L VXSOLPHQWDUH GLQ IDFWRUXO [L FkQG FHLODO L IDFWRUL U PkQ QHVFKLPED L úL VH QXPHVFUDQGDPHQWHPDUJLQDOHVDXSURGXVHPDUJLQDOH

3HQWUX PRGHODUHD PDWHPDWLF D SURFHVHORU GH SURGXF LH VH IRORVHVF GLIHULWH H[SUHVLL PDWHPDWLFH DOH IXQF LLORU GH SURGXF LH &HOH PDL GHV IRORVLWH VXQW XUP WRDUHOHIXQF LLGHSURGXF LH GHWLS&REE'RXJODV \ $. D /E

GHWLS6DWR \

GHWLS$OOHQ \

$. / $ ! D ! E ! D. E/ $ G./ D. E / $ ! D E ! úL G ! DE

GHWLS&(6 \ $ D. U E /U U XQGH . UHSUH]LQW YROXPXOFDSLWDOXOXLIL[PLOOHL / UHSUH]LQW YROXPXOIRU HL GHPXQF PLLGHSHUVRDQH $ HVWHXQVFDODUFDUHVHGHWHUPLQ H[SHULPHQWDOLDU \ HVWHYROXPXOSURGXF LHLPLOOHL D E G U VHGHWHUPLQ H[SHULPHQWDO 3URSXQHPFDH[HUFL LXFDOFXODUHDGHULYDWHORUSDU LDOHSHQWUXILHFDUHIXQF LHvQ UDSRUWFX . úL / 'LIHUHQ LDELOLWDWHDIXQF LLORUGHPDLPXOWHYDULDELOH )LH I RIXQF LHGHGRX YDULDELOHGHILQLW SHRPXO LPH ( \ úL D E XQ SXQFWLQWHULRUDOOXL ( 'HILQL LH 6HVSXQHF IXQF LD I HVWHGLIHUHQ LDELO vQSXQFWXO D E GDF H[LVW GRX QXPHUHUHDOH O úL P úLRIXQF LH Z [ \ GHILQLW SH ( FRQWLQX vQ

D E úLQXO

vQDFHVWSXQFW

OLP Z [ \ ZD E [oD \ oE

DVWIHOvQFkWvQRULFHSXQFW [ \ (

I [ \ I D E O [ D P \ E Z [ \ [ D \ E 'DF ( HVWHRPXO LPHGHVFKLV VHVSXQHF I HVWHGLIHUHQ LDELO SH ( GDF HVWH GLIHUHQ LDELO vQRULFHSXQFWGLQ (

6HYDQRWD U

U [ \

[ D \ E

GHFLHJDOLWDWHDGHPDLVXVVH

VFULH

I [ \ I D E O[ D P \ E Z[ \ U XQGH OLP U [ \ [oD \ oE

/HPD 'DF IXQF LD Z [ \ GHILQLW SH ( DUH OLPLWD vQ D E DWXQFL H[LVW GRX IXQF LL Z úL Z GHILQLWH SH ( DVWIHO vQFkW DX OLPLWD vQ

D E úL

Z[ \ U

Z [ \ [ D Z [ \ \ E [ \ ( 5HFLSURF 'DF IXQF LLOH Z úL Z GHILQLWH SH ( DX OLPLWD vQ SXQFWXO D E DWXQFL H[LVW R IXQF LH Z[ \ FX OLPLWD vQ D E FDUH V YHULILFH

HJDOLWDWHDSUHFHGHQW )RORVLQGDFHDVW OHP UH]XOW LPHGLDW 3URSR]L LD )XQF LD I HVWH GLIHUHQ LDELO vQ SXQFWXO D E GDF úL QXPDLGDF H[LVW GRX QXPHUHUHDOH O úL P úLGRX IXQF LL Z úL Z GHILQLWHSH

( FRQWLQXHvQ D E úLQXOHvQDFHVWSXQFW OLP ZL [ \ ZL D E L [oD \ oE

DVWIHOvQFkWSHQWUXRULFH [ \ (

I [ \ I D E O[ D P \ E Z [ \ [ D Z D \ \ E $FHDVW HJDOLWDWHVHPDLVFULH

>O Z [ \ @[ D >P Z [ \ @ \ E 3URSR]L LD'DF IXQF LD I HVWHGLIHUHQ LDELO vQ D E DWXQFLHDDUH GHULYDWHSDU LDOHvQ D E úL I [c D E O I \c D E P I [ \ I D E

(JDOLWDWHDGHGHILQL LHDGLIHUHQ LDELOLW LLVHVFULHDWXQFLDVWIHO

I [ \ I D E

I [c D E [ D I \c D E \ E Z [ \ U

'HPRQVWUD LH'DF vQ

I [ \ I D E O[ D P \ E Z[ \ U VHFRQVLGHU \ E DWXQFL I [ E I D E O [ D Z [ E [ D

3HQWUX [ z D VHGHGXFH

I [ E I D E [D

[D

'DU

Z [ E

OLP

I [ E I D E [D

[oD

[D

Z [ E

O Z [ E úL

[D

OLP Z [ E [oD

O DGLF I [c D E O

ÌQPRGDQDORJVHGHPRQVWUHD] I \c D E

[D

P

ZD E

GHFL

&RURODU 'DF I HVWH GLIHUHQ LDELO SH ( DWXQFL HD DUH GHULYDWH SDU LDOH I [c úL I \c SH (

3URSR]L LD'DF I HVWHGLIHUHQ LDELO vQSXQFWXO D E DWXQFLHDHVWH FRQWLQX vQDFHVWSXQFW 'HPRQVWUD LH7R LWHUPHQLLGLQGUHDSWDDLHJDOLW LL I [ \ I D E O[ D P \ E Z[ \ U

D E

vQ

OLP I [ \

I D E DGLF I HVWHFRQWLQX vQ D E

[oD \ oE

GHFL

OLP> I [ \ I D E @ GH XQGH

DX OLPLWD

[oD \ oE

&RURODU 'DF I HVWH GLIHUHQ LDELO SH ( DWXQFL HD HVWH FRQWLQX SH ( 8OWLPHOH GRX SURSR]L LL DUDW F H[LVWHQ D XQHL GHULYDWH SDU LDOH úL FRQWLQXLWDWHD XQHL IXQF LL VXQW FRQGL LL QHFHVDUH GDU QX VXILFLHQWH SHQWUX GLIHUHQ LDELOLWDWHDVD 3URSR]L LDXUP WRDUHG FRQGL LLVXILFLHQWHGHGLIHUHQ LDELOLWDWH 3URSR]L LD'DF I DUHGHULYDWHSDU LDOH I [c úL I \c vQWURYHFLQ WDWH

9 D OXL D E úL GDF DFHVWH GHULYDWH SDU LDOH VXQW FRQWLQXH vQ D E DWXQFL IXQF LD I HVWHGLIHUHQ LDELO vQ D E 5HFLSURFDSURSR]L LHLQXHVWHDGHY UDW ([HPSOX)LH

I [ \

° [ \ VLQ [ \ ® ° ¯

[ \ z

[ \ 6 DU W PF IXQF LDHVWHGLIHUHQ LDELO vQRULJLQH3HQWUX [ \ I [ \ I

[

\ VLQ

[ \

[ \ [ \ VLQ

[ \

1RWkQG

Z[ \

[ \ VLQ

[ \

[ \

DWXQFL

Z [ \ úL OLP [ \ [ o

[ \ VLQ

[ \

d [ \

GHFL OLP Z [ \ [ o \ o

\ o

$úDGDU IXQF LD I HVWH GLIHUHQ LDELO vQ RULJLQH 5H]XOW vQ SDUWLFXODU

I [c úL I \c

6 FDOFXO PGHULYDWHOHSDU LDOHvQSXQFWHOH [ \ z

I [c [ \ [ VLQ I \c [ \ \ VLQ

[ \ [ \

[

[ \ \

[ \

FRV FRV

[ \ [ \

$FHVWH GHULYDWH SDU LDOH QX DX OLPLW vQ RULJLQH úL FX DWkW PDL PXOW QX VXQW

FRQWLQXH vQ RULJLQH GHRDUHFH IXQF LLOH VLQ

[ \

úL FRV

[ \

QX DX

OLPLW vQRULJLQH )LH I R IXQF LH UHDO GHILQLW SH ( \ úL GLIHUHQ LDELO vQ D E ( &XP Z DUHOLPLWD vQ D E DYHPDSUR[LPDWLY

I [ \ I D E | I [c D E [ D I \c D E \ E

'HILQL LH)XQF LDGHGRX YDULDELOH

GI D E [ \

I [c D E [ D I \c D E \ E

VHQXPHúWHGLIHUHQ LDODOXL I vQ D E

)LH IXQF LLOH M ( o \ \ ( o \ GDWH GH M[ \ [ \ [ \ \ DWXQFL Mc[ [ \ { Mc\ [ \ { úL \ c[ [ \ { \ c\ [ \ { GHFL

GM [ \ X Y { X úL G\ [ \ X Y { Y 1RWkQG [ D X úL \ E Y YRPDYHD GI [ \ I [c [ \ G[ I \c [ \ G\

VDX

wI wI G[ G\ w[ w\ 3HQWUXRIXQF LHGH Q YDULDELOH I [ [ [ Q GLIHUHQ LDODHVWH GI

I [cG[ I \cG\

GI

Q

L

wI

¦ w[

G[L L

XQGH G[L HVWHGLIHUHQ LDODIXQF LHL M L [ [ Q

[L

'HULYDWHSDU LDOHGHRUGLQVXSHULRU )LH I RIXQF LHUHDO GHILQLW SH ( \ 6HSUHVXSXQHF IXQF LLOH I [c úL

I \c VXQWGHILQLWHSH ( úLF DXGHULYDWHSDU LDOHSH ( $WXQFLH[LVW XUP WRDUHOH GHULYDWHSDU LDOHGHRUGLQXO,,

w I w[ w I w\w[

I [cc

I [c c [

w § wI · ¨ ¸ w[ © w[ ¹

I [\cc

I [c c \

I \[cc

I \c c [

w § wI · ¨ ¸ w\ © w[ ¹ w § wI · ¨ ¸ w[ ¨© w\ ¸¹

w I w[w\

I cc

I \c c \

w § wI · ¨ ¸ w\ ¨© w\ ¸¹

w I w\

\

)XQF LLOH I [\cc úL I \[cc VHQXPHVFGHULYDWHPL[WHGHRUGLQXO,,

2IXQF LHGH Q YDULDELOH I [ [ [ Q SRDWHDYHD Q GHULYDWHSDU LDOH

GHRUGLQXOGRL I [cLc[ M L M

Q

(QXQ PXUP WRDUHOHWHRUHPH &ULWHULXO OXL 6FKZDUW] 'DF IXQF LD I DUH GHULYDWH SDU LDOH PL[WH GH

RUGLQXOGRL I [\cc úL I \[cc vQWURYHFLQ WDWH 9 DXQXLSXQFW D E ( úLGDF I [\cc úL

I \[cc VXQWFRQWLQXHvQ D E DWXQFL I [\cc D E

I \[cc D E

&ULWHULXO OXL
I [c úL I \c vQWURYHFLQ WDWH 9 DOXL D E úLGDF I [c úL I \c VXQWGLIHUHQ LDELOHvQ

D E DWXQFL GHULYDWHOH SDU LDOH PL[WH GH RUGLQXO GRL vQ I [\cc D E I \[cc D E

I [c úL I \c H[LVW úL

'HILQL LH )LH I R IXQF LH UHDO GH GRX YDULDELOH GHILQLW SH R PXO LPH ( \ úL D E XQ SXQFW LQWHULRU OXL ( 6H VSXQH F I HVWH GLIHUHQ LDELO GH Q RULvQSXQFWXO D E GDF WRDWHGHULYDWHOHGHRUGLQXO Q DOH OXL I H[LVW vQWURYHFLQ WDWH 9 DOXL D E úLVXQWGLIHUHQ LDELOHvQ D E 'LIHUHQ LDODGHRUGLQXO Q vQSXQFWXO D E VHGHILQHúWHSULQHJDOLWDWHD G

Q

I [ \ D E

Q

§w · w ¨¨ G[ G\ ¸¸ I D E w\ ¹ © w[

XQGHH[SRQHQWXO Q LQGLF GH]YROWDUHDVXPHLGLQSDUDQWH] GXS UHJXODELQRPXOXLOXL 1HZWRQúLDSRLVHvQPXO HúWHIRUPDOFX I D E 'LIHUHQ LDODGHRUGLQXO Q SHQWUXRIXQF LHGH P YDULDELOHYDIL

G

Q

I [ [ P

Q

I [c G[ I [cP G[ P

· § P w ¨¨ ¦ G[ N ¸¸ I ¹ © N w[ N

Q

([HPSOH 6 VH FDOFXOH]H GLIHUHQ LDOD GH RUGLQXO Q SHQWUX I [ \

\

6ROX LH I [c

I \cc

D H D[ E\ « I Q [ Q

DH D[ E\ I [cc

E H D[ E\ « I Q \ Q

6

VH

¦&

I [ \ ]

6ROX LH

N

FDOFXOH]H

N Q

I [cc

I \c

I \cc

I ]cc

G I

EH D[ E\

D Q N E N H D[ E\ GHFL

D Q N E N H D[ E\ G[ Q N G\ N

GLIHUHQ LDOD [ \ ] OQ [ \ ]

I [c

D Q H D[ E\ I \c

E Q H D[ E\ « I Q [ Q N \ N Q

G Q I

H D[ E\ GHILQLW SH

GH

RUGLQXO

,,

D

IXQF LHL

I ]c OQ [ \ ]

I [\cc

I \]cc

[ \]

I []cc

G[ G\ G] [ \] )RUPXODOXL7D\ORU

)LH I ( \ o \ úL D E ( 6 SUHVXSXQH F I DGPLWH GHULYDWH SDU LDOHGHRUGLQXO Q úLGHULYDWHOHSDU LDOHPL[WHQXGHSLQGGHRUGLQHDYDULDELOHORU vQUDSRUWFXFDUHVHGHULYHD] 2ULF UXLSXQFW [ \ ( LVHSRDWHDVRFLDSROLQRPXO

7Q [ \

O N O O N N O N N & O I [ \ D E [ D \ E ¦ ¦ O O N I D E I [c [ D I \c \ E I [cc [ D I [\cc [ D \ E I \cc \ E Q

>

@

2SHUDWRUXO 7Q [ \ VHVFULH

º ª w w I D E « [ D \ E » I D E ¬ w[ w\ ¼

7Q [ \

º ªw w « [ D \ E » I D E ¬ w[ w\ ¼ Q

º ªw w « [ D \ E » I D E Q ¬ w[ w\ ¼

3ROLQRPXO 7Q [ \ VHQXPHúWHSROLQRPXOOXL7D\ORUGHRUGLQXO Q DVRFLDW

IXQF LHL I vQSXQFWXO D E

3HQWUXILHFDUHSXQFW [ \ ( DYHPIRUPXODOXL7D\ORUGHRUGLQXO Q

I [ \ 7Q [ \ 5Q [ \ GLQFDUHRE LQHPUHVWXOGHRUGLQXO Q DOGH]YROW ULLvQVHULH7D\ORU 5Q [ \ I [ \ 7Q [ \ 2EVHUYD LH'DF IXQF LD I HVWHGLIHUHQ LDELO GH Q RULvQWURYHFLQ WDWH 9 DOXL D E SHQWUXRULFHSXQFW [ \ 9 H[LVW XQSXQFW [ K 9 VLWXDWSH VHJPHQWXOFDUHXQHúWHSXQFWXO D E FXSXQFWXO [ \ DúDF ªw [ D w \ E º» 5 Q [ \ « Q ¬ w[ w\ ¼ (VWHFODUF OLP 5Q [ \

Q

I [ K

[ \ o D E

([WUHPHOHIXQF LLORUGHPDLPXOWHYDULDELOH 'HILQL LH8QSXQFW D E ( VHQXPHúWHSXQFWGHPD[LPORFDOUHVSHFWLY GH PLQLP ORFDO DO IXQF LHL I ( \ o \ GDF H[LVW R YHFLQ WDWH 9 D OXL

D E

DVWIHO vQFkW SHQWUX RULFH [ \ 9 ( V DYHP I [ \ d I D E

UHVSHFWLY I [ \ t I D E $FHVWH SXQFWH VH QXPHVF SXQFWHGHH[WUHPORFDO DOHIXQF LHL 9DORDUHD I D E DIXQF LHLvQWUXQSXQFWGHPD[LPPLQLP ORFDOVHQXPHúWH D

PD[LPXOPLQLPXO ORFDODOIXQF LHL9RPQRWDSULQ ( LQWHULRUXOPXO LPLL ( 3URSR]L LD 'DF IXQF LD I DUH GHULYDWH SDU LDOH vQWUXQ SXQFW GH D

H[WUHP D E ( DWXQFL GHULYDWHOH SDU LDOH VH DQXOHD] vQ DFHVW SXQFW

I [c D E I \c D E

'HPRQVWUD LH ÌQWUDGHY U IXQF LD SDU LDO I [

I [ \ GHILQLW SH

[ [ \ [ E ( HVWHGHULYDELO vQSXQFWXO D LDU IcD

(E

I [c D E LDU

D

D (E HVWH XQ SXQFW GH H[WUHP DO IXQF LHL GHFL FRQIRUP WHRUHPHL OXL )HUPDW DYHP I cD DGLF I [c D E /DIHOVHDUDW F I \c D E JHQHUDOL]DUH DWHRUHPHLOXL)HUPDWSHQWUXIXQF LLGHGRX YDULDELOH 'HILQL LH 8Q SXQFW D E ( VH QXPHúWH SXQFW VWD LRQDU DO IXQF LHL I

GDF IXQF LD I HVWH GLIHUHQ LDELO vQ D E úL GDF GLIHUHQ LDOD VD HVWH QXO vQ DFHVWSXQFW GI D E I [c D E G[ I \c D E G\ 'DU GI D E

GDF úLQXPDLGDF I [c D E I \c D E $úDGDU D E HVWH XQ SXQFW VWD LRQDU FULWLF DO IXQF LHL I FkQG IXQF LD HVWH GLIHUHQ LDELO vQ SXQFWXO D E úLDUHGHULYDWHOHSDU LDOHQXOHvQDFHVWSXQFW 3URSR]L LD2ULFHSXQFWGHH[WUHPORFDOGLQLQWHULRUXOPXO LPLL ( vQ FDUH IXQF LD I HVWH GLIHUHQ LDELO HVWH SXQFW VWD LRQDU DO IXQF LHL 5HFLSURFD QX HVWHDGHY UDW 'HPRQVWUD LH ÌQWUDGHY U FRQIRUP SURSR]L LHL

I \c D E GHFL D E HVWHXQSXQFWVWD LRQDUDOIXQF LHL

I \ o \ \ I [c I \c

([HPSOX

I \c [ \

)LH

I [ \

[ \

I [c D E úL I [c [ \ [

)XQF LD HVWH GLIHUHQ LDELO vQ RULJLQH GHRDUHFH GHULYDWHOH SDU LDOH VXQW FRQWLQXHGHFL HVWHXQSXQFWVWD LRQDUDOIXQF LHLGDU QXHVWHSXQFWGH H[WUHP ÌQWUDGHY U SHQWUX SXQFWHOH GH IRUPD [ GH SH D[D 2[

I [ [ t I LDU SHQWUX SXQFWHOH GH IRUPD \ GH SH D[D 2\ I \ \ d I DVWIHOvQFkWvQ IXQF LDQXDUHQLFLPLQLPQLFL

PD[LP ORFDO VLWXD LH VLPLODU IXQF LLORU GH R VLQJXU YDULDELO FkQG VH DQXOHD] GHULYDWD,I U VFKLPEDUHGHVHPQSXQFWHGHLQIOH[LXQH 3XQFWHOHVWD LRQDUHDOHIXQF LHL I FDUHQXVXQWSXQFWHGHH[WUHPDOHVDOHVH QXPHVFSXQFWHúDDOHOXL I ,QWHUSUHWDUH JHRPHWULF *UDILFXO IXQF LHL I HVWH R VXSUDID 6 D F UHL HFXD LHHVWH ]

I [ \ úLDUHvQSXQFWXOúDXQSODQWDQJHQWDF UXLHFXD LHHVWH ] I D E I [c D E [ D I \c D E \ E

'DF D E HVWH SXQFW VWD LRQDU I [c D E

I \c D E SODQXO WDQJHQW

I D E HVWHSDUDOHOFXSODQXO [2\ ÌQ FRQFOX]LH GDF I HVWH GLIHUHQ LDELO SH R PXO LPH GHVFKLV ( SXQFWHOH VWD LRQDUHDOHOXL I VXQWWRDWHVROX LLOH [ \ DOHVLVWHPXOXL I [c [ \ ® c ¯ I \ [ \ ]

&XPRULFHSXQFWGHH[WUHPORFDOHVWHSXQFWVWD LRQDUUH]XOW F SXQFWHOHGH H[WUHP ORFDO VH DIO SULQWUH VROX LLOH VLVWHPXOXL GH PDL VXV GDU QX WRDWH VROX LLOH VLVWHPXOXLVXQWSXQFWHGHH[WUHP &D úL OD IXQF LL GH R VLQJXU YDULDELO XQGH SHQWUX D LGHQWLILFD XQ SXQFW GH H[WUHPDQDOL] PVHPQXOGHULYDWHLDGRXDvQDFHOSXQFWSHQWUXDLGHQWLILFDSULQWUH SXQFWHOH VWD LRQDUH XQHOH SXQFWH GH H[WUHP GDU QX QHDS UDW WRDWH SXQFWHOH GH H[WUHP YDWUHEXLV UHFXUJHPODGHULYDWHOHSDU LDOHGHRUGLQXOGRL 7HRUHP 'DF D E HVWHXQSXQFWVWD LRQDUDOIXQF LHL I úLGDF

I DUHGHULYDWHSDU LDOHGHRUGLQXOGRLFRQWLQXHvQWURYHFLQ WDWH 9 DOXL D E

DWXQFL 'DF I cc D E I cc D E I [\cc D E ! DWXQFL D E HVWH XQ SXQFW GH [

\

>

@

H[WUHPORFDODOIXQF LHL I úLDQXPH

GDF I cc D E ! D E HVWHXQSXQFWGHPLQLP

[

GDF I cc D E D E HVWHXQSXQFWGHPD[LP

[

>

@

'DF I cc D E I cc D E I [\cc D E DWXQFL D E QXHVWHXQSXQFWGH [

\

H[WUHPDOIXQF LHL I

'HPRQVWUD LHÌQWUDGHY U D E HVWHSXQFWVWD LRQDUúLDWXQFL I [c D E

úL

I \c D E 'HRDUHFH I DUH GHULYDWH SDU LDOH GH RUGLQXO GRL FRQWLQXH SH R

YHFLQ WDWH 9 D OXL D E SXWHP VFULH IRUPXOD OXL 7D\ORU GH RUGLQXO GRL SHQWUX

[ \ 9 I [ \

I D E I [c D E [ D I \c D E \ E

I [cc D E [ D I [\cc D E [ D \ E I \cc D E \ E Z [ \ §¨ [ D \ E ·¸ © ¹ úL OLP Z [ \

[oD \ oE

LQkQGVHDPDF I [c D E

I \c D E úLWUHFkQG I D E vQPHPEUXOVWkQJ

I [ \ I D E I [cc D E [ D I [\cc D E [ D \ E I \cc D E \ E Z [ \ U º § \ E· § [ D ·§ \ E · §[D· U ª ¸¸ Z [ \ » ¸¸ I \cc D E ¨¨ ¸¸¨¨ ¸¸ I [\cc D E ¨¨ « I [cc D E ¨¨ «¬ »¼ © U ¹ © U ¹© U ¹ © U ¹

§ \ E· ¸¸ VHRE LQH GHFLGDF VHG IDFWRUFRPXQ ¨¨ © U ¹

'DU OLP Z [ \ [oD \ oE

I [ \ I D E

§ \ E· ¸ ¨ © ¹

ª º §[D· § [D· ¸¸ I [\cc D E ¨¨ ¸¸ I \cc D E » « I [cc D E ¨¨ «¬ »¼ © \ E¹ © \ E¹

[D úL SHQWUX F UDSRUWXO SRDWH OXD RULFH YDORDUH SR]LWLY VDX QHJDWLY FkQG \ E [ o D \ o E vQ PRG LQGHSHQGHQW XQXO GH DOWXO XUPHD] F H[SUHVLD GLQ PHPEUXO GRL S VWUHD] VHPQ FRQVWDQW vQ YHFLQ WDWHD OXL D E QXPDL FkQG

I cc

GLVFULPLQDQWXO '

[\

I [cc I \cc SULQ XUPDUH GLQ GLVFX LD VHPQXOXL

WULQRPXOXLGHJUDGXO,,VHRE LQXUP WRDUHOHFD]XUL I [ \ I D E ! DGLF I DGPLWH XQ PLQLP ORFDO vQ D E GDF

> I cc D E @

[\

I [cc D E I \cc D E I [cc D E !

I [ \ I D E DGLF I DGPLWH XQ PD[LP ORFDO vQ D E GDF

> I cc D E @ I cc D E I cc D E I cc D E 'DF > I cc D E @ I cc D E I cc D E ! I [ \ I D E QX S VWUHD]

[\

[

\

[

[

[\

\

VHPQ FRQVWDQW vQ YHFLQ WDWHD SXQFWXOXL D E SXQFWXO D E QXPLQGXVH SXQFWúD 'DF I [\cc D E I cc D E I cc D E

>

@

[

\

VHPQXOH[SUHVLHL I [ \ I D E

GHSLQGHGHYDORULOHGHULYDWHORUSDU LDOHGHRUGLQVXSHULRUOXLGRL ([HPSOX )LH I [ \ [ \ I [c [ \ [ I \c [ \

[

\

HVWHSXQFWVWD LRQDU I [cc I \cc I [\cc

'

> I cc D E @

[\

I [cc D E I \cc D E

\

GDU I [ \ I ! RULFDUHDUIL [ úL \ GHFL HVWHXQSXQFWGHPLQLP

[ \ DFHODúL QX HVWH SXQFW GH H[WUHP GHRDUHFH SHQWUX I \ \ GDF \ úL I \ \ ! GDF \ ! )LH I ( \ Q o \ D D D Q HVWH XQ SXQFW GH PLQLP PD[LP ORFDOGDF I [ ! I D UHVSHFWLY I [ I D 'DF D ( HVWHXQSXQFWVWD LRQDUDWXQFL I [cL D L Q 'DF I [ \

3XQFWXO D HVWHVWD LRQDUGDF I HVWHGLIHUHQ LDELO vQ D úLGDF GI D úLVHRE LQHGLQUH]ROYDUHDVLVWHPXOXLGHULYDWHORUSDU LDOH 7HRUHP )LH D SXQFWVWD LRQDUDOOXL I 6 SUHVXSXQHPF IXQF LD I DUHGHULYDWHSDU LDOHGHRUGLQXOGRLFRQWLQXHvQWURYHFLQ WDWH 9 DOXL D Q

¦ I cc

'DF IRUPDS WUDWLF M

L M

[L [ M

D L D M HVWHGHILQLW DWXQFL D HVWHXQSXQFW

GH H[WUHP úL DQXPH XQ SXQFW GH PD[LP VDX GH PLQLP GXS FXP M VDX M ! 'DF IRUPDS WUDWLF M HVWHQHGHILQLW DWXQFL D QXHVWHSXQFWGHH[WUHPDO IXQF LHL )XQF LLLPSOLFLWH )LH

HFXD LD

) [ \

FX

) ( \ o \

úL

[ \ \ [ \ ( 2 IXQF LH I $ o \ VH QXPHúWH VROX LH vQ

$ ([

UDSRUWFX \ DHFXD LHL ) [ \ SHPXO LPHD $ GDF ) [ I [ { SHQWUX [ $ (FXD LD ) [ \ SRDWHV QXDLE VROX LLFDvQFD]XOFHUFXOXLLPDJLQDU

[ \ vQ UDSRUW FX QLFL R YDULDELO 3RDWH DYHD R VLQJXU VROX LH FD vQ FD]XO SULPHL ELVHFWRDUH [ \ úL DQXPH \ [ VDX SRDWH DYHD PDL PXOWH VROX LLSHPXO LPH $ FDvQFD]XOHFXD LHL ) [ \

[ \ $FHDVW HFXD LH vQUDSRUWFX \ DUHRLQILQLWDWHGHVROX LLSHPXO LPHD >f GHH[HPSOX \

° [ ® °¯ [

XQGH D HVWHDUELWUDUvQWUH úL f

[ > D [ >Df

)LH ) [ [ Q \ XQGH ) ( \ Q o \ \

I [ [ Q

Q

I $ \ o \ HVWHRVROX LHvQUDSRUWFX \ DDFHVWHLHFXD LLSHPXO LPHD

$ GDF ) [ [ Q I [ [ Q { SHQWUX RULFH SXQFW [ [ Q $ XQGH

[

[ [Q HVWHRYDULDELO

UHDO VDXYHFWRULDO

'DF H[LVW R VLQJXU IXQF LH I $ \ Q o \ FDUH V YHULILFH HFXD LD

) [ \ HYHQWXDO úL DOWH FRQGL LL VXSOLPHQWDUH VH VSXQH F IXQF LD I HVWH GHILQLW LPSOLFLWGHHFXD LD ) [ \ 5H]ROYkQGHFXD LD ) [ \ vQUDSRUW FX \ H[SOLFLWkQGR VHRE LQHIXQF LDH[SOLFLW \ I [

)XQF LLOH GHILQLWH FX DMXWRUXO HFXD LLORU VH QXPHVF IXQF LL GHILQLWH LPSOLFLW IXQF LLLPSOLFLWH D

D

7HRUHPD )LH $ \ Q Q t % \ [ $ \ % úL IXQF LD UHDO ) $ u % o 5 'DF ) [ \ ) DUH GHULYDWHOH )[c « )[cQ )\c FRQWLQXH SH R YHFLQ WDWH 8 u 9 D OXL

[ \ )\c [ \

$WXQFL D H[LVW RYHFLQ WDWH 8 DOXL [ úLRYHFLQ WDWH 9 DOXL \ úLRIXQF LHXQLF

\ I [ I 8 o 9 DVWIHO FD I [ \ úL ) [ I [ { SHQWUX [ 8 E IXQF LD I DUHGHULYDWHSDU LDOH I [c I [cQ FRQWLQXHSH 8 úLSHQWUXILHFDUH L I [cL

)[cL [ I [ )\c [ I [

[ 8

F GDF ) DUHGHULYDWHSDU LDOHGHRUGLQXO N FRQWLQXHSH 8 u 9 DWXQFL I DUH GHULYDWHSDU LDOHGHRUGLQXO N FRQWLQXHSH 8 )LH IXQF LD GH GRX YDULDELOH ) [ \

'DF VH GLIHUHQ LD] IRUPDO VH G\ RE LQH )[cG[ )\cG\ ÌPS U LQG SULQ )\cG[ úL QRWkQG \ c VH RE LQH G[ )[c )c \ c DGLF \ c [ )\c )\c ([WUHPHFRQGL LRQDWHOHJDWH )LH I [

I [ [ Q R IXQF LH UHDO GHILQLW SH R PXO LPH ( \ Q úL $ ( )XQF LD I DUHvQ D $ XQH[WUHPUHODWLYOD $ GDF UHVWULF LDOXL I OD $ DUHvQ D XQH[WUHPRELúQXLW

ÌQ D HVWHXQPD[LPPLQLP UHODWLYOD $ GDF H[LVW RYHFLQ WDWH 9 DOXL D DVWIHOvQFkW I [ t I D UHVSHFWLY I [ d I D SHQWUXRULFHSXQFW [ 9 $ ([WUHPHOH IXQF LHL I UHODWLYH OD VXEPXO LPHD $ ( VH QXPHVF H[WUHPH FRQGL LRQDWHOHJDWH )LH ) [ )N [ N Q IXQF LL UHDOH FDUH GHILQHVF PXO LPHD $ SULQ PXO LPHDVROX LLORUVLVWHPXOXLUHVWULF LLORU )L [ [ Q L N

L N ` ÌQ DFHVW FD] H[WUHPHOH IXQF LHL I UHODWLYH OD $ VH QXPHVF H[WUHPH

$úDGDU $

^[ ( ) [ L

FRQGL LRQDWHGHVLVWHPXO $FHDVWD DUDW F FHOH Q YDULDELOH [ [ Q VXQW OHJDWH vQWUH HOH SULQ FHOH N UHOD LLDOHVLVWHPXOXL GHDFHHDOHPDLQXPLPúLH[WUHPHOHJDWH 7HRUHP )LH D R VROX LH D VLVWHPXOXL 6 SUHVXSXQHP F IXQF LLOH I [ ) [ )N [ DXGHULYDWHSDU LDOHFRQWLQXHvQWURYHFLQ WDWH 9 DOXL D úLPDWULFHDIXQF LRQDO I Mc DUHvQSXQFWXO D UDQJXO N 'DF D HVWHXQ SXQFW GH H[WUHP DO IXQF LHL I FRQGL LRQDW GH VLVWHPXO DWXQFL H[LVW N QXPHUH O O N PXOWLSOLFDWRULLOXL/DJUDQJH DVWIHOvQFkW

wI D N w)L D M Q ¦ OL ° w[ M L ® w[ M ° ) D ) D ) D N ¯

2ULFH VROX LH D

D D Q

D VLVWHPXOXL VH QXPHúWH SXQFW

VWD LRQDU FRQGL LRQDW DO IXQF LHL I 2ULFH SXQFW GH H[WUHP FRQGL LRQDW HVWH XQ SXQFWVWD LRQDUFRQGL LRQDWUHFLSURFDQXHVWHDGHY UDW (WDSHGHFDOFXODOHH[WUHPHORUOHJDWH 6H IRUPHD] IXQF LD DX[LOLDU DMXW WRDUH ) [ [ Q O O N I [ O ) [ O N )N [ FX FRHILFLHQ LL

O O N QHGHWHUPLQDQ L

° )[c )[c )[cQ FX °¯ ) ) )N

6H IRUPHD] VLVWHPXO FHORU Q N HFXD LL ®

Q N QHFXQRVFXWH [ [ Q O O N úL VH FDXW VROX LLOH DFHVWXL VLVWHP

FDUHVXQWSXQFWHFULWLFHVWD LRQDUH 'DF [ [ Q O O N HVWH R VROX LH D DFHVWXL VLVWHP DWXQFL SXQFWXO

[ [Q HVWHSXQFWVWD LRQDUFRQGL LRQDWDOIXQF LHL I

3ULQWUH SXQFWHOH VWD LRQDUH FRQGL LRQDWH DVWIHO RE LQXWH VH DIO úL SXQFWHOH H[WUHPFRQGL LRQDW

9RPF XWDFRQGL LLVXILFLHQWHFDUHV SHUPLW V VHLGHQWLILFHGLQWUHSXQFWHOH VWD LRQDUHSXQFWHOHGHH[WUHPFRQGL LRQDW )LH SXQFWXO VWD LRQDU D GHFL )L D L N úL N QXPHUH O O N DVWIHOFDV ILHVDWLVI FXWVLVWHPXO 3HQWUXDYHGHDGDF D HVWHVDXQXSXQFWGHH[WUHPFRQGL LRQDWGHVLVWHPXO VHYDVWXGLDVHPQXOGLIHUHQ HL I [ [ Q I D D Q SHQWUXSXQFWHOH

[ [Q FDUHYHULILF VLVWHPXO ) [ I [ I D ) [ ) D VH UHGXFH OD ) [ ) D

LPSOLF ) [

I [ GHFL

VWXGLXO VHPQXOXL GLIHUHQ HL

3XQFWXO D YHULILFkQGVLVWHPXO HVWHSXQFWVWD LRQDUSHQWUX ) [ GHFL

GHULYDWHOHVDOHSDU LDOHGHRUGLQXO,VHDQXOHD] vQ D 3HGHDOW SDUWHIXQF LD ) [ DUHGHULYDWHSDU LDOHFRQWLQXHvQWURYHFLQ WDWHDOXL D GHFLVHSRDWHVFULHIRUPXOD OXL7D\ORUGHRUGLQXOGRL

)[cLc[ M D G[L G[ M Z [ U ¦

) [ ) D XQGH OLP Z [ [oD

Q

¦ [

U

L

DL úL G[L

L

'XS FXP IRUPD SDWUDWLF

Q

¦

L M

G ) ZU

[L DL L Q

)[cLc[ M D G[L G[ M S VWUHD] vQ MXUXO OXL D

DFHODúLVHPQVDXQXS VWUHD] DFHODúLVHPQSXQFWXO D HVWHVDXQXSXQFWGHH[WUHP FRQGL LRQDW )XQF LLRPRJHQHGHPDLPXOWHYDULDELOH )XQF LD I [ [ Q VH QXPHúWH RPRJHQ GH JUDGXO N vQ UDSRUW FX YDULDELOHOH [L L

Q GDF SHQWUXXQ W RDUHFDUHHVWHDGHY UDW UHOD LD

I W[ W[ Q W N I [ [ Q

7HRUHPDOXL(XOHU2IXQF LHRPRJHQ VDWLVIDFHUHOD LD [ I [c [ Q I [cQ NI [ [ Q

([HPSOX)LH I [ \

D I W[ W\

E [I [c \I \c

[\ \

W[ W[ W\ W [\ \ [\ \ [ \ [\ \

W I [ \

I [ \

)XQF LLRPRJHQHvQHFRQRPLH

I [ \ RIXQF LHRPRJHQ GHJUDGXOvQWkLGHGRX YDULDELOH

)LH ]

§ \· [M¨ ¸ ©[¹

)XQF LDSRDWHILVFULV VXERULFDUHGLQIRUPHOH ] úL \ VXQWIXQF LLGHRVLQJXU YDULDELO

§[· \\¨¨ ¸¸ XQGH M © \¹

w] w] [ úL VXQWIXQF LLGH w[ w\ \ w] w] \ D 7HRUHPDOXL(XOHUHVWH [ w[ w\ 'HULYDWHOHSDU LDOH

ÌQWUXFkW WHRUHPD OXL (XOHU D IRVW GHPRQVWUDW vQ FD]XO JHQHUDO VH YRU GHPRQVWUDQXPDLSULPHOHGRX SURSULHW L 'HRDUHFH I O[ O\ SHQWUX O QXPDLGH

DGLF ] [ \ [

7RWDVWIHOGDF O

§ \· OI [ \ SHQWUXRULFH O DWXQFL I ¨ ¸ I [ \ © [¹ [ § \· § \· § \· [I ¨ ¸ [M¨ ¸ GHRDUHFH I ¨ ¸ HVWH IXQF LH © [¹ ©[¹ © [¹

DWXQFL ] \

§[ · \I ¨¨ ¸¸ ©\ ¹

§[· \\¨¨ ¸¸ © \¹

§ \· [M¨ ¸ vQUDSRUWFX [ HVWH ©[¹ w] § \· \ § \· § \· § \· w § \· M¨ ¸ [Mc¨ ¸ ¨ ¸ M¨ ¸ Mc¨ ¸ w[ ©[¹ [ © [¹ ©[¹ © [ ¹ w[ © [ ¹ \ § \· § \· XQGH Mc¨ ¸ HVWHGHULYDWDIXQF LHLGHRVLQJXU YDULDELO M¨ ¸ vQUDSRUWFX [ © [¹ ©[¹ w] w] w] § \· § \· w § \· 7RWDVWIHO FkWúL VXQWIXQF LL [Mc¨ ¸ ¨ ¸ Mc¨ ¸ 'HFLDWkW w\ w[ w\ ©[¹ © [ ¹ w\ © [ ¹ \ QXPDLGHUDSRUWXO [ (VWHLQWHUHVDQWFD]XOFkQGIXQF LDGHSURGXF LHDXQHLP UIL ; HVWHRPRJHQ GHJUDGvQWkLvQUDSRUWFXIDFWRULLYDULDELOHL $ $ $Q 3RUQLQGGHODGHILQL LHúL 'HULYDWDSDU LDO DOXL ]

GH OD SURSULHW LOH úL GH PDL VXV DFHVW FD] HVWH FDUDFWHUL]DW GH DFHHD F R FUHúWHUH UHODWLY GDW WXWXURU IDFWRULORU GXFH OD R DFHHDúL FUHúWHUH UHODWLY D UH]XOWDWXOXL I U D PRGLILFD SURGXVXO PHGLX VDX SURGXVXO PDUJLQDO DO RULF UXL IDFWRU

$FHVWD HVWH FD]XO ÄYHQLWXULORU FRQVWDQWH OD VFDU ´ FkQG QXPDL FDQWLW LOH UHODWLYH IRORVLWH GH ILHFDUH IDFWRU VXQW LPSRUWDQWH QX úL VFDUD OD FDUH VH IDFH SURGXF LD 'DF H[LVW GRL IDFWRUL $ úL % úL YHQLWXUL FRQVWDQWH OD VFDU VXSUDID D SURGXF LHLHVWHULJODW GHGUHSWHFDUHWUHFSULQRULJLQHúLRULFHVHF LXQHSULQ 2[ HVWH RGUHDSW &XUEHOHSURGXF LHLFRQVWDQWHGLQSODQXO D2E VHRE LQXQDGLQDOWDSULQ SURLHF LLUDGLDOHLDUGLPHQVLXQLOHORUYDULD] vQUDSRUWXOSURGXF LLORUFRQVWDQWHFDUH OH GHILQHVF ÌQ SDUWLFXODU RULFH UD] FDUH WUHFH SULQ 2 LQWHUVHFWHD] FXUEHOH vQ SXQFWHvQFDUHWDQJHQWHOHVXQWSDUDOHOH (FXD LLGLIHUHQ LDOH 6XQW PXOWH SUREOHPH HFRQRPLFH FDUH VH UHGXF OD UH]ROYDUHD XQRU HFXD LL QXPLWH HFXD LL GLIHUHQ LDOH RUGLQDUH VDX PDL VFXUW HFXD LL GLIHUHQ LDOH FDUH OHDJ vQWUHHOHRYDULDELO LQGHSHQGHQW [ RIXQF LHQHFXQRVFXW GH [ SHFDUHRQRW P \ úLSULPHOHHL Q GHULYDWH \ c \ cc \ Q )LH ) R IXQF LH GHILQLW SH XQ GRPHQLX ' GLQ \ Q FX YDORUL UHDOH FRQWLQX vQDFHVWGRPHQLX 'HILQL LH2UHOD LHGHIRUPD

) [ \ \ c \ Q

VHQXPHúWHHFXD LHGLIHUHQ LDO GHRUGLQXO Q )LH M D E o \ RIXQF LHGHULYDELO GH Q RULvQRULFHSXQFWDOLQWHUYDOXOXL

D E XQGH D SRDWHIL f LDU E SRDWHIL f

6HVSXQHF IXQF LD M HVWHVROX LHDHFXD LHLGLIHUHQ LDOH GDF vQORFXLQG

vQHFXD LDGLIHUHQ LDO IXQF LD \ FX M [ VHRE LQHRLGHQWLWDWHRULFDUHDUIL

[ D E DGLF

) [ M [ Mc [ M Q [ 'DF vQ VLVWHPXO GH FRRUGRQDWH [2\ VH UHSUH]LQW JUDILF IXQF LD M VH RE LQHRFXUE GHHFXD LH \ M [ QXPLW úLFXUE LQWHJUDO DHFXD LHL ÌQ XQHOH FD]XUL vQ ORFXO VROX LLORU \ M [ VH J VHVF VROX LL GH IRUPD * [ \ FDUH GHILQHVF VROX LL LPSOLFLWH FX \ GHSLQ]kQG GH [ LDU FXUEHOHSH

FDUHVHGHILQHVFVHQXPHVFFXUEHLQWHJUDOH 'DF IXQF LD ) FH LQWU vQ GHILQL LD HFXD LHL GLIHUHQ LDOH vQGHSOLQHúWH FRQGL LL VXILFLHQWH SHQWUX D SXWHD VFRDWH GLQ HFXD LD ) [ \ \ c \ Q SH \ Q FDIXQF LHGHFHOHODOWHYDULDELOHDGLF

\ Q I [ \ \ c \ Q Q XQGH I ' \ o \ HVWH R IXQF LH GH Q YDULDELOH GHILQLW SH GRPHQLX ' FX YDORUL UHDOH úL FRQWLQX vQ DFHVW GRPHQLX (FXD LD VH QXPHúWH WRW HFXD LH

GLIHUHQ LDO GH RUGLQXO Q GDU HVWH GH R IRUP PDL SDUWLFXODU ID GH ILLQGF FRQ LQHSH \ Q H[SOLFLWDWvQUDSRUWFX [ \ \ c \ Q 3UREOHPD OXL &DXFK\ SHQWUX HFXD LD GLIHUHQ LDO GH RUGLQXO Q GH IRUPD FRQVW vQ GHWHUPLQDUHD VROX LHL HFXD LHL FDUH VDWLVIDFH FRQGL LLOH LQL LDOH \ [ \ \ c [ \ « \ Q [ \ Q XQGH

[ \ \c \ Q ' \ Q HVWHXQSXQFWFRQVWDQW 6H SRDWH GHPRQVWUD F DWXQFL FkQG IXQF LD I VDWLVIDFH DQXPLWH FRQGL LL

SHQWUX RULFH SXQFW [ \ \ c \ Q ' H[LVW R XQLF VROX LH D HFXD LHL GLIHUHQ LDOH FDUH VDWLVIDFH FRQGL LLOH OXL &DXFK\ UH]ROY SUREOHPD OXL &DXFK\ vQDFHOSXQFW 'HILQL LH3ULQVROX LHJHQHUDO DHFXD LHLGLIHUHQ LDOH VHvQ HOHJHR VROX LH \ M [ F F F Q D HL FH GHSLQGH úL GH Q FRQVWDQWH F F F Q FRQVLGHUDWHFDSDUDPHWULUHDOLúLFXDMXWRUXOF UHLDVHSRDWHUH]ROYDRSUREOHP D OXL&DXFK\SHQWUXRULFHSXQFWGLQGRPHQLXO ' (FXD LLGLIHUHQ LDOHFDUHQXFRQ LQYDULDELOHLQGHSHQGHQWH $FHVWWLSGHHFXD LLFDUHQXFRQ LQYDULDELODLQGHSHQGHQW úLVXQWGHRUGLQXO vQWkLDXXUP WRDUHDIRUP JHQHUDO

I \ VDX

\c

G\ G[

I \

FX I FRQWLQX úLGLIHULW GH]HURSHLQWHUYDOXO D E XQGH D SRDWHIL f LDU E SRDWHIL f ÌQ ORFXO DFHVWHL HFXD LL VH UH]ROY HFXD LD HFKLYDOHQW

I \ z DF UHLVROX LHJHQHUDO HVWH [

[ ³

\

\

G[ G\

SHQWUX I \

G\ I \

ÌQ DFHDVW UHOD LH [ [ HVWH R IXQF LH FRQWLQX úL VWULFW PRQRWRQ GH \ GHFL H[LVW IXQF LD LQYHUV \ FRQVLGHUDWH ([HPSOX)LH \ c VROX LDJHQHUDO [

M [ [ FDUH HVWH VROX LD JHQHUDO D HFXD LHL

\ FX \ f 6HUH]ROY HFXD LD

[ OQ

\ \ FX \ ! GHXQGH \ \

H

[ [

G[

G\

\

\

\ H

FDUHDUH [ [

7UHEXLH REVHUYDW F HFXD LD \ c

I \ DUH VHQV úL SHQWUX I \

)XQF LLOH \ \ FX I \ VXQWHYLGHQWVROX LLFDUHQXVHRE LQSULQPHWRGD GHPDLVXV(OHVXQWQXPLWHVROX LLVLQJXODUH (FXD LLFXYDULDELOHVHSDUDELOH $FHVWHHFXD LLVXQWGHIRUPD

\c

I [ J\

)XQF LD I RSUHVXSXQHPúLFRQWLQX SHXQLQWHUYDO D E úL J \ GHILQLW

FRQWLQX úL GLIHULW GH ]HUR SH XQ LQWHUYDO F G (FXD LD VH PDL SRDWH

VFULH I [ G[ J \ G\ 'DF ) HVWHRSULPLWLY DIXQF LHL I úL * RSULPLWLY DIXQF LHL J VROX LD JHQHUDO D HFXD LHL HVWH GDW VXE IRUPD LPSOLFLW GH UHOD LD ) [ * \ & XQGH & HVWHRFRQVWDQW DUELWUDU (FXD LLRPRJHQH 6XQWHFXD LLGHIRUPD

G\ G[

I [ \

XQGH I HVWH R IXQF LH RPRJHQ GH JUDGXO ]HUR DGLF VDWLVIDFH FRQGL LD

I W[ W\

I [ \ RULFDUH DU IL W DVWIHO vQFkW W[ W\ V ILH GH GRPHQLXO GH GHILQL LHDOIXQF LHL I

3XQkQG W

VH RE LQH I [ \ [

HFXD LDGLIHUHQ LDO HVWHGHIRUPD

G\ G[

§ \· I ¨ ¸ © [¹

§ \· M¨ ¸ GH XQGH UH]XOW F ©[¹

§ \· M¨ ¸ ©[¹ \ VDX \ X[ GHULYkQG VH RE LQH 3ULQ VFKLPEDUHD GH IXQF LH X [ G\ GX GX X[ úLGHFLHFXD LD VHWUDQVIRUP vQ X [ MX HFXD LH G[ G[ G[

FXYDULDELOHVHSDUDELOH

3UHVXSXQkQG IXQF LD M FRQWLQX úL MX X z QRWkQG FX

) X

GX

§ \·

³ MX X VROX LD JHQHUDO D HFXD LHL HVWH ) ¨© [ ¸¹

OQ [ OQ F

RE LQXW SULQLQWHJUDUHDPHPEUXFXPHPEUXÌQPHPEUXODOGRLOHDFRQVWDQWDUHDO FDUH WUHEXLH DG XJDW OD OQ [ SHQWUX D VH RE LQH SULPLWLYHOH IXQF LHL FRQVLGHUDW OQ F XQGH F !

VD [

(FXD LLUHGXFWLELOHODHFXD LLRPRJHQH 6HYRUFRQVLGHUDHFXD LLGHIRUPD

§ D[ E\ F · G\ ¸¸ I ¨¨ G[ © D c[ Ec\ F c ¹ XQGH D E F Dc Ec Fc \ VXQWFRQVWDQWH D E 'DF HFXD LD VH UHGXFH OD R HFXD LH FX YDULDELOH VHSDUDWH D c Ec D E ÌQWUDGHY U DWXQFL GH XQGH UH]XOW D c DD E c ED GHFL D c Ec D D c[ Ec\ DD[ E\ úL I FkQG VFKLPEDUHD GH IXQF LH X D[ E\ GH XQGH GX DG[ EG\ VHRE LQHHFXD LD § GX DG[ · § XF · ¨ ¸ I¨ ¸ E © G[ ¹ © DX F c ¹ VDX

GX E G[

GX § XF · D MX I¨ ¸ VDX G[ © DX F c ¹ E D E D[ E\ F 'DF z VLVWHPXO GH HFXD LL ® DUH R VROX LH D c Ec ¯D c[ Ec\ F c

[ ¯\

XQLF [ \ ) FkQGVFKLPEDUHDGHYDULDELO úLGHIXQF LH ®

G[ ® ¯G\

[ W \ X

GHXQGH

GW úLHFXD LD GHYLQH GX

GX GW

§ D [ W E \ X F · ¸¸ I ¨¨ © D c [ W Ec \ X F c ¹

vQV

D[ E[ F

úL

D c[ Ec\ F c

GHFL

HD

GHYLQH

GX GW

§ DW EX · I¨ ¸ DGLF RHFXD LHRPRJHQ SHQWUXF IXQF LD I HVWHRPRJHQ © D cW E cX ¹ GHJUDGXO]HURvQYDULDELOHOHHL W úL X (FXD LLOLQLDUHGHRUGLQXOvQWkL )RUPDJHQHUDO DDFHVWRUHFXD LLHVWH

$ [ \ c % [ \ & [ 3UHVXSXQkQGF IXQF LLOH $ % & VXQWGHILQLWHúLFRQWLQXHSHXQLQWHUYDO D E úL F $[ z vQ RULFH SXQFW DO DFHVWXL LQWHUYDO VH vPSDUWH SULQ $[ úL

HFXD LD GHYLQH XQGH 3 [ (FXD LD

\ c 3[ \ 4[ %[ & [ úL 4 [ $ [ $ [ \ c 3[ \

VHQXPHúWHHFXD LHOLQLDU I U PHPEUXODOGRLOHDVDXHFXD LDOLQLDU RPRJHQ 2EVHUYD LH 2PRJHQLWDWHD HFXD LHL VH UHIHU OD DEVHQ D WHUPHQXOXL 4 [ GLQPHPEUXOVWkQJDOHFXD LHL

G\ G[

(FXD LD HVWHRHFXD LHFXYDULDELOHVHSDUDELOHGHFLVHSRDWHUH]ROYDVFULLQG

3 [ \ VDX

OQ \ OQ F

G\ \

3 [ G[ ,QWHJUkQG ILHFDUH PHPEUX DYHP

³ 3 [ G[ VDX OQ \ F

JHQHUDO HVWH

\

³ 3 [ G[ 1RWkQG r

3 [ G[ FH ³

F

F VROX LD

3HQWUX HFXD LD VH FDXW R VROX LH GH IRUPD XQGH F HVWH FRQVLGHUDW RIXQF LHGH [ $FHDVW PHWRG HVWHFXQRVFXW VXEQXPHOHGHPHWRGD YDULD LHLFRQVWDQWHL 'HULYkQGvQ VHRE LQH

\c

3 [ G[ 3 [ G[ F [ 3 [ H ³ F c[ H ³

úLvQORFXLQGvQ UH]XOW

3 [ G[ 3 [ G[ 3 [ G[ F [ 3 [ H ³ F[ 3[ H ³ F c[ H ³ 3 [ G[ GF GHXQGH 4 [ H ³ úLDSRL G[

4 [

F[

§

³ ¨© 4[ H

úLVROX LDJHQHUDO DHFXD LHL HVWH

\

³ 3 [ G[ ·G[ F ¸ ¹

3 [ G[ § 3 [ G[ · · § H ³ ¨ F ³ ¨ 4 [ H ³ ¸G[ ¸ © ¹ ¹ ©

6H REVHUY F VROX LD JHQHUDO D HFXD LHL QHRPRJHQH HVWH HJDO FX VROX LD JHQHUDO D HFXD LHL RPRJHQH OD FDUH VH DGDXJ R VROX LH SDUWLFXODU D HFXD LHL QHRPRJHQH$FHDVW VROX LHVHRE LQHGLQUHOD LDJHQHUDO SHQWUX F 6ROX LD SDUWLFXODU D HFXD LHL QHRPRJHQH SRDWH IL vQORFXLW FX RULFDUH DOWD ÌQWUDGHY UV SUHVXSXQHPFXQRVFXW RVROX LHSDUWLFXODU \ DHFXD LHL ) FkQG VFKLPEDUHD GH IXQF LH \

\ ] HFXD LD QHRPRJHQ GHYLQH G\ 3\ 4 QH U PkQH 4 vQV LQkQG VHDPD F G[

G\ G] 3\ 3] G[ G[ G] 3] GHFL ] HVWHVROX LDJHQHUDO DHFXD LHLRPRJHQH G[

8QHOHDSOLFD LLvQHFRQRPLHDHFXD LLORUGLIHUHQ LDOH )XQF LD FHUHULL XQXL SURGXV SH SLD &RQVLGHU P FD]XO FkQG FDQWLWDWHD [ GLQWUXQDQXPLWSURGXV ; GHSLQGHGHSUH XOFXUHQWDODFHVWXLSURGXVúLGHYHQLWXO FRQVXPDWRULORU ÌQ UHDOLWDWH SH OkQJ DFHúWL GRL IDFWRUL IXQGDPHQWDOL PDL H[LVW IDFWRUL FX LQIOXHQ H PDL UHGXVH VDX LQGLUHFWH FD GH H[HPSOX SUH XULOH FHORUODOWH P UIXUL SH FDUH OH FXPS U FRQVXPDWRUXO RIHUWD SURGXVHORU IDFWRUL VRFLDO HFRQRPLFLúLGHPRJUDILFLVLVWHPXOGHYkQ] ULFXSODWDvQUDWHHWF $FHDVW IRUPXODUH D FRQGL LLORU SLH HL SRDWH IL WUDGXV vQ VLPEROXUL PDWHPDWLFH)LH S SUH XOSHQWUXSURGXVXO ; vQXQLW LGDWH 9 YHQLWXOPHGLXDO XQXL FRQVXPDWRU úL [ FDQWLWDWHD GH SURGXV ; FHUXW SH SLD vQ XQLW L GDWH $WXQFL ; HVWHRIXQF LHXQLYRF GH S úL Y FDUHSRDWHILVFULV SULQ

I S Y &RQVLGHU PF YDULDELOHOHLQGHSHQGHQWH S Y úLYDULDELODGHSHQGHQW [ LDX QXPDL YDORUL SR]LWLYH 3HQWUX XQ SUH FRQVWDQW S VDX XQ YHQLW FRQVWDQW Y FHUHUHD [ SRDWHILFRQVLGHUDW FDRIXQF LH I VDX I GHSLQ]kQGQXPDLGH Y VDX QXPDLGH S DGLF [ I S Y I Y VDX [ I S Y I Y )XQF LDFKHOWXLHOLORUGHSURGXF LHSHQWUXXQDQXPLWSURGXV ; vQWURSULP DSUR[LPD LHRSXWHPFRQVLGHUDFDGHSLQ]kQGQXPDLGHFDQWLWDWHD [ UHDOL]DW GLQ [

DFHVWSURGXVúLDQXPH

FS

J [

3HQWUXDFHDVW IXQF LHúLSHQWUXDOWHOHFDUHGHVFULXIHQRPHQHHFRQRPLFHDX VHPQLILFD LH úL LPSRUWDQ HFRQRPLF QR LXQLOH GH YDORDUH PHGLH YDORDUH

PDUJLQDO YLWH] UHODWLY GHURWD LHúLYLWH]DYDULD LHLUHODWLYHDIXQF LHLvQUDSRUWFX YDULD LDUHODWLY DYDULDELOHLFDUHVHQXPHúWHHODVWLFLWDWHDIXQF LHL )LH J R DVHPHQHD IXQF LH GH YDULDELO [ 9DORDUHD PHGLH HVWH

J [ [

9DORDUHDPDUJLQDO DIXQF LHL J vQSXQFWXO [ HVWH J c [ DGLF YDORDUHDGHULYDWHL IXQF LHL vQ SXQFWXO [ 9LWH]D YDULD LHL UHODWLYH D IXQF LHL vQ SXQFWXO [ HVWH

GJ [ [ GJ [ LDU HODVWLFLWDWHD vQ SXQFWXO [ HVWH úL VH QRWHD] J [ G[ J [ G[ (J [ (J [ [ GJ [ VDX ( [ J [ GHFL ([ ([ J [ G[

)RORVLQGQR LXQLOHLQWURGXVHDQWHULRUV UH]ROY PXUP WRDUHOHSUREOHPH 'DF HODVWLFLWDWHD XQHL OHJL D FHUHULL [ I S HVWH FRQVWDWDW DGLF

(I (S

D D ! V VHJ VHDVF DFHDVW OHJH

6ROX LH 'LQ

S I

GI GS

D FDUH HVWH R HFXD LH GLIHUHQ LDO GH RUGLQXO

GI DGS ,QWHJUkQG UH]XOW I S OQ I OQ S D OQ E XQGH E ! VDX OQ I OQ E S D GHFL [ I S E S D 'DF VDU FXQRDúWH FHUHUHD [ SHQWUX XQ DQXPLW SUH S DWXQFL FHUHUHD HVWH

vQWkL FX YDULDELOH VHSDUDWH VH RE LQH

SHUIHFWGHWHUPLQDW 3HQWUXDFHDVWDVHUH]ROY SUREOHPDOXL&DXFK\úLDQXPHLPSXQkQG FRQGL LD I S [ DGLF ES D [ UH]XOW

[

I S

D

§ S · [ ¨¨ ¸¸ © S ¹

&DUH HVWH OHJHD FHUHULL GDF YLWH]D UHODWLY GH YDULD LH HVWH FRQVWDQW DGLF

GI I GS

D D !

GI GI D UH]XOW DGS ,QWHJUkQG DYHP I GS I OQ I DS OQ E XQGH E HVWH R FRQVWDQW DUELWUDU VWULFW SR]LWLY GH XQGH [ I S EH DS 6ROX LH 'LQ

'DF VH FHUH OHJHD FHUHULL FDUH YHULILF FRQGL LD I S

[

E

H

DS

[ GH XQGH

úLOHJHDGHYLQH

I S

[

[ H

§ S · ¸ D¨ ¨S ¸ © ¹

&DUH HVWH OHJHD FKHOWXLHOLORU GH SURGXF LH F S

I [ SHQWUX FDUH YDORDUHD

PHGLHHVWHHJDO FXYDORDUHDPDUJLQDO 6ROX LH'LQ

FS

GF S

[

G[

XQGH D ! úLGHFL F S

UH]XOW

I [ D[

,PSXQkQG FRQGL LD F

GF S

G[ úLLQWHJUkQG OQ F S [

FS

I [ UH]XOW D[

S

GHWHUPLQDW GH

I [ F S

FS

S

F D

F S [

OQ [ OQ D

úL OHJHD HVWH

[ [

6H REVHUY F YDORDUHD GH SURGXF LH HVWH FRQVWDQW FX [ SHQWUX F

FS [

I [ [

F S [

FRQVWDQW

6H úWLH F HODVWLFLWDWHD XQHL OHJL D FHUHULL vQ IXQF LH GH SUH HVWH IRUPD

(I ([

D ES XQGH D úL E VXQWFRQVWDQWH&DUHHVWHDFHDVW

6ROX LH

OQ I

S GI I GS

D ES VDX

GI I

OQ S D ES OQ F XQGH F ! VDX OQ [ ,PSXQkQGFRQGL LD I S

D ES GS ,QWHJUkQG DYHP S

I FS D

ES GHXQGH

I S FS D H ES D

[ UH]XOW FS H

OHJHDFHUHULLGHYLQH

[

OHJHDFHUHULL"

I S

ES

[ GHFL F

ES

[ H S D

úL

D

§ S · E S S [ ¨¨ ¸¸ H © S ¹

7(25,$352%$%,/,7

,/25ù,67$7,67,& 0$7(0$7,&

&kPSGHHYHQLPHQWH3UREDELOLWDWH &kPSGHHYHQLPHQWH 7HRULDSUREDELOLW LORUVWXGLD] OHJLOHGXS FDUHHYROXHD] IHQRPHQHOHDOHDWRDUH 9RPGDFkWHYDH[HPSOHGHIHQRPHQHDOHDWRDUH &HOPDLVLPSOXH[HPSOXHVWHGDWGHH[SHULPHQWXOFDUHFRQVW vQDUXQFDUHDFX]DUXO XQFXEFXúDVHIH HQXPHURWDWHGHODOD UH]XOWDWXOH[SHULPHQWXOXLILLQGGDWGH FLIUDDU WDW GH]DUODRSULUH5HSHWkQGH[SHULPHQWXOGHXQQXP UGHRULQXSXWHP SUHYHGHDFDUHYDILFLIUDDU WDW GH]DUvQILHFDUHDUXQFDUHGHRDUHFHDFHDVWDGHSLQGH GH PXO L IDFWRUL vQWkPSO WRUL LPSXOVXO LQL LDO GDW ]DUXOXL SR]L LD OXL vQ PRPHQWXO DUXQF ULLSDUWLFXODULW LOHIH HLSHFDUHFDGHHWF 8QDYLRQHIHFWXHD] XQQXP URDUHFDUHGH]ERUXULUHJXODWHvQWUHGRX RUDúH7LPSXO GH]ERUQXHVWHFRQVWDQWFLSUH]LQW PLFLYDULD LLGHODXQ]ERUODDOWXOWRWGDWRULW XQRUIDFWRULvQWkPSO WRULFRQGL LLOHPHWHRURORJLFHHWF 1X VH SRDWH úWL GLQDLQWH FDUH YD IL SURFHQWXO GH UHEXWXUL OD IDEULFDUHD XQXL DQXPLW SURGXV ÌQDFHVWHH[SHULPHQWHFRQGL LLOHHVHQ LDOHDOHH[SHULPHQWXOXLU PkQQHVFKLPEDWH 7RDWH DFHVWH YDULD LL DX ORF GDWRULW XQRU IDFWRUL VHFXQGDUL FDUH LQIOXHQ HD] UH]XOWDWXO H[SHULPHQWXOXL'LQPXOWLWXGLQHDIDFWRULORUFDUHLQWHUYLQvQIHQRPHQHOHVWXGLDWHvLYRP VHOHF LRQDSHFHLGHFLVLYLúLYRPQHJOLMDLQIOXHQ DIDFWRULORUVHFXQGDUL$FHDVW PHWRG H X]XDO vQVWXGLXOIHQRPHQHORUIL]LFHPHFDQLFHúLvQDSOLFD LLWHKQLFHHFRQRPLFH ÌQVWXGLXODFHVWRUIHQRPHQHHYLGHQWH[LVW RGLIHUHQ GHSULQFLSLXvQWUHPHWRGHOH FDUH SHUPLW V LQHP FRQW GH IDFWRULL HVHQ LDOL FDUH GHWHUPLQ FDUDFWHUXO SULQFLSDO DO IHQRPHQXOXL úL PHWRGHOH FDUH LQ VHDPD GH IDFWRULL VHFXQGDUL D F URU LQIOXHQ VH PDQLIHVW SULQ HURUL VDX SHUWXUED LL ÌQWkPSODUHD FRPSOH[LWDWHD PXOWLWXGLQHD FDX]HORU FDUH LQWHUYLQ FRQGXF OD PHWRGH VSHFLDOH GH VWXGLHUH D IHQRPHQHORU DOHDWRDUH PHWRGH HODERUDWHGHWHRULDSUREDELOLW LORU $SOLFDUHDPDWHPDWLFLLODVWXGLHUHDIHQRPHQHORUDOHDWRDUHVHED]HD] SHIDSWXOF SULQUHSHWDUHDGHPDLPXOWHRULDXQXLH[SHULPHQWvQFRQGL LLSUDFWLFLGHQWLFHIUHFYHQ D UHODWLY DDSDUL LHLXQXLUH]XOWDWDQXPLWUDSRUWXOGLQWUHQXP UXOH[SHULPHQWHORUvQFDUH DSDUH UH]XOWDWXO úL QXP UXO WXWXURU H[SHULPHQWHORU HIHFWXDWH HVWH DSUR[LPDWLY DFHHDúL RVFLOkQGvQMXUXOXQXLQXP UFRQVWDQW'DF DFHVWOXFUXVHvQWkPSO XQXLHYHQLPHQWGDWvL SXWHP DVRFLD XQ QXP U SUREDELOLWDWHD VD /HJ WXUD DFHDVWD GLQWUH VWUXFWXU VWUXFWXUD XQXL FkPS GH HYHQLPHQWH úL QXP U HVWH R UHIOHFWDUH vQ PDWHPDWLF D SUREOHPHL WUDQVIHUXOXLFDOLW LLvQFDQWLWDWH3UREOHPDFRQYHUWLULLvQQXP UDVWUXFWXULLXQXLFkPSGH HYHQLPHQWHUHYLQHODDGHILQLRIXQF LHQXPHULF SHDFHDVW VWUXFWXU FDUHV ILHRP VXU DSRVLELOLW LORUGHUHDOL]DUHDHYHQLPHQWHORU5HDOL]DUHDXQXLHYHQLPHQWILLQGSUREDELO DFHDVW IXQF LHSRDUW GHQXPLUHDGHSUREDELOLWDWH7HRULDSUREDELOLW LORUVHSRDWHDSOLFD

QXPDLDFHORUIHQRPHQHFDUHSUH]LQW RDQXPLW VWDELOLWDWHDIUHFYHQ HORUUHODWLYHvQMXUXO SUREDELOLW LL IHQRPHQH RPRJHQH GH PDV $FHDVWD HVWH ED]D OHJ WXULL WHRULHL SUREDELOLW LORUFXOXPHDUHDO FXSUDFWLFDGHWRDWH]LOHOH 'HFL GHILQL LD úWLLQ LILF D SUREDELOLW LL WUHEXLH V UHIOHFWH vQ SULPXO UkQG FRPSRUWDUHDUHDO DIHQRPHQXOXL1R LXQLOHúLWHRULLOHSUREDELOLVWLFHQXVXQWDUWLILFLLGH FDOFXO FL PRGHOH DOH XQRU VW UL úL FDUDFWHULVWLFL RELHFWLY GHWHUPLQDWH DOH H[LVWHQ HL úL GHYHQLULL DFHVWHLD 3UREDELOLWDWHD QX HVWH H[SUHVLD JUDGXOXL VXELHFWLY GH vQFUHGHUH D RPXOXL vQ SURGXFHUHD HYHQLPHQWXOXL FL FDUDFWHUL]DUHD OHJ WXULL RELHFWLY H[LVWHQWH vQWUH FRQGL LLúLHYHQLPHQWvQWUHFDX] úLHIHFW 3UREDELOLWDWHDXQXLHYHQLPHQWDUHVHQVDWkWDWLPSFkWDQVDPEOXOGHFRQGL LLU PkQH QHVFKLPEDW RULFH PRGLILFDUH D DFHVWRU FRQGL LL DWU JkQG GXS VLQH PRGLILFDUHD SUREDELOLW LLúLGHFLPRGLILFDUHDOHJLLVWDWLVWLFHDIHQRPHQXOXL'HVFRSHULUHDDFHVWRUOHJL VWDWLVWLFHHVWHUH]XOWDWXOXQXLSURFHVvQGHOXQJDWGHDEVWUDFWL]DUH2ULFHOHJHVWDWLVWLF HVWH FDUDFWHUL]DW SH GH R SDUWH GH LQFRQVWDQ D UHODWLY YDULDELOLWDWHD GLQ FRPSRUWDUHD GLIHULWHORURELHFWHGDWRULW F UHLDQXSXWHPSUHYHGHDvQPRGXQLYRFFRPSRUWDUHDXQXL RELHFWVLQJXODULDUSHGHDOW SDUWHIDSWXOF vQWURPXO LPHPDUHGHIHQRPHQHDUHORFR FRQVWDQ VWDELO FDUHSURSULX]LVHVWHH[SULPDW GHOHJHDVWDWLVWLF 6WDWLVWLFDSUDFWLF VHUHIHU PDLFXVHDP ODFkPSXULGHHYHQLPHQWHILQLWHIRORVLQG úLFkPSXULGHHYHQLPHQWHLQILQLWHSHFkQGH[SHULHQ HOHGLQGRPHQLXOIL]LFLLúLDOWHKQLFLL GDXORFvQJHQHUDOODFkPSXULGHHYHQLPHQWHLQILQLWH ÌQ WHRULD SUREDELOLW LORU H[SHULPHQWHOH VWXGLDWH VXQW H[SHULPHQWH DOHDWRDUH úL ILHFDUHUHDOL]DUHDXQXLDVWIHOGHH[SHULPHQWVHYDQXPLSURE 5H]XOWDWXOXQHLSUREHHVWH XQHYHQLPHQW ([HPSOX ÌQ DUXQFDUHD FX ]DUXO PXO LPHD UHDOL] ULORU SRVLELOH YD IL : ^` &kWHYD HYHQLPHQWH $ ^` UH]XOWDW LPSDU % ^`

UH]XOWDW LQIHULRU OXL & ^` UH]XOWDW SDU 'DF OD R DUXQFDUH DSDUH ID D FX QXP UXO VXQWUHDOL]DWHHYHQLPHQWHOH $ úL % 1RWkQG SULQ : PXO LPHD WXWXURU UH]XOWDWHORU SRVLELOH DOH XQXL H[SHULPHQW úL SULQ : PXO LPHD WXWXURU S U LORU OXL : HYHQLPHQWHOH DOHDWRDUH VXQW HOHPHQWH

DOHOXL: ÌQ PXO LPHD 6 D HYHQLPHQWHORU DVRFLDWH XQXL H[SHULPHQW VH SRW LQWURGXFH WUHL RSHUD LLFRUHVSXQ] WRDUHRSHUD LLORUORJLFHÄVDX´ÄúL´ÄQRQ´)LH $ % 6 D Ä $ VDX % ´HVWHHYHQLPHQWXOFDUHVHUHDOL]HD] GDF úLQXPDLGDF VHUHDOL]HD] FHO SX LQXQXOGLQWUHHYHQLPHQWHOH $ VDX % $FHVWHYHQLPHQWVHQRWHD] SULQ $ * % úLVHYDQXPLUHXQLXQHDHYHQLPHQWHORU $ úL % E Ä $ úL % ´ HVWH HYHQLPHQWXO FDUH VH UHDOL]HD] GDF úL QXPDL GDF VH UHDOL]HD] DPEHOH HYHQLPHQWH $ úL % QXPLW LQWHUVHF LD DFHVWRU HYHQLPHQWH úL QRWDWSULQ $ % F ÄQRQ $ ´HVWHHYHQLPHQWXOFDUHVHUHDOL]HD] GDF úLQXPDLGDF QXVHUHDOL]HD] $ $FHVWHYHQLPHQWvOYRPQXPLFRQWUDUOXL $ úLVHQRWHD] $&

'DF ILHF UXLHYHQLPHQWvLDWDú PPXO LPHDGHSUREHSULQFDUHVHUHDOL]HD] DWXQFL RSHUD LLOH GLQWUH HYHQLPHQWH UHYLQ OD RSHUD LLOH UHVSHFWLYH GLQWUH PXO LPLOH GH SUREH FRUHVSXQ] WRDUH FHHD FH MXVWLILF QRWD LLOH D E úL F 5H]XOWDWHOH RSHUD LLORU FX HYHQLPHQWHVXQWWRWHYHQLPHQWHDWDúDWHH[SHULPHQWXOXLUHVSHFWLY 'DF $ % GHFL $ úL % QXVHSRWUHDOL]DVLPXOWDQVSXQHPF $ úL % VXQWHYHQLPHQWHLQFRPSDWLELOH ÌQ PXO LPHD 6 D HYHQLPHQWHORU DVRFLDWH XQXL DQXPLW H[SHULPHQW H[LVW GRX HYHQLPHQWH FX R VHPQLILFD LH GHRVHELW úL DQXPH HYHQLPHQWHOH : $ * $& úL

$ $& 3ULPXO FRQVW vQ SURGXFHUHD HYHQLPHQWXOXL $ VDX vQ SURGXFHUHD HYHQLPHQWXOXL $& FHHDFHDUHORFHYLGHQWvQWRWGHDXQDSULQXUPDUHDFHVWHYHQLPHQWQX GHSLQGHGHHYHQLPHQWXO $ vQVHQVXOF : $ * $& % * % & % ILLQGHYHQLPHQW GLQ PXO LPHD 6 (VWH QDWXUDO V QXPLP HYHQLPHQWXO : HYHQLPHQWXO VLJXU (YHQLPHQWXO FRQVW vQSURGXFHUHDHYHQLPHQWXOXL $ úLvQSURGXFHUHDHYHQLPHQWXOXL $& FHHD FH QX SRDWH DYHD ORF QLFLRGDW $FHVW HYHQLPHQW VH YD QXPL HYHQLPHQW

LPSRVLELO )LHHYHQLPHQWHOH $ % 6 6SXQHPF HYHQLPHQWXO $ LPSOLF HYHQLPHQWXO % úLVFULHP $ % GDF DWXQFLFkQGVHUHDOL]HD] $ VHUHDOL]HD] vQPRGQHFHVDU % 'DF DYHP VLPXOWDQ $ % úL % $ DWXQFL HYHQLPHQWHOH $ úL % VXQW HFKLYDOHQWH úL QRW P $ % DFHDVWD UHYLQH OD HJDOLWDWHD PXO LPLORU GH SUREH FDUH FRUHVSXQGHYHQLPHQWHORU ,PSOLFD LD GLQWUH HYHQLPHQWH HVWH R UHOD LH GH RUGRQDUH SDU LDO vQ PXO LPHD HYHQLPHQWHORUúLFRUHVSXQGHUHOD LHLGHLQFOX]LXQHGLQDOJHEUHOH%RROH 'HILQL LH 8Q HYHQLPHQW $ 6 HVWH FRPSXV GDF H[LVW GRX HYHQLPHQWH % & 6 % z $ & z $ DVWIHO FD $ % * & ÌQ FD] FRQWUDU HYHQLPHQWXO HVWH HOHPHQWDU $WRPLL DOJHEUHL %RROH D HYHQLPHQWHORU VH QXPHVF HYHQLPHQWH HOHPHQWDUH DOH FkPSXOXLQRWDWH Z HYHQLPHQWXOVLJXUHVWH : LDUHYHQLPHQWXOLPSRVLELO 'DF PXO LPHD : FRQ LQH XQ QXP U ILQLW GH HYHQLPHQWH HOHPHQWDUH : ^Z Z ZQ `DWXQFLXQHYHQLPHQWHVWHRSDUWHDOXL : úLGHFLYDFRQ LQHúLHO XQQXP UILQLW U Q GHHYHQLPHQWHHOHPHQWDUHÌQDFHVWFD]PXO LPHDHYHQLPHQWHORU 6 HVWH FKLDU : vQ JHQHUDO vQV DYHP 6 : úL 6 VH EXFXU GH SURSULHW L

DQDORDJHFXDOHOXL: $QDOL]D XQXL QXP U PDUH GH H[SHULPHQWH DOHDWRDUH D FRQGXV OD FRQFOX]LD XUP WRDUH $[LRP 0XO LPHD HYHQLPHQWHORU DVRFLDWH XQXL H[SHULPHQW FRQVWLWXLH R DOJHEU %RROH 'HILQL LH $OJHEUD %RROH D HYHQLPHQWHORU DVRFLDWH XQXL H[SHULPHQW VH QXPHúWH FkPSXOGHHYHQLPHQWHDOH[SHULPHQWXOXLUHVSHFWLY 'HFL FkPSXO GH HYHQLPHQWH YD IL R PXO LPH : vQ]HVWUDW FX XQ FRUS GH HYHQLPHQWH 6 úLVHYDQRWDSULQ ^: 6`

'HILQL LH 9RP QXPL FRUS ERUHOLDQ GH HYHQLPHQWH V FkPS R PXO LPH : vQ]HVWUDW FXXQFkPSERUHOLDQ V FkPS GHHYHQLPHQWH 6 úLVHYDQRWDGHDVHPHQHD SULQ ^: 6` 2EVHUYD LH8Q V FkPSHVWHFHHDFHvQWHRULDP VXULLQXPLPVSD LXP VXUDELO ([HPSOH 2XUQ FRQ LQH GHELOHQXPHURWDWHGHOD OD 6HH[WUDJHRELO úLvLUH LQHP QXP UXO6HFHUH D 6 VHVFULHHYHQLPHQWXOVLJXU E )LHHYHQLPHQWHOH $ ÄUH]XOWDWXOHVWHSDU´ % ÄUH]XOWDWXOHVWHPXOWLSOXGH´ úL & ÄUH]XOWDWXO HVWH R SXWHUH D OXL ´ 6 VH VFULH HYHQLPHQWHOH $ * %

$ % $& 6 VHDUDWHLPSOLFD LLOHGLQWUHHYHQLPHQWH&DUHHYHQLPHQWHVXQW

LQFRPSDWLELOH" 5 VSXQV D : ^` E $ * % ÄUH]XOWDWXOHVWHSDUVDXPXOWLSOXGH´ $ % ÄUH]XOWDWXOHVWHPXOWLSOX GH´ $& ÄUH]XOWDWXOHVWHLPSDU´ & $ úL & %

ÌQH[SHULHQ DDUXQF ULLFX]DUXOV VHVFULHFkPSXOGHHYHQLPHQWHDWDúDWH[SHULHQ HLúL V VHFDOFXOH]HQXP UXOGHHYHQLPHQWHGLQFkPS 5 VSXQV $YHP

6 ^ ^` L ^L M` ^L M N ` ^L M N O` ^L M N O P` :` XQGH L M N O P LDX YDORUL LQGHSHQGHQWH GH OD OD LDU vQ FDGUXO XQHL JUXSH WR L LQGLFLL VXQW GLIHUL L 'RX JUXSH FX DFHODúL QXP U GH LQGLFL GLIHU FHO SX LQ SULQWUXQ L ÄDSDUL LDIH HLFXQXP UXO L ´SULQ ^L M` ÄDSDUL LDIH HLFX LQGLFH6DQRWDWSULQ ^` QXP UXO L VDXDIH HLFXQXP UXO M ´GHFL ^L M`

L VXQWvQQXP UGH & (YHQLPHQWHOH ^`

^` L * ^ M` HWF ^L M`vQQXP UGH & ^L M N ` vQQXP U

GH & HWFGHFLvQFkPSDYHP & & & & &

HYHQLPHQWH

2XUQ FRQ LQH ELOHDOEH D D D D úL ELOHQHJUH Q Q 6HH[WUDJVLPXOWDQ GRX ELOH6HFHUH D 6 VHSUHFL]H]HSUREHOHH[SHULHQ HL E 6HFRQVLGHU HYHQLPHQWHOH $ ±RE LQHUHDDGRX ELOHQHJUH $ ±RE LQHUHD DGRX ELOHDOEH $ ±RE LQHUHDDFHOSX LQDXQHLELOHQHJUH $ ±RE LQHUHD XQHLVLQJXUHELOHDOEH $ ±RE LQHUHDXQHLVLQJXUHELOHQHJUH $ ±RE LQHUHD DGRX ELOHYHU]L 6 VHSUHFL]H]HFDUHGLQWUHHOHVXQWDOHDWRDUHHOHPHQWDUHVDXFRPSXVH SHUHFKL GH HYHQLPHQWH FRPSDWLELOH úL LQFRPSDWLELOH SHUHFKL GH HYHQLPHQWH HJDOHLPSOLFD LLOHGLQWUHHYHQLPHQWH

5 VSXQV D 1RWkQGVLPEROLFSULQ D D H[WUDJHUHDELOHORU D úL D HWFSUREHOHH[SHULHQ HL

VXQW D D D D D D D D D D D D D Q D Q

D Q D Q D Q D Q D Q D Q Q Q 1XP UXOSUREHORUHVWH &

E (YHQLPHQWHOH $ $ $ $ $ VXQWDOHDWRDUH (YHQLPHQWXO $ HVWHLPSRVLELOHOQXHVWHQLFLHOHPHQWDUQLFLFRPSXV (YHQLPHQWXO $ HVWH HOHPHQWDU HO VH UHDOL]HD] SULQWUR VLQJXU SURE

Q Q $YHP $ ^Q Q `

(YHQLPHQWHOH $ $ $ $ VXQWHYHQLPHQWHFRPSXVH $YHP $ $ GHRDUHFHUHDOL]DUHDOXL $ DWUDJHGXS VLQHUHDOL]DUHDOXL $ úL UHFLSURF6HREVHUY DFHDVWDúLGLQHJDOLWDWHDPXO LPLORUGHSUREH $ ^D Q D Q D Q D Q D Q D Q D Q D Q `

$

^Q D Q D Q D Q D Q D Q D Q D Q D `

'HDVHPHQHDDYHP

$ ^D D D D D D D D D D D D ` $ ^D Q D Q D Q D Q D Q D Q D Q D Q Q Q ` 6XQWFRPSDWLELOHSHUHFKLOH $ $ $ $ 6HSRWUHDOL]DVLPXOWDQ $ $ 6XQW LQFRPSDWLELOH SHUHFKLOH $ $ $ $ $ $ $ $ $ $ $ $ (YHQLPHQWHOH $ úL $ $ úL $ $ úL $ $ úL $ $ úL $ VXQW FRQWUDUH $YHPLPSOLFD LLOH $ $ $ $ $ $ $ $ 9RPGDFkWHYDSURSULHW LDOHHYHQLPHQWHORUHOHPHQWDUH ( )LH $ 6 XQ HYHQLPHQW HOHPHQWDU úL % 6 XQ HYHQLPHQW RDUHFDUH 'DF % $ DWXQFL % VDX % $ 3UHVXSXQkQG % z úL % z $ UH]XOW F HYHQLPHQWXO & % $ HVWHGLIHULWGH $ úLGH GHFL $ % * & FHHDFHHVWHLPSRVLELOGHRDUHFH $ HVWHHOHPHQWDU ( &RQGL LD QHFHVDU úL VXILFLHQW FD XQ HYHQLPHQW $ 6 $ z V ILH HOHPHQWDUHVWHV QXH[LVWHXQHYHQLPHQW % 6 % z FX % $ 3UHVXSXQkQG F H[LVW % 6 FX % z úL % $ UH]XOW % z $ 'LQ $ $ % * % & $ % * $ % & LQkQG VHDPD F % $ % GHRDUHFH

% $ UH]XOW $

% * $ %

&

$ % & DYHP & z $ GHRDUHFHvQFD]FRQWUDUDPDYHD % $ % & % $ % & % $ % & % $ ÌQUHOD LD $ % * & DYHP % z $ & z $ FHHDFHHVWHDEVXUGGHRDUHFH $ 1RWkQG &

HVWHXQHYHQLPHQWHOHPHQWDU ÌQPRGDQDORJVHGHPRQVWUHD] ( &RQGL LDQHFHVDU úLVXILFLHQW FDXQHYHQLPHQW $ z V ILHHOHPHQWDUHVWH FDSHQWUXRULFHHYHQLPHQW % V DYHP $ % VDX $ % $ ( 'RX HYHQLPHQWHHOHPHQWDUHGLVWLQFWHVXQWLQFRPSDWLELOH )LHHYHQLPHQWHOHHOHPHQWDUH $ úL $ FX $ z $ 3UHVXSXQHP $ $ z (YHQLPHQWXO $ HVWH HOHPHQWDU GHFL FRQIRUP FX ( $ ILLQGHOHPHQWDUDYHP $

$ $ $QDORJ $ $ $ 'LQDFHVWHUHOD LLUH]XOW $ $ FHHDFHQXVH

SRDWHGHFL $ $ ( ÌQWUR DOJHEU ILQLW GH HYHQLPHQWH SHQWUX RULFH HYHQLPHQW FRPSXV % 6 H[LVW XQHYHQLPHQWHOHPHQWDU $ $ % 'HPRQVWUD LDHVWHLPHGLDW LQkQGVHDPDGH ( ( 2ULFHHYHQLPHQWGLQWURDOJHEU ILQLW GHHYHQLPHQWHVHSRDWHVFULHVXEIRUP XQLF FDRUHXQLXQHGHHYHQLPHQWHHOHPHQWDUH )LH % 6 XQHYHQLPHQWFRPSXV LQkQGVHDPDGH ( H[LVW XQHYHQLPHQW HOHPHQWDU $ FX $ % 1RW P %

% $ GHFL %

$ * %

'DF % HVWHHYHQLPHQWHOHPHQWDUSULPDSDUWHDSURSR]L LHLHVWHGHPRQVWUDW 'DF % HVWHHYHQLPHQWFRPSXVH[LVW XQHYHQLPHQWHOHPHQWDU $ % 1RW P

%

% $ GHFL % $ * % úLGHFL % $ * $ * % 'DF % HVWHHYHQLPHQWHOHPHQWDUQHRSULPDLFLFXGHVFRPSXQHUHD'DF %

HVWHHYHQLPHQWFRPSXVFRQWLQX PSURFHGHXO$OJHEUDILLQGILQLW GXS XQQXP UILQLWGH SDúLRE LQHP % $ * $ * * $N XQGH $L L N VXQWHYHQLPHQWHHOHPHQWDUH 6 SUHVXSXQHPF GHVFRPSXQHUHD QXHVWHXQLF GHFLF % $ * $ * * $N $c * $c * * $Uc XQGHVSUHH[HPSOX $ z $Vc V U $YHP

$ $ * $ * * $N $ $c * $c * * $c GHXQGH LQkQGVHDPDGH ( úLGHUHOD LD UH]XOW $ FHHDFHHVWHDEVXUG

'HDLFLUH]XOW ( ÌQWUR DOJHEU ILQLW GH HYHQLPHQWH HYHQLPHQWXO VLJXU HVWH UHXQLXQHD WXWXURU HYHQLPHQWHORUHOHPHQWDUH

3UREDELOLWDWHSHXQFkPSILQLWGHHYHQLPHQWH

6 FRQVLGHU PRXUQ 8 FDUHFRQ LQH Q ELOHGLQWUHFDUH P DOEHúL Q P QHJUH ELOHGLIHU QXPDLSULQFXORDUH 6HH[WUDJHODvQWkPSODUHRELO $YHP Q HYHQLPHQWH HOHPHQWDUH )LH $ HYHQLPHQWXO ÄELOD H[WUDV V ILH DOE ´ $FHVW HYHQLPHQW VH SRDWH UHDOL]DSULQ P SUREH P d Q 'HILQL LH 6H QXPHúWH SUREDELOLWDWHD HYHQLPHQWXOXL $ UDSRUWXO GLQWUH QXP UXO FD]XULORUIDYRUDELOHUHDOL] ULLOXL $ úLQXP UXOFD]XULORUHJDOSRVLELOH'HFL

3 $

P Q

$FHDVWD HVWH GHILQL LD FODVLF D SUREDELOLW LL (D VH SRDWH IRORVL QXPDL vQ H[SHULPHQWHFXHYHQLPHQWHHOHPHQWDUHHJDOSRVLELOH 6 FRQVLGHU PDFXPRXUQ FDUHFRQ LQH Q ELOHGLQWUHFDUH D ELOHGHFXORDUHD F D ELOHGHFXORDUHD F DV ELOHGHFXORDUHD FV $VWIHO Q D D DV %LOHOHGLIHU vQWUHHOHQXPDLSULQFXORDUH6HH[WUDJHRELO GLQXUQ ÌQDFHVWFD]H[WUDF LDXQHLELOHHVWH HYHQLPHQWHOHPHQWDU3UREDELOLWDWHDH[WUDJHULLXQHLELOHGHFXORDUH FO YDILGDW GHGHILQL LD FODVLF D SUREDELOLW LL 3

DO GHFL HYHQLPHQW IDYRUDELO HVWH H[WUDF LD XQHL ELOH GH Q

FXORDUH FO 8Q HYHQLPHQW RDUHFDUH DO FkPSXOXL HVWH DSDUL LD XQHLD GLQ ELOH DYkQG FXORDUHD FO FO FOV QRWDW $ SHQWUXFDUH

3 $

DO DO DOV Q

'HDLFLUH]XOW F SUREDELOLWDWHD ILHF UXL HYHQLPHQW HVWH R IXQF LH GH DFHVW HYHQLPHQW DYkQG YDORUL SR]LWLYH

D D DQ Q GDF $ $ * $ FX $ $ DWXQFL 3 $ 3 $ 3 $ HYHQLPHQWHOHHOHPHQWDUHVXQWHJDOSUREDELOHDXSUREDELOWDWHD Q SUREDELOLWDWHDHYHQLPHQWXOXLVLJXU : HVWH 3 :

6HREVHUY F H[SHULPHQWXOH[WUDF LHLGLQWURXUQ SRDWHILLQWHUSUHWDWFXDMXWRUXOD GRX FkPSXUL GH HYHQLPHQWH FkPSXO FRQVLGHUDW PDL VXV SHQWUX FDUH HYHQLPHQW HOHPHQWDU HVWH H[WUDF LD XQHL ELOH úL XQ DOW FkPS ** SHQWUX FDUH HYHQLPHQW

HOHPHQWDU HVWH H[WUDF LD XQHL ELOH GH FXORDUH FO O V )XQF LD 3 $ FDUH UHSUH]LQW SUREDELOLWDWHDXQXLHYHQLPHQWRDUHFDUHGLQ * DUHSURSULHW LOHúLGDUQX YHULILF vQ JHQHUDO SURSULHWDWHD GHRDUHFH HYHQLPHQWHOH HOHPHQWDUH GLQ * QX DX

SUREDELOLW L HJDOH GHFkW SHQWUX Q Q QV ÌQ DFHVW FD] QX VH PDL DSOLF GHILQL LDFODVLF DSUREDELOLW LL 6 FRQVLGHU PRXUQ FX ELOHQXPHURWDWHGHOD OD 6HH[WUDJHODvQWkPSODUH RELO 1RWkQGFX $L L HYHQLPHQWXOFDUHFRQVW vQH[WUDJHUHDELOHLFXQXP UXO L DYkQG vQ YHGHUH F ELOHOH GLIHU vQWUH HOH QXPDL SULQ QXP UXO vQVFULV UH]XOW F HYHQLPHQWHOH $L VXQWHJDOSRVLELOHGHFLvQPRGILUHVFRIXQF LHGHSUREDELOLWDWHGHILQLW SHPXO LPHD $L dLd VDWLVIDFHFRQGL LD 3 $L

S XQGH S

(YHQLPHQWXO $L * $ M L z M HVWH XQ HYHQLPHQW GH GRX RUL PDL SUREDELO GHFkW ILHFDUH GLQ HYHQLPHQWHOH $L GHFL SUHOXQJLUHD IXQF LHL 3 OD HYHQLPHQWHOH

$L * $ M

WUHEXLH

GHILQLW

FD

3 $L * $ M 3 $L 3 $ M ÌQJHQHUDO

3 $L * * $LN

3 $L * 3M

L z M

GHRDUHFH

N d L d d LN d

úL 3: XQGH : HVWHHYHQLPHQWXOVLJXU

'HFLvQFD]XOXQXLFkPSILQLWGHHYHQLPHQWH ^: 6` RSUREDELOLWDWHSHDFHVWFkPS RYRPGHILQLDVWIHO 'HILQL LH6HQXPHúWHSUREDELOLWDWHSH 6 RDSOLFD LH 3 6 o \ FDUHVDWLVIDFH XUP WRDUHOHD[LRPH 3 $ t SHQWUXRULFH $ 6 3:

3 $ * $ 3 $ 3 $ SHQWUXRULFH $ $ 6 FX $ $ 3URSULHWDWHD VH H[WLQGH SULQ UHFXUHQ OD RULFH QXP U ILQLW GH HYHQLPHQWH LQFRPSDWLELOHGRX FkWHGRX 'HFLGDF $L $ M L z M L M Q DWXQFL

§ Q · 3¨¨ $L ¸¸ ©L ¹

Q

¦ 3 $ L

L

([HPSOX ÌQWUR SXQJ VH J VHVF ELOHWH GH ORWR GLQWUH FDUH XQ ELOHW FkúWLJ WRU D OHL ELOHWH FkúWLJ WRDUH D OHL ILHFDUH ELOHWH FkúWLJ WRDUH D OHLILHFDUHúL ELOHWHFkúWLJ WRDUHD OHLILHFDUH&LQHYDFXPS U XQELOHW &DUHHVWHSUREDELOLWDWHDFDFXPS U WRUXOV FkúWLJHFHOSX LQ OHL" 9RP FRQVLGHUD XUP WRDUHOH HYHQLPHQWH $ FXPS U WRUXO FkúWLJ FHO SX LQ OHL $ ± FXPS U WRUXO FkúWLJ OHL $ ± FXPS U WRUXO FkúWLJ

OHL $ ±FXPS U WRUXOFkúWLJ OHL

$YHPHYLGHQW $

$ * $ * $ FX $L $ M

3 $ 3 $ 3 $ 3 $

L z M L M 'HFL

'HILQL LH1XPLPFkPSGHSUREDELOLWDWHILQLWXQFkPSILQLWGHHYHQLPHQWH ^: 6`

vQ]HVWUDWFXRSUREDELOLWDWH 3 QRWDW ^: 6 3` 'LQ UHJXOD GH DGXQDUH D SUREDELOLW LORU GHGXFHP F SHQWUX D FXQRDúWH SUREDELOLW LOH WXWXURU HYHQLPHQWHORU $ 6 HVWH VXILFLHQW V FXQRDúWHP SUREDELOLW LOH HYHQLPHQWHORU HOHPHQWDUH ZL d L d U FDUH DOF WXLHVF PXO LPHD ILQLW

^Z ZU `

: $

GHRDUHFH GDF QRW P 3^ZL `

SL d L d U úL GDF

ZL * * ZLN DWXQFL 3 $

3 ZL * * ZL

3 ZL

N

3 ZL

N

SL SL N

'HFL XQ FkPS ILQLW GH SUREDELOLWDWH HVWH FRPSOHW FDUDFWHUL]DW GH QXPHUHOH QHQHJDWLYH S S SU FX

U

¦S L

L

N XQGH N UHSUH]LQW QXP UXOGHHYHQLPHQWH U HOHPHQWDUH FDUH LQWU vQ FRPSXQHUHD HYHQLPHQWXOXL $ HYHQLPHQWH HOHPHQWDUH IDYRUDELOHHYHQLPHQWXOXL $ 6HDMXQJHDVWIHOODGHILQL LDFODVLF DSUREDELOLW LL 'DF S

3

SU DWXQFL 3 $

'LQGHILQL LDSUREDELOLW LLUH]XOW XUP WRDUHOHSURSULHW L 3HQWUXRULFH $ 6 3 $& 3 $

'LQ $ * $& : $ $& úLGLQD[LRPHOH úL UH]XOW LPHGLDWDFHDVW SURSULHWDWH ([HPSOX 8Q DSDUDW DFKL]L LRQDW GH R X]LQ WUHEXLH SXV vQ IXQF LXQH 6H SRW LYL XUP WRDUHOHVLWXD LL D REXQ VWDUHGHIXQF LRQDUH E XQXúRUGHUHJODM F WUHEXLHvQORFXLWHFkWHYDSLHVH G VHLPSXQHRUHYL]LHJHQHUDO ÌQSULPXOFD]DSDUDWXOFRQWLQX V IXQF LRQH]HÌQFD]XOE UHJODMXOGXUHD] PLQXWHvQFD]XOF SLHVHOHVHvQORFXLHVFvQWURRU LDUUHYL]LDJHQHUDO VHIDFHvQ RUH 3UREDELOLW LOHFHORUSDWUXHWDSHVXQW 6 VHGHWHUPLQHSUREDELOLWDWHDFDDSDUDWXOV ILHvQP VXU V IXQF LRQH]HGXS FHO SX LQGRX RUHGHODLQVWDODUH 5 VSXQV &RQVLGHU P XUP WRDUHOH HYHQLPHQWH $ DSDUDWXO HVWH JDWD GH IXQF LRQDUH GXS RUH $ DSDUDWXOSRDWHIXQF LRQDLPHGLDW $ DSDUDWXOQHFHVLW XQUHJODM $ HVWHQHFHVDUV vQORFXLPFkWHYDSLHVH

$YHPHYLGHQW $

$ * $ * $ 'HFL 3 $ 3 $ 3 $

3 $

VDX

3 $ 3 $& 3 $YHP 3 $FHDVWDUH]XOW LPHGLDWGLQ 3 GLQREVHUYD LD & : úLD[LRPD 3 3HQWUXRULFH $ 6 DYHP d 3 $ d $[LRPD QH VSXQH F 3 $ t 'LQ úL SURSULHWDWHD 3 UH]XOW 3 $ d 3 3HQWUXRULFH $ $ 6 FX $ $ DYHP 3 $ d 3 $ $YHP $ $ * $ $& XQGH $ $ $& GHFL GLQ UH]XOW 3 $ 3 $ 3 $ $& 'DU 3 $ $& t GHXQGH 3 $ t 3 $ 3 3HQWUXRULFH $ $ 6 DYHP 3 $ $ 3 $ 3 $ $ 'LQ $ $ $ * $ $ $ $ $ $ úL D[LRPD

UH]XOW SURSULHWDWHDHQXQ DW 3 'DF $ $ $ $ 6 DWXQFL 3 $ $

3 $ 3 $

$FHDVW SURSULHWDWH UH]XOW GLQ SURSULHWDWHD 3 3 GHRDUHFH vQ DFHVW FD]

$ $

$ 3 3 $ * $ 3 $ 3 $ 3 $ $ RULFDUHDUIL $ $ 6 'LQUHOD LLOH $ * $ $ * $ $ $ $ $ $ $ GLQ D[LRPD úL SURSULHWDWHD 3 DSOLFDW SHQWUX $ $ $ UH]XOW SURSULHWDWHD HQXQ DW 'HDLFLUH]XOW LPHGLDW 3 3 $ * $ d 3 $ 3 $ RULFDUHDUIL $ $ 6 'DF $L dLdQ 6 DWXQFL

3

§ Q · 3 ¨ $L ¸ ©L ¹

Q

¦ 3$ ¦ 3$ $ L

L

¦

dL M d Q

dL M N d Q

L

M

3 $L $M $N

Q

§ Q · 3 ¨ $L ¸ ©L ¹

$FHDVW UHOD LH VH GHPRQVWUHD] SULQ LQGXF LH úL LQkQG VHDPD GH SURSULHWDWHD

3

3 )LHHYHQLPHQWHOH $L dLdQ 6 FX 3 $ $Q z DWXQFL

§ Q · 3 ¨ $N ¸ ©N ¹

3 $ 3 $ $ 3 $ $ $ 3 $Q $ $Q

)RUPXOD VH GHPRQVWUHD] SULQ LQGXF LH 3UREDELOLW LOH GLQ PHPEUXO GRL H[LVW GHRDUHFHGLQ $ $Q $ $Q $ $ $ UH]XOW 3 $ $Q d 3 $ $Q d d 3 $ $ d 3 $

&DLOXVWUDUHDSURSULHW LORU 3 úL 3 V FRQVLGHU PXUP WRDUHOHSUREOHPH ([HPSOX3UREOHPDFRQFRUGDQ HORU>@ÌQWURXUQ VXQW Q ELOHQXPHURWDWHGH OD OD Q ([WUDJHP SH UkQG FkWH R ELO I U D R UHSXQH vQ XUQ (VWH SRVLELO FD vQ H[WUDF LDGHUDQJ L V H[WUDJHPELODQXPHURWDW FX L "6SXQHPvQDFHVWFD]F DYHPR FRQFRUGDQ 5 VSXQV )LH S SUREDELOLWDWHDFDI FkQG Q H[WUDF LLV DSDU FHOSX LQRFRQFRUGDQ 'DF QRW P SULQ $L HYHQLPHQWXOFDvQH[SHULPHQWXOGHUDQJ L d L d Q V DSDU R

Q

GHRDUHFHVXQW Q Q SRVLELOH Q FD]XULFHOH Q ELOHVHSRWH[WUDJHvQ Q PRGXULGLIHULWH úL Q FD]XUL IDYRUDELOHGHRDUHFHELODQXPHURWDW FXQXP UXO L WUHEXLHH[WUDV H[DFWvQH[WUDF LDGH UDQJ L GHFLQXPDLFHOH Q ELOHU PDVHVHSRWSHUPXWDRULFXPvQWUHHOH FRQFRUGDQ DYHP S

$QDORJ

3 $ * * $Q XQGH 3 $L

3 $L $ M $N

Q

d L M d Q Q QQ Q d L M N d Q HWF Q QQ Q

3 $L $ M

ÌQUHOD LDGLQ 3 ILHFDUHWHUPHQHVWHODUkQGXOV XRVXP GHWHUPHQLHJDOLúL DQXPH &QN WHUPHQLXQGH N HVWHQXP UXOLQGLFLORUGXS FDUHVHVXPHD] $YHPGHFL

S VDX

Q

Q &Q &Q &QQ Q QQ QQ Q Q S

Q Q

2EVHUY PF QRWkQGSULQ T SUREDELOLWDWHDHYHQLPHQWXOXLFRQWUDUDWXQFL

T S LDUSHQWUX Q o f RE LQHP T o

H

Q Q

([HPSOX8QORWGH SURGXVHHVWHVXSXVXQXLFRQWUROGHFDOLWDWH/RWXOHVWH UHVSLQVGDF VHJ VHúWHFHOSX LQXQUHEXWOD SLHVHFRQWURODWHODvQWkPSODUHùWLLQGF ORWXOFRQ LQH SLHVHGHIHFWHV VHGHWHUPLQHSUREDELOLWDWHDFDORWXOV ILHUHVSLQV 5 VSXQV 1RWkQGFX $ HYHQLPHQWXOÄORWXOWUHEXLHUHVSLQV´YRPFDOFXOD 3 $& 1RWkQG

FX $N HYHQLPHQWXOÄSLHVD N FRQWURODW HVWHEXQ ´ d N d úL LQkQGVHDPDGHIDSWXO F HYHQLPHQWHOH $N QXVXQWLQGHSHQGHQWHDYHP

3 $&

LDU 3 $

3 $ $

3 $ 3 $ $ 3 $ $ $ 3 $ $ $ $ $

3 $&

V FkPSGHSUREDELOLWDWH

&DOHD SH FDUH R XUP ULP vQ GHILQLUHD V FkPSXOXL GH SUREDELOLWDWH FRUHVSXQGH D[LRPDWLFLLWHRULHLSUREDELOLW LORUGDW GH$1.ROPRJRURY>@vQ 'HILQL LH )LH ^: 6` XQ V FkPS GH HYHQLPHQWH 1XPLP SUREDELOLWDWH SH FkPSXO ^: 6` RIXQF LHQXPHULF SR]LWLY 3 GHILQLW SH 6 GDF

3:

§

· $L ¸¸ ¦ 3 $L SHQWUX RULFH IDPLOLH QXP UDELO GH HYHQLPHQWH © L, ¹ L, $L L, 6 LQFRPSDWLELOHGRX FkWHGRX 2EVHUY PF SUREDELOLWDWHDHVWHRP VXU SHQWUXFDUH P: 'HFLXQ V FkPSGHSUREDELOLWDWHYDILXQ V FkPSGHHYHQLPHQWH ^: 6` vQ]HVWUDWFXRSUREDELOLWDWHHOVHYDQRWDFX ^: 6 3`

3¨¨

3URSULHW LOHSUREDELOLW LLDPLQWLWHSHQWUXXQFkPSILQLWGHSUREDELOLWDWHVHH[WLQGúL OD V FkPSXULOH GH SUREDELOLWDWH ÌQ SOXV GDF ^: 6 3` HVWH XQ V FkPS GH SUREDELOLWDWHDYHPXUP WRDUHOHSURSULHW L 3 3HQWUX RULFH úLU GH HYHQLPHQWH $Q Q` 6 SHQWUX FDUH $Q $Q GHVFHQGHQW DYHP

OLP 3 $Q Q of

§ · 3¨ $ ¨ Q ¸¸ © Q` ¹

úL SHQWUX RULFH úLU GH HYHQLPHQWH DVFHQGHQW DYHP

OLP 3 $Q Q of

$Q Q` 6

SHQWUX FDUH $Q $Q

§ · 3¨ $ Q ¸ ¨ ¸ © Q` ¹

3HQWUX GHPRQVWUD LD SULPHL UHOD LL YRP DU WD F GDF

OLP 3 $Q

Q`

$Q

DWXQFL

Q of

ÌQ DGHY U GLQ $Q

f P Q

$P $P

DYHP 3 $Q

f

¦ 3 $

P Q

P

$P

3HQWUX Q VHULD HVWH FRQYHUJHQW UHVWXO VHULHL ILLQG FRQYHUJHQW F WUH ]HUR 3XWHPVFULH f

OLP ¦ 3 $P $P Q of

GHFL

P Q

OLP 3 $Q Q of

1RW P %

%Q

Q`

Q`

$Q %Q

$Q % ùLUXO

%Q Q`

HVWH GHVFHQGHQW úL

GHFL OLP 3 %Q Q of

'DU

3 %Q

3 $Q 3 %

GHFL

§ · 3 $Q 3 ¨ $Q ¸ ¨ ¸ © Q` ¹

§ · OLP 3 $Q 3¨¨ $Q ¸¸ Q of © Q1 ¹

3HQWUXGHPRQVWUD LDFHOHLODOWHUHOD LLVHDUDW F DFHDVWDHVWHHFKLYDOHQW FXSULPD GHPRQVWUD LHSHFDUHRO V PSHVHDPDFLWLWRULORU 3 3§¨ OLP $Q ·¸ d OLP 3 $Q d OLP 3 $Q d 3 OLP $Q

© Q of ¹ $Q Q` 6 &XQRWD LD %Q

Q of

f S

Q of

SHQWUX

$Q S %Q Q` HVWHDVFHQGHQWúL

3§¨ OLP $Q ·¸ © Q of ¹

Q of

3 OLP %Q Q of

OLP 3%Q d OLP 3 $Q Q of

Q of

RULFH

úLU

GHRDUHFH 3 %Q d 3 $Q S SHQWUXRULFH S ` $QDORJ 3 OLP $Q t OLP 3 $Q 'DU OLP 3 $Q d OLP 3 $Q Qof

Qof

Q of

Q of

'HDLFLUH]XOW FDRFRQVHFLQ LPHGLDW 3 SURSULHWDWHD GH FRQWLQXLWDWH VHFYHQ LDO D SUREDELOLW LL 'DF úLUXO

$Q Q` 6 3 OLP $Q Qof

HVWH

FRQYHUJHQW

OLP 3 $Q

§ OLP $ ¨ Q of Q ©

OLP $Q ·¸ Q of ¹

DWXQFL

Qof

§ · $Q ¸ d ¦ 3 $Q ¨ ¸ © Q` ¹ Q`

3 3 ¨

$YHP

§ · 3¨¨ $Q ¸¸ © Q1 ¹

Q § Q · OLP 3¨¨ $L ¸¸ d OLP ¦ 3 $L Qof © L ¹ Q of L

¦ 3 $

Q1

Q

$YHPHJDOLWDWHQXPDLGDF HYHQLPHQWHOHVXQWPXWXDOGLVMXQFWH (YHQLPHQWHLQGHSHQGHQWH3UREDELOLWDWHFRQGL LRQDW 6 FRQVLGHU P H[SHULPHQWXO FDUH FRQVW vQ DUXQFDUHD D GRX PRQH]L úL ILH HYHQLPHQWHOH $ V RE LQHPVWHPDSHSULPDPRQHG úL % V DSDU VWHPDSHPRQHGD DGRXD ÌQ DFHVW FD] SUREDELOLWDWHD HYHQLPHQWXOXL $ QX GHSLQGH GH UHDOL]DUHD HYHQLPHQWXOXL % GHFLHYHQLPHQWXO $ HVWHLQGHSHQGHQWGHHYHQLPHQWXO % 6 FRQVLGHU P R XUQ FDUH FRQ LQH ELOH DOEH úL ELOH QHJUH 'RX SHUVRDQH H[WUDJILHFDUHFkWHRELO GLQXUQ )LHHYHQLPHQWHOH $ SULPDSHUVRDQ DH[WUDVRELO DOE úL $ DGRXDSHUVRDQ DH[WUDVRELO DOE 3UREDELOLWDWHDHYHQLPHQWXOXL $ vQ DEVHQ D LQIRUPD LLORU DVXSUD OXL $ HVWH SUREDELOLWDWHD HYHQLPHQWXOXL $ HVWH GH GHSLQGHGHHYHQLPHQWXO $

'DF HYHQLPHQWXO $ VD UHDOL]DW

GH XQGH FRQFOX]LD F HYHQLPHQWXO $

'HILQL LH (YHQLPHQWHOH $ % DOH FkPSXOXL GH SUREDELOLWDWH ^: 6 3` VXQW 3 LQGHSHQGHQWHGDF 3 $ % 3 $ 3% 6H SRDWH DU WD FX XúXULQ F GDF HYHQLPHQWHOH $ % 6 VXQW

3 LQGHSHQGHQWH DWXQFL SHUHFKLOH GH HYHQLPHQWH $ % & % $& $& % & VXQW 3 LQGHSHQGHQWH

$SOLFD LH 'RL WU J WRUL WUDJ VLPXOWDQ DVXSUD XQHL LQH FkWH XQ IRF ILHFDUH 3UREDELOLW LOHGHQLPHULUHD LQWHLVXQW SHQWUXSULPXOWU J WRUúL SHQWUXDOGRLOHD WU J WRU6 VHGHWHUPLQHSUREDELOLWDWHDFD LQWDV ILHDWLQV GHFHOSX LQXQWU J WRU 5 VSXQV )LHHYHQLPHQWHOH $L WU J WRUXOFXQXP UXO L L QLPHUHúWH LQWD$YHP

3 $ * $ 3 $ 3 $ 3 $ $ 'HILQL LH(YHQLPHQWHOH $L dLdQ 6 VXQW 3 LQGHSHQGHQWH P FkWH P GDF SHQWUX K d P úL d L L LK d Q DYHP 3 $L $LK 3 $L 3 $L 3 $LK 'DF P

Q HYHQLPHQWHOHVXQW 3 LQGHSHQGHQWHvQWRWDOLWDWHDORU

2EVHUYD LH 'DF Q HYHQLPHQWH VXQW LQGHSHQGHQWH GRX FkWH GRX QX VXQW QHDS UDW LQGHSHQGHQWH vQ WRWDOLWDWHD ORU $FHVW OXFUX VH YHGH GLQ H[HPSOXO XUP WRU GDWRUDW OXL61%HUQúWHLQ 6HFRQVLGHU XQWHWUDHGUXRPRJHQFXIH HOHFRORUDWHvQDOEQHJUXURúXúLDSDWUD vQ FHOH WUHL FXORUL (IHFWX P H[SHULPHQWXO DUXQF ULL DFHVWXL FRUS R VLQJXU GDW 6 QRW PFX $L HYHQLPHQWXOFDWHWUDHGUXOV VHDúH]HSHID DFXQXP UXO L L (YHQLPHQWHOH $L VXQW HYHQLPHQWH HOHPHQWDUH DOH FkPSXOXL DVRFLDW H[SHULPHQWXOXL GHVFULV

L 'DF QRW P $ $ * $ % $ * $ $ * $ DYHP 3 $ 3% 3 & GHRDUHFHSHQWUXILHFDUHFXORDUH $YHP 3 $L

&

VXQWSDWUXFD]XULSRVLELOHúLGRX FD]XULIDYRUDELOH±ID DFXFXORDUHDUHVSHFWLY úL ID DFXWRDWHFXORULOH 'H

DVHPHQHD

3 $ % 3% & 3& $

GHFL

HYHQLPHQWHOH $ % & VXQW 3 LQGHSHQGHQWH GRX FkWH GRX $YHP vQV

3 $ 3 % 3 & GH XQGH UH]XOW F HYHQLPHQWHOH $ % & QXVXQW 3 LQGHSHQGHQWHvQWRWDOLWDWHDORU 3 $ % & 3 $

'HILQL LH6SXQHPF HYHQLPHQWHOH $Q Q` 6 VXQW 3 LQGHSHQGHQWHGDF

RULFHQXP UILQLWGHHYHQLPHQWHGLQDFHVWúLUVXQW 3 LQGHSHQGHQWH $SOLFD LH 8Q DSDUDW VH FRPSXQH GLQ WUHL HOHPHQWH D F URU ILDELOLWDWH GXUDWD GH IXQF LRQDUH I U GHIHF LXQH WRW WLPSXO vQWUXQ LQWHUYDO GH WLPS GDW HVWH HJDO FX úL

3ULPXOHOHPHQWHVWHLQGLVSHQVDELOSHQWUXIXQF LRQDUHDDSDUDWXOXLGHIHFWDUHDXQXLDGLQ FHOHODOWH GRX HOHPHQWH IDFH FD DSDUDWXO V IXQF LRQH]H FX XQ UDQGDPHQW LQIHULRU LDU GHIHFWDUHD VLPXOWDQ D HOHPHQWHORU GRL úL WUHL IDFH LPSRVLELO IXQF LRQDUHD DSDUDWXOXL (OHPHQWHOH VH GHIHFWHD] LQGHSHQGHQW XQXO GH DOWXO 6H FHUH SUREDELOLWDWHD FD DSDUDWXO V IXQF LRQH]HWRWWLPSXOvQWUXQLQWHUYDOGHWLPSGDW 5 VSXQV )LHHYHQLPHQWHOH $L HOHPHQWXO L L IXQF LRQHD] I U GHIHF LXQHúL $ DSDUDWXOIXQF LRQHD] FKLDUFXXQUDQGDPHQWLQIHULRU$YHP $ $ $ $ * $ $& $ * $ $ $& $VWIHO

3 $

3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ $ $ 3 $ $& $ 3 $ $ $&

&

&

ÌQH[HPSOXOFXXUQDDPY ]XWF UH]XOWDWXOH[SHULPHQWXOXLGHFDUHHVWHOHJDW $

LQIOXHQ HD] FRQGL LLOHH[SHULPHQWXOXLGHFDUHHVWHOHJDW $ H[WU JkQGGLQXUQ RELO DOE SULPDSHUVRDQ YRUU PkQHvQXUQ SHQWUXH[WUDF LDFHYDILHIHFWXDW GHSHUVRDQDD GRXDQXPDL ELOHDOEHúL QHJUH 'HFL SUREDELOLWDWHD HYHQLPHQWXOXL $ YDULD] vQ IXQF LH GH UHDOL]DUHD OXL $ vQ

GDF VDUHDOL]DW $ VDX GDF QXVDUHDOL]DW $ (VWH GHFL QDWXUDO V QXPLP SUREDELOLWDWHD HYHQLPHQWXOXL $ FRQGL LRQDW GH HYHQLPHQWXO $ úLV RQRW PSULQ 3 $ $ VDX 3$ $

VHQVXOF DFHDVW SUREDELOLWDWHHVWH

'HILQL LH )LH ^: 6 3` XQ V FkPS GH SUREDELOLWDWH úL $ % 6 FX

3% z 1XPLPSUREDELOLWDWHDHYHQLPHQWXOXL $ FRQGL LRQDW GHHYHQLPHQWXO %

UDSRUWXO

3 $ %

1RW PúL 3 $ %

3 %

3 $ %

3% $

7ULSOHWXO ^: 6 3% `HVWHXQ V FkPSGHSUREDELOLWDWHGDF ^: 6 3`HVWHXQ V FkPSGHSUREDELOLWDWH6HYHULILF FXXúXULQ D[LRPHOHGLQGHILQL LDSUREDELOLW LL

$QDORJ SXWHP GHILQL SUREDELOLWDWHD HYHQLPHQWXOXL % FRQGL LRQDW GH 3 $ % HYHQLPHQWXO $ 3 % $ XQGH 3 $ z 3 $

'LQFHOHGRX UHOD LL LQkQGVHDPDGHSURSULHWDWHDGHFRPXWDWLYLWDWHDLQWHUVHF LHL UH]XOW 3 $ 3 % $ 3% 3 $ %

3 $

'LQ UH]XOW F vQFD]XODGRX HYHQLPHQWHLQGHSHQGHQWH 3 $ %

'HILQL LH1XPLPVLVWHPFRPSOHWGHHYHQLPHQWHRIDPLOLHFHOPXOWQXP UDELO GH HYHQLPHQWH $L L, 6 FX $L $ M SHQWUXRULFH L z M L M , úL $L : L,

)RUPXODSUREDELOLW LLWRWDOH)LH $L L, 6 XQVLVWHPFRPSOHWGHHYHQLPHQWH

FX 3 $L z L , 3HQWUX $ 6 DYHP

3 $

¦ 3 $ 3$ $ L

L,

L

3HQWUX GHPRQVWUD LH V REVHUY P F SHQWUX ILHFDUH 3 $ $L 3 $L 3 $ $L GHXQGHvQVXPkQGGXS L RE LQHP

¦ 3 $ 3$ $ ¦ 3 $ $ L

L,

GDU

¦ 3 $ $ L

L,

L

L , DYHP

L

L,

§ § ·· 3¨¨ $ ¨¨ $L ¸¸ ¸¸ © L, ¹ ¹ ©

3 $ : 3 $

([HPSOX=HFHDSDUDWHGHDFHODúLWLSVXQWGDWHvQH[SORDWDUHWUHLSURYLQGHODX]LQD 8 FLQFLSURYLQGHODX]LQD 8 LDUGRX GHODX]LQD 8 $SDUDWHOHVXQWVXSXVHXQHL SUREH GH YHULILFDUH &HOH FDUH SURYLQ GH OD SULPD X]LQ WUHF SURED GH YHULILFDUH FX SUREDELOLWDWHD FHOHFDUHSURYLQGHODX]LQD 8 FXSUREDELOLWDWHD LDUFHOHFDUH SURYLQGHODX]LQD 8 FXSUREDELOLWDWHD 6HDOHJHODvQWkPSODUHXQDSDUDW&DUHHVWH SUREDELOLWDWHDFDDSDUDWXOV WUHDF SUREDGHYHULILFDUH" 5 VSXQV )DFHP XUP WRDUHOH LSRWH]H $L DSDUDWXO DOHV SURYLQH GH OD X]LQD 8 L

'DF QRW P SULQ $ HYHQLPHQWXO ÄDSDUDWXO DOHV WUHFH SURED GH YHULILFDUH´ DYHP 3 $ $ L $YHP 3 $

3 $

3 $

3 $ $ 3 $ $ úL 3 $

¦ 3 $ 3$ $ L

L

L

)RUPXOD OXL %D\HV VDX WHRUHPD LSRWH]HORU )LH XQ VLVWHP FRPSOHW GH HYHQLPHQWH $L L, 6 3UREDELOLW LOHDFHVWRUHYHQLPHQWHLSRWH]H VXQWGDWHvQDLQWH

GHHIHFWXDUHDXQXLH[SHULPHQW([SHULPHQWXOHIHFWXDWUHDOL]HD] XQDOWHYHQLPHQW $ 6 DU W P FXP UHDOL]DUHD HYHQLPHQWXOXL $ VFKLPE SUREDELOLW LOH LSRWH]HORU 7UHEXLH V GHWHUPLQ P GHFL SUREDELOLW LOH 3 $L $ SHQWUX ILHFDUH LSRWH] $L L , $YHP

3 $L $ UH]XOW

3 $L $ GDU 3 $L $ 3 $L 3 $ $L úL LQkQG VHDPD GH 3 $ 3 $L $

3 $L 3 $ $L

¦ 3$ 3 $ $ M

M,

M

([HPSOH ÌQFRQGL LLOHH[HPSOXOXLDQWHULRUVHDOHJHODvQWkPSODUHXQDSDUDWúLVHFRQVWDW F HO WUHFHSUREDGHYHULILFDUH&DUHHVWHSUREDELOLWDWHDFDHOV SURYLQ GHODSULPDX]LQ " 5 VSXQV $YHP

3 $ $

3 $ 3 $ $

¦ 3$ 3 $ $ M

M

XQGH HYHQLPHQWHOH $ úL $L L

3 $ $

M

VXQW QRWDWH FD OD H[HPSOXO DQWHULRU $VWIHO

>@ 6H FRQVLGHU GRX ORWXUL GH SURGXVH GLQWUH FDUH XQ ORW DUH WRDWH SLHVHOH FRUHVSXQ] WRDUHLDUDOGRLOHDORWDUH

GLQSLHVHUHEXWXUL6HDOHJHODvQWkPSODUHXQ

ORWúLVHH[WUDJHGLQHORSLHV FRQVWDQWkQGXVHF HVWHEXQ 6HUHLQWURGXFHSLHVDvQ ORWúLVHH[WUDJHGLQDFHODúLORWRSLHV &DUHHVWHSUREDELOLWDWHDFDSLHVDH[WUDV V ILH XQUHEXW" 5 VSXQV )LH $ HYHQLPHQWXOÄDGRXDSLHV H[WUDV HVWHUHEXW´LDU $ $ HYHQLPHQWHOH GHDH[WUDJHDFHDVW SLHV GLQSULPXOUHVSHFWLYDOGRLOHDORW)RUPXODSUREDELOLW LLWRWDOH QHG 3 $ 3 $ 3 $ $ 3 $ 3 $ $

$YHP 3 $ $

3 $ $

'LQ IRUPXOD OXL %D\HV YRP FDOFXOD 3 $ 1RW PFX % % HYHQLPHQWHOHFD SULPDH[WUDF LHV VHIDF GLQSULPXOUHVSHFWLYDOGRLOHDORWLDU % HYHQLPHQWXOÄSLHVD

H[WUDV HVWH EXQ ´ $WXQFL 3 %

3%

3 % %

3 % % úL

GHFL 3 $ ,QHJDOLWDWHDOXL%RROH)LH ^: 6 3`XQFkPSGHSUREDELOLWDWHúL $L L, 6 R

3 $ 3 % %

PXO LPHFHOPXOWQXP UDELO GHHYHQLPHQWH'DF L,

$L 6 DWXQFL

§ · 3¨¨ $L ¸¸ t ¦ 3 $L& L, © L, ¹

§ Q · Q 3¨¨ $L ¸¸ t ¦ 3 $L Q ©L ¹ L

ÌQSDUWLFXODU

'HPRQVWUD LDHVWHLPHGLDW GDF VFULHP

& §§ · § · ·¸ · § ¨ 3¨¨ $L ¸¸ 3 ¨¨ $L ¸¸ 3¨¨ $L& ¸¸ ¨ © L, ¹ ¸ ¹ © L, © L, ¹ © ¹ úLDSOLF PSURSULHWDWHD 3 ÌQSDUWLFXODU Q § Q · 3¨¨ $L ¸¸ t ¦ 3 $L& L ©L ¹

Q

¦ 3 $L L

Q

¦ 3 $ Q L

L

9DULDELOHDOHDWRDUH&DUDFWHULVWLFLQXPHULFH)XQF LHGHUHSDUWL LH

8QDGLQWUHQR LXQLOHIXQGDPHQWDOHDOHWHRULHLSUREDELOLW LORUHVWHDFHHDGHYDULDELO DOHDWRDUH (YHQLPHQWHOHXQXLFkPSGHSUREDELOLWDWHQXVXQWSULQFLSLDOP ULPLvQvQ HOHVXODWULEXLW DFHVWRUDvQúWLLQ HOHQDWXUDOHVDXvQWHKQLF HOHVHGHVFULXvQV FXDMXWRUXOXQRUP ULPLDYkQG YDORULUHDOHúLFDUHvQJHQHUDOVXQWUH]XOWDWXOXQRUP VXU WRUL3ULQFLSDOXOPHULWDODFWXDOHL VLVWHPDWL] UL D FDOFXOXL SUREDELOLW LORU FRQVW vQ GHILQLUHD YDULDELOHORU DOHDWRDUH GHFL D P ULPLORUSHFDUHQLOHSUH]LQW H[SHULPHQWXOGLUHFWVDXWHRULLOHGHVWLQDWHV OLQWHUSUHWH]H 'DF vQ HOHJHP SULQ YDULDELO DOHDWRDUH R IXQF LH UHDO GHILQLW SH PXO LPHD HYHQLPHQWHORU HOHPHQWDUH DVRFLDWH H[SHULPHQWXOXL FRQVLGHUDW YRP SXWHD LOXVWUD SULQ H[HPSOHWLSLFHSHQWUXWHRULDSUREDELOLW LORUFXPVHWUHFHGHODXQHYHQLPHQWODRYDULDELO DOHDWRDUHúLDQXPH ([HPSOX6 FRQVLGHU PXQH[SHULPHQWFDUHDUHFDUH]XOWDWHYHQLPHQWXO $ ÌQ ORFXOHYHQLPHQWXO $ SXWHPFRQVLGHUDYDULDELODDOHDWRDUH [ FDUHLDYDORDUHD GDF VD UHDOL]DW $ úL GDF VDUHDOL]DW $& $PGHILQLWRYDULDELO DOHDWRDUHEHUQXROOLDQ FX GRX YDORULYDULDELO LQGLFDWRDUHDHYHQLPHQWXOXL $ SULQUHOD LD

SHQWUX Z $ [Z ® & Z SHQWUX $ ¯

ÌQ SUDFWLF HVWH GH PXOWH RUL PDL FRPRG FD vQ ORFXO HYHQLPHQWHORU V XWLOL] P YDULDELOHOHDOHDWRDUHLQGLFDWRDUHFDUHOHVXQWDVRFLDWH $FHDVW VFKHP SRDWHILH[WLQV vQVHQVXOF SXWHPFRQVLGHUDXQH[SHULPHQWFDUH DUHFDUH]XOWDWXQVLVWHPFRPSOHWGHHYHQLPHQWH $L dLdQ 'DF FRQYHQLPV DWULEXLP YDORDUHD Q M vQ FD]XOvQFDUHVDUHDOL]DWHYHQLPHQWXO $ M d M d Q DPGHILQLWR YDULDELO DOHDWRDUHEHUQRXOOLDQ FX Q YDORUL [ SULQUHOD LD [Z

Q M GDF Z $ M

d M d Q

9DULDELOHDOHDWRDUHGLVFUHWH

)LH ^: 6 3` XQ V FkPS GH SUREDELOLWDWH úL $L L, 6 XQ VLVWHP FRPSOHW

ILQLWVDXQXP UDELO GHHYHQLPHQWH6LVWHPXOQXPHULF SL 3 $L L , VHQXPHúWHGLVWULEX LD V FkPSXOXLGHSUREDELOLWDWH 'HILQL LH 1XPLP YDULDELO DOHDWRDUH GLVFUHW R IXQF LH [ GHILQLW SH PXO LPHD HYHQLPHQWHORUHOHPHQWDUH Z : FXYDORULUHDOHGDF [ LDYDORULOH [L L ,

^Z [Z

[L ` 6 L ,

2 YDULDELO DOHDWRDUH GLVFUHW SHQWUX FDUH , HVWH ILQLW VH QXPHúWH YDULDELO DOHDWRDUHVLPSO 6FKHPDWLFYDULDELODDOHDWRDUH [ VHQRWHD] SULQ

§[ · [ ¨¨ L ¸¸ ¦ SL © SL ¹ L, L,

7DEORXO VHQXPHúWHGLVWULEX LDVDXUHSDUWL LDYDULDELOHLDOHDWRDUH [ 1XP UXOSURGXVHORUGHIHFWHGLQWUXQORWH[DPLQDWQXP UXOGHGHIHF LXQLFDUHDSDU vQWURDQXPLW SHULRDG GHIXQF LRQDUHDXQXLGLVSR]LWLYLQGLFDWRUXOXQXLHYHQLPHQW $ VXQWYDULDELOHDOHDWRDUHGLVFUHWH SL QH VXJHUHD] LGHHD F DFHDVW VXP VH UHSDUWL]HD] vQWUXQ )DSWXO F

¦ L,

DQXPLW PRG vQWUH DFHVWH YDORUL [L GHFL GLQ SXQFW GH YHGHUH SUREDELOLVWLF R YDULDELO DOHDWRDUHHVWHFRPSOHWGHWHUPLQDW GDF VHG RDVWIHOGHUHSDUWL LH9RPVWDELOLRDVWIHOGH OHJHGHUHSDUWL LH 8QD GLQ IRUPHOH FHOH PDL VLPSOH vQ FDUH SXWHP UHSUH]HQWD R DVWIHO GH OHJH HVWH IRUPDVFKHPDWLF VDXVXEIRUPDXQXLWDEHO

[L

[

SL

S

[ ! S !

[L ! S ! L

[Q SQ

2 DOW IRUP HVWH FHD JUDILF OXkQG SH D[D DEVFLVHORU YDORULOH [L LDU SH D[D RUGRQDWHORUSUREDELOLW LOHFRUHVSXQ] WRDUH3XWHPRE LQHXQLQGDFHVWHSXQFWHSROLJRQXO GHUHSDUWL LH

VDXGLDJUDPDvQEDWRDQH

)LJXUD

)LJXUD

([HPSOX8QORWGHSLHVHHVWHVXSXVXQXLFRQWUROGHFDOLWDWHvQPRGXOXUP WRUVH H[WUDJHSHUkQGFkWHRSLHV FDUHVHFHUFHWHD] GDF SRDWHILDGPLV VDXQX6HFHUFHWHD] SLHVH'DF SLHVDGLQH[WUDF LDGHUDQJ N QXFRUHVSXQGHORWXOVHUHVSLQJH 6 VH VFULH WDEORXO GH UHSDUWL LH DO YDULDELOHL DOHDWRDUH FDUH UHSUH]LQW QXP UXO GH SLHVH FHUFHWDWHGDF SUREDELOLWDWHDFDRSLHV OXDW ODvQWkPSODUHGLQORWV ILHDGPLV HVWH 6 VHWUDVH]HSROLJRQXOGHUHSDUWL LHFRUHVSXQ] WRU 5 VSXQV9DULDELODDOHDWRDUH [ SRDWHOXDYDORULOH D GDF SULPDSLHV HVWHUHEXWGHFL 3[

E GDF SULPDSLHV H[WUDV HEXQ LDUDGRXDUHEXWFkQG 3[ F GDF SULPHOHGRX SLHVHVXQWEXQHúLDWUHLDUHEXWúL 3 [

G SULPHOH WUHL SLHVH VXQW EXQH LDU D SDWUD UHEXW SHQWUX FDUH 3[

H SULPHOHSDWUXSLHVHVXQWEXQH 3 [ 'HFL

§ [ ¨ ¨ ©

· ¸ ¸¹

3ROLJRQXOGHUHSDUWL LHHVWHFHOGLQILJXUD

L

)LJXUD

'DF [ HVWH R YDULDELO DOHDWRDUH GLVFUHW FDUH SRDWH OXD YDORULOH GLIHULWH [L

SXWHPIDFHV LFRUHVSXQG XQVLVWHPFRPSOHWGHHYHQLPHQWH $L L

IHOvQFkW $L

^Z [Z

F $L $ M

L z M úL

DúD

[L ` LQkQGVHDPDGHIDSWXOF YDORULOH [L VXQWGLIHULWHUH]XOW f L

$L

§f · : GHFL 3¨¨ $L ¸¸ ©L ¹

f

¦ 3 $ L

L

5HFLSURFDDIRVWDU WDW PDLVXV 'HILQL LH)LH [ úL K GRX YDULDELOHDOHDWRDUHGHILQLWHSULQ

[Z [Q SHQWUX Z $Q Q KZ \P SHQWUX Z %P P

^ $Q ` úL ^%P `ILLQGGRX VLVWHPHFRPSOHWHGHHYHQLPHQWH6SXQHPF YDULDELOHOHDOHDWRDUH [ úL K VXQWLQGHSHQGHQWHGDF SHQWUXRULFH P úL Q DYHP

3 $Q %P

3 $Q 3 %P

&XDOWHFXYLQWHVLVWHPHOHFRPSOHWH ^$Q ` úL ^%P `VXQWLQGHSHQGHQWH

)LH [ úL K GRX YDULDELOHDOHDWRDUHGHILQLWHSULQ úL I RIXQF LHUHDO GH GRX YDULDELOH UHDOH 9DULDELOD DOHDWRDUH ]

I [ K LD YDORULOH ] QP

HVWHGHILQLW GHVLVWHPXOFRPSOHWGHHYHQLPHQWH &QP

^Z [Z

I [Q \P úL

[Q KZ

\P `

$YHP

3]Z

]

¦ 3[Z

[Q KZ

I [Q \P ]

\P

'DF [ úL K VXQWLQGHSHQGHQWHDYHP

3[Z [Q KZ \P 3[Z [Q 3KZ \P &XQRWD LLOH SQ 3 [Z [Q TP 3 KZ \P UH]XOW

3] Z

3HQWUX I [ \

]

¦S T

¦S T

Q P I [Q \P ]

[ \ DYHP 3] Z ]

[Q \P ]

Q P

'DF vQSDUWLFXODU [ úL K QXSRWOXDGHFkWYDORULvQWUHJLQHQHJDWLYHDYHP N

3 ] Z N

¦S T

M N M

M

'LVWULEX LDOXL ] [ K VHQXPHúWHFRPSXQHUHDOXL ] úL K 6SUHH[HPSOXILHYDULDELOHOHDOHDWRDUHVLPSOH

XQGH

§ [ " [Q · §\ " ¸¸ K ¨¨ [ ¨¨ © S " SQ ¹ © T " 9DULDELODDOHDWRDUH [ K DUHWDEORXOGHGLVWULEX LH § [ \ [ \ " [L \ M [ K ¨¨ S " SLM © S 3 [Z KZ

SLM FX

[L \ M 3 ^Z [Z Q

P

¦¦ S L M

'DF [ úL K VXQWLQGHSHQGHQWH SLM

LM

\P · ¸ TP ¸¹ " [Q \ P · ¸ " SQP ¸¹ [L ` Z KZ

\M

SL T M

9DULDELODDOHDWRDUH [K DUHWDEORXOGHGLVWULEX LH

§ [ \ [K ¨¨ © S

FX

SLM

3 [Z KZ

[ \ " [L \ M " [Q \P · ¸ S " SLM " SQP ¸¹ [L \ M 3 ^Z [Z

[L ` Z KZ

\M

2SHUD LLOHGHVXP úLSURGXVVHH[WLQGODRULFHQXP UILQLWGHYDULDELOHDOHDWRDUH 5H]XOW GHFL 3XWHUHDXQHLYDULDELOHDOHDWRDUHDUHWDEORXOGHGLVWULEX LH

§ [ N " [QN · ¸ [ N ¨¨ ¸ S " S N ¹ © 3[Z [L SL

GHRDUHFH 3 [ N Z [LN ,QYHUVDXQHLYDULDELOHDOHDWRDUHFXYDORULQHQXOHDUHWDEORXOGHGLVWULEX LH

§ " ¨ [ ¨ [ ¨S " ©

· ¸ [Q ¸ SQ ¸¹

'DF YDULDELODDOHDWRDUH K DGPLWHLQYHUV DWXQFLGHILQLPFkWXO

[ K

[K úLDUH

WDEORXOGHGLVWULEX LH

[L \M SLM

§ [ " [ ¨ ¨ \ K ¨ © S "

" "

[Q · ¸ \P ¸ SQP ¸¹

2 FRQVWDQW D SRDWH IL LQWHUSUHWDW FD R YDULDELO DOHDWRDUH GHILQLW SH RULFH PXO LPHGHHYHQLPHQWHHOHPHQWDUHLDUWDEORXOHLGHGLVWULEX LHLQWHUSUHWDW FDYDULDELO

§D· ©¹

DOHDWRDUHYDIL D ¨¨ ¸¸ GHFLYRPSXWHDIDFHWRWGHDXQDRSHUD LLFXYDULDELOHDOHDWRDUHúL FRQVWDQWH ([HPSOX6HG HFXD LD D[ E\ F vQFDUHFRHILFLHQ LL D E F VHGHWHUPLQ SULQDUXQFDUHDXQXL]DU6 VHGHWHUPLQHSUREDELOLWDWHDFDGUHDSWDDVWIHORE LQXW V WUHDF SULQSXQFWXOGHFRRUGRQDWH 5 VSXQV([SHULPHQWXOXLGHGHWHUPLQDUHDXQXLFRHILFLHQWvLDWDú PYDULDELODDOHDWRDUH [ FDUHLDFDYDORULQXP UXOGHSXQFWHDS UXWGHFL

§ [¨ ¨ ©

· ¸ ¸ ¹

)LH [ [ [ YDULDELOHOH DOHDWRDUH FRUHVSXQ] WRDUH GHWHUPLQ ULL FRHILFLHQ LORU

D E F $FHVWHYDULDELOHDOHDWRDUHVXQWLQGHSHQGHQWH'UHDSWDWUHFHSULQSXQFWXO [ [ [ 'HFL WUHEXLH V GHWHUPLQ P FkQG

3 [ [ [

3[

[ [

LQkQGVHDPDGHIDSWXOF YDULDELOHOHDOHDWRDUHVXQWLQGHSHQGHQWHSXWHPVFULH

3 [ [ [

¦ 3^[ N

¦ 3[ N

[

N ` ^[

N 3[ [

N ` N

$YHP 3 [

N

N

úL

¦ 3[ N

N 3[ [ d

[

ILLQGSUREDELOLWDWHDFDVXPDSXQFWHORURE LQXWHODDUXQFDUHDDGRX ]DUXULV ILHPDLPLF GHFkW LQkQG VHDPD GH IDSWXO F WDEORXO GH GLVWULEX LH D YDULDELOHL DOHDWRDUH FDUH UHSUH]LQW VXPDSXQFWHORURE LQXWHHVWH

§ ¨ ¨ ©

DYHP

¦ 3[

[

N

N

GHFL

3[

[ [

· ¸ ¸ ¹

0RPHQWHOHXQHLYDULDELOHDOHDWRDUHGLVFUHWH

0RPHQWHOHXQHLYDULDELOHDOHDWRDUHGLVFUHWHVXQWYDORULOHWLSLFHFHOHPDLIUHFYHQW XWLOL]DWHvQDSOLFD LL 'HILQL LH )LH [ R YDULDELO DOHDWRDUH GLVFUHW FDUH LD YDORULOH [L FX

¦ [ S HVWHDEVROXWFRQYHUJHQW H[SUHVLD 0 [ ¦ [ S

SUREDELOLW LOH SL L , 'DF VHULD

L,

L,

L

L

L

L

VHQXPHúWHYDORDUHPHGLHDYDULDELOHLDOHDWRDUHGLVFUHWH [ 'DF [ HVWH R YDULDELO DOHDWRDUH VLPSO FDUH LD YDORULOH [ [Q FX SUREDELOLW LOH S SQ DWXQFLYDORDUHDPHGLHYDIL

0 [ 3

Q

¦[ S L

L

L

9RPGDvQFRQWLQXDUHFkWHYDSURSULHW LDOHYDORULORUPHGLL 'DF [ úL K VXQWGRX YDULDELOHDOHDWRDUHGLVFUHWHGHILQLWHSULQ úLGDF

0 [ úL 0 K H[LVW DWXQFLH[LVW YDORDUHDPHGLH 0 [ K úL 0 [ K 0 [ 0 K

^

1RWkQG SULQ &LM HYHQLPHQWXO Z [Z

&LM

FRPSOHW GH HYHQLPHQWH úL

¦ 3& LM

M

L

3 $L GHFL

\L ` ^&LM ` IRUPHD] XQ VLVWHP

[L KZ

% M

&LM

M

¦ 3&

$L GH XQGH

3 % M

LM

L

¦¦ [ \ 3 & ¦¦ [ 3 & ¦¦ \ 3 &

0 [ K

L

L

M

M

LM

L

L

M

LM

L

M

M

LM

¦ [ ¦ 3 & ¦ \ ¦ 3 & ¦ [ 3 $ ¦ \ 3 % L

L

LM

M

M

M

LM

L

L

L

L

M

M

M

0 [ 0 K 3

3ULQUHFXUHQ VHRE LQH )LH [ N N Q Q YDULDELOH DOHDWRDUH GLVFUHWH 'DF 0 [ N H[LVW

§

Q

¦[ ©

DWXQFL 0 ¨

N

3

N

· ¸ H[LVW úL ¹ · § Q 0 ¨ ¦ [N ¸ ©N ¹

Q

¦ 0 [

N

N

)LH [ R YDULDELO DOHDWRDUH GLVFUHW úL F R FRQVWDQW 'DF 0 [ H[LVW

DWXQFL 0 F[ H[LVW úL

0 F[ F0 [

3URSULHWDWHDUH]XOW LPHGLDWGLQGHILQL LHúLDQXPH

0 F[

¦ S F[ F¦ S [ L

L

L

L

L L

F0 [

3URSULHW LOH3 úL3 FRQGXFOD 3 )LH [ N N Q Q YDULDELOHDOHDWRDUHGLVFUHWHúL FN Q FRQVWDQWH'DF

§ Q · 0 [ N N Q H[LVW DWXQFL 0 ¨ ¦ FN [ N ¸ H[LVW úL ©N ¹ Q Q § · 0 ¨ ¦ FN [ N ¸ ¦ FN 0 [ N ©N ¹ N 3 9DORDUHDPHGLHDYDULDELOHLDOHDWRDUH [ 0 [ K HVWHQXO K VHQXPHúWH DEDWHUHDYDULDELOHLDOHDWRDUH [ 'HRDUHFH 0 [ HVWH R FRQVWDQW YDORDUHD PHGLH D XQHL FRQVWDQWH HVWH DFHHD

FRQVWDQW GHFL

0 [ 0 [ 0 [ 0 [

3

,QHJDOLWDWHDOXL6FKZDU])LH [ úL K GRX YDULDELOHDOHDWRDUHGLVFUHWHSHQWUX

FDUHH[LVW 0 [ úL 0 K $WXQFL

0 [K d 0 [ 0 K

3HQWUX GHPRQVWUD LH YRP FRQVLGHUD YDULDELOD DOHDWRDUH ] O HVWHXQSDUDPHWUXUHDO$YHP

[ OK XQGH O

0 ] O 0 [ O0 [K O 0 K

'DU ] O t GHFL 0 ] O t SHQWUXRULFH O UHDO'HDLFLUH]XOW

0 [ O0 [K O 0 K t O \

GHXQGH 3 'DF [ úL K VXQW GRX YDULDELOH DOHDWRDUH GLVFUHWH LQGHSHQGHQWH úL GDF

0 [ úL 0 K H[LVW DWXQFL 0 [K H[LVW úL 0 [K 0 [ 0 K 1RWkQGSULQ &LM

Z [Z

[L KZ

0 [K

\ M DYHP

¦¦ [ \ 3& L

M

'DU [ úL K VkQWLQGHSHQGHQWHGHFL

3 &LM 3[

L

[L 3 K

M

LM

\M

SL T M

úL

· § ·§ 0 [K ¨ ¦ [L SL ¸¨¨ ¦ \ M T M ¸¸ 0 [ 0 K © L ¹© M ¹ ([HPSOX8QDSDUDWHVWHIRUPDWGLQ HOHPHQWHFDUHVHSRWGHIHFWDLQGHSHQGHQW XQXO GH DOWXO 1XPHURW P HOHPHQWHOH GH OD OD úL ILH SN N SUREDELOLWDWHD V VH GHIHFWH]H HOHPHQWXO FX QXP UXO N N 6 VH FDOFXOH]H YDORDUHDPHGLHDQXP UXOXLGHGHIHF LXQL 5 VSXQV)LH [ N YDULDELODDOHDWRDUHDVRFLDW HOHPHQWXOXLFXQXP UXO N FDUHLDYDORULSH

VDX GXS FXPHOHPHQWXOVHGHIHFWHD] VDXQX § · ¸¸ N [ N ¨¨ © N N ¹ 9DULDELODDOHDWRDUHFDUHG QXP UXOXLGHGHIHF LXQLHVWH [ [ [ [ [ [ GHFL

0 [ 0 [ 0 [ 0 [ 0 [ 0 [ $YHP 0 [ N N GHXQGH 0 [

¦ > N @ N

'HILQL LH )LH [ R YDULDELO DOHDWRDUHD GLVFUHW úL U XQ QXP U QDWXUDO 'DF H[LVW YDORDUHD PHGLH D YDULDELOHL DOHDWRDUH [ U DWXQFL DFHDVW YDORDUH PHGLH VH QXPHúWHPRPHQWGHRUGLQ U DOYDULDELOHLDOHDWRDUH [ úLVHQRWHD]

¦[

D U [ 0 [ U

N

U N

SN

U

9DORDUHDPHGLHDYDULDELOHLDOHDWRDUH [ VHQXPHúWHPRPHQWDEVROXWGHRUGLQ

U DOYDULDELOHLDOHDWRDUH [ úLVHQRWHD]

E U [ 0 [

¦[

U

N

U

SN

N

'HILQL LH )LH R YDULDELO DOHDWRDUH GLVFUHW [ 0RPHQWXO GH RUGLQXO U DO YDULDELOHLDOHDWRDUHDEDWHUHDOXL [ VHQXPHúWHPRPHQWFHQWUDWGHRUGLQXO U DOXL [ úL VHQRWHD] P U [ D U [ 0 [ 0RPHQWXO FHQWUDW GH RUGLQXO GRL D YDULDELOHL DOHDWRDUH GLVFUHWH [ VH QXPHúWH

GLVSHUVLHVDXYDULDQW úLVHQRWHD] SULQ ' [ VDX V GHFL

' [ V

P [

P [ VHQXPHúWHDEDWHUHPHGLHS WUDWLF DOXL [ 1XP UXO '[ V 9RPGDvQFRQWLQXDUHFkWHYDSURSULHW LDOHGLVSHUVLHLúLDOHDEDWHULLPHGLLS WUDWLFH 3 $UHORFHJDOLWDWHD ' [ 0 [ >0 [ @ ÌQWUDGHY U LQkQGVHDPDGHGHILQL LH

0 >[ 0 [ @

' [

3

'DF P

0 [ [0 [ >0 [ @

0 [ >0 [ @ >0 [ @

0 [ >0 [ @

D[ E FX D úL E FRQVWDQWHDWXQFL 'K

$YHP

D '[

0 K D0 [ E D 0 [ DE0 [ E

0 K GHXQGH ' K D ' [ ÌQSDUWLFXODUSHQWUX E DYHP ' D[ D ' [ 3 )LH [ N dN dQ Q YDULDELOHDOHDWRDUHGLVFUHWHGRX FkWHGRX LQGHSHQGHQWHúL F FQ Q FRQVWDQWH$WXQFL

§ Q · ' ¨ ¦ FN [ N ¸ ©N ¹

Q

¦ F ' [ N

N

N

LQkQGVHDPDGH DYHP

§ Q · ' ¨ ¦ FN [ N ¸ ©N ¹

§§ Q · · ª § Q ·º 0 ¨ ¨ ¦ FN [ N ¸ ¸ « 0 ¨ ¦ FN [ N ¸ » ¨© N ¹ ¸¹ ¬ © N ¹¼ ©

§ Q · ª Q º 0 ¨ ¦ FN[ N ¦ FK FN [ K[ N ¸ « ¦ FN 0 [ N » K N ©N ¹ ¬N ¼ Q

Q

¦ F 0 [ ¦ F F 0 [ [ ¦ F N

N

N

K N

K N

K N

N

N

ª¬ 0 [ N º¼

¦ FK FN 0 [ K 0 [ N 'DU 0 [ K [ N

KN

0 [ K 0 [ N GHFL § Q · ' ¨ ¦ FN [ N ¸ ©N ¹

Q

¦F N

N

0 [ N 0 [ N

GHXQGH 3 ,QHJDOLWDWHDOXL&HEvúHY)LH [ RYDULDELO DOHDWRDUH$WXQFL

3 Z [Z 0 [ t H

' [ H

D

SHQWUXRULFH H ! $FHDVW LQHJDOLWDWH SRDWH IL SXV VXE R IRUP IRDUWH GHV IRORVLW vQ DSOLFD LL úL DQXPHOXkQG H D'[ VHVFULH

3 [ 0 [ t D'[ 'HH[HPSOXGDF OX P D

GLQ GHGXFHP 3 [ 0 [ t '[

DGLF SUREDELOLWDWHD FD R YDORDUH D XQHL YDULDELOH DOHDWRDUH V LDV GLQ LQWHUYDOXO

0 [ '[ 0 [ '[ HVWH PDL PLF GHFkW GHFL PDMRULWDWHD YDORULORU

YDULDELOHLDOHDWRDUHVHYRUJUXSDvQMXUXOYDORULLPHGLLSHXQLQWHUYDOGHOXQJLPH '[ $FHDVWDHVWHUHJXODFHORU V 9DULDELOHDOHDWRDUHGHWLSFRQWLQXX )LH ^: 6 3`XQ V FkPSGHSUREDELOLWDWH 'HILQL LH 6H QXPHúWH YDULDELO DOHDWRDUH R IXQF LH [ : o \ GHILQLW SH PXO LPHDHYHQLPHQWHORUHOHPHQWDUHFXYDORULUHDOH DVWIHOvQFkWWRDWHPXO LPLOHGHIRUPD $[ Z [Z [ DSDU LQOXL 6 SHQWUXRULFH [ \

^

`

9RPGDvQFRQWLQXDUHFkWHYDSURSULHW LDOHYDULDELOHORUDOHDWRDUH

3

)LH [ RYDULDELO DOHDWRDUHúL F RFRQVWDQW DWXQFL [ F F[ [ [

FX [

[ z VXQWYDULDELOHDOHDWRDUH ÌQWUDGHY UIXQF LLOH [ F úL F[ VXQWYDULDELOHDOHDWRDUHGHRDUHFH

^Z [Z F [` ^Z [Z [ F`

^Z F[Z [` 'HDVHPHQHD

Z [Z [

°®Z [Z °¯ ® °Z [Z ! °®¯ ¯

[½ ¾ 6 SHQWUX F ! F¿ [½ ¾ 6 SHQWUX F F¿

^Z [Z [`* ^Z [Z ! [` 6

Z [ Z [

Z [Z [ 6

° ½° [¾ ®Z ¯° [ Z ¿°

3

° Z [ Z ° ° ½ ° ® Z [ Z ®Z [ Z ! ¾ [¿ ¯ ° ° § ° Z [ Z * ¨ Z [ Z ! ®Z [ Z ¯ © ¯° )LH [ úL K GRX YDULDELOHDOHDWRDUHDWXQFL

3

'DF [ úL K VXQWGRX YDULDELOHDOHDWRDUHDWXQFL [ K [ K [K

SHQWUX [

SHQWUX [ ½ · SHQWUX [ ! ¾¸ [ ¿¹

^Z [Z ! KZ ` 6 ^Z [Z t K[ ` 6 ^Z [Z

K[ ` 6

K z VXS[ K úL LQI [ K VXQWGHDVHPHQHDYDULDELOHDOHDWRDUH

[ FX K

'LQ3 UH]XOW

^Z [Z KZ [` ^Z [Z KZ [` 6

)DSWXOF [ K HVWHYDULDELO DOHDWRDUHUH]XOW GLQ [ K DQWHULRDU

[ K úLUHOD LD

2EVHUY PF

[K

[ K [ K [ K

[

K

[ K [ K LQI [ K [ K [ K 'LQ IDSWXO F VXS[ K úL LQI [ K VXQW YDULDELOH DOHDWRDUH UH]XOW F SDUWHD VXS[ K

SR]LWLY [ úLSDUWHDQHJDWLY [ DXQHLYDULDELOHDOHDWRDUH [ VXQWYDULDELOHDOHDWRDUH

GHRDUHFH [ VXS[ [ LQI [ 7HRUHPD 'DF [ HVWH R YDULDELO DOHDWRDUH QHQHJDWLY H[LVW XQ úLU

FUHVF WRU [ Q Q` GHYDULDELOHDOHDWRDUHVLPSOHQHQHJDWLYHFDUHFRQYHUJHF WUH [ 'HPRQVWUD LH1RW P

L L L SHQWUX Q d [Z Q L Q Q ° [ Q Z ® Q °¯Q SHQWUX [Z t Q SHQWUX Q $WXQFL [ Q VXQWYDULDELOHDOHDWRDUHVLPSOHQHQHJDWLYH 'DF [Z f DYHP [Z [ Q Z Q GHFL OLP [ Q Z [Z Q of 'DF [Z f DWXQFL SHQWUX RULFH Q ` DYHP [ Q Z Q GHFL

OLP [ Q Z [Z Q of

'DF [ QXHVWHQHQHJDWLY DYHP [ [ [ FX [ úL [ YDULDELOHDOHDWRDUH QHQHJDWLYHúLWHRUHPDHVWHGHDVHPHQHDDGHY UDW 7HRUHPD'DF [ Q Q` HVWHXQúLUGHYDULDELOHDOHDWRDUHDWXQFL VXS [ Q Q`

LQI [ Q OLP [ Q úL OLP [ Q VXQWGHDVHPHQHDYDULDELOHDOHDWRDUH

Q`

Qof

Qof

'HILQL LH 9RP VSXQH F YDULDELOHOH DOHDWRDUH [ [ Q VXQW LQGHSHQGHQWH GDF SHQWUXWRDWHVLVWHPHOHUHDOH [ [Q DYHP

3[ [ [ Q [Q 3[ [ 3[ Q [Q )XQF LHGHUHSDUWL LH

'HILQL LH6HQXPHúWHIXQF LHGHUHSDUWL LHDYDULDELOHLDOHDWRDUH [ IXQF LD

) [ 3 ^Z [Z [` GHILQLW SHQWUXRULFH [ \

'LQ DFHDVW GHILQL LH UH]XOW F RULFH YDULDELO DOHDWRDUH SRDWH IL GDW SULQ LQWHUPHGLXOIXQF LHLVDOHGHUHSDUWL LH

'DF [ HVWHRYDULDELO DOHDWRDUHGLVFUHW FX SQ UH]XOW ) [ SQ

3[

[Q Q , DWXQFLGLQ

¦

[Q [

úLVHQXPHúWHIXQF LHGHUHSDUWL LHGHWLSGLVFUHW5H]XOW F vQDFHVWFD] ) HVWHRIXQF LH vQVFDU DGLF LDYDORULFRQVWDQWHSHLQWHUYDOHOHGHWHUPLQDWHGHSXQFWHOH [L L , ([HPSOH )LHYDULDELODDOHDWRDUH

· § ¸¸ [ ¨¨ © ¹

&RQIRUPFX UH]XOW

) [

)LJXUD

° ° ° ® ° ° ° ¯

SHQWUX [ SHQWUX d [ SHQWUX d [ SHQWUX d [ SHQWUX d [ SHQWUX [ t

*UDILFXOHLHVWHFHOGLQILJXUD

N · ¸ FX P YDORUL GDF HYHQLPHQWHOH $ M VH N P N ¸ ©& S T ¹ §

ÌQ FD]XO XQHL YDULDELOH [ ¨¨

N P

3[

UHDOL]HD] FXSUREDELOLWDWHD S M d M d P DGLF S M

P M IXQF LDGH

UHSDUWL LHFRUHVSXQ] WRDUHHVWH

) [

°S ° °° S S ® ° ° S S SP ° °¯

SHQWUX [ SHQWUX d [ SHQWUX d [ SHQWUX P d [ P SHQWUX [ t P

7HRUHPD)XQF LDGHUHSDUWL LHDXQHLYDULDELOHDOHDWRDUHDUHXUP WRDUHOH SURSULHW L 'DF [ [ DWXQFL ) [ d ) [ [ [ \

) [ ) [ SHQWUXRULFH [ \ OLP ) [

Qof

OLP ) [

Qof

'HPRQVWUD LH )LH [ [

$[

GRX

^Z [Z [ `

QXPHUH

) [ 3 $[ d 3 $[

UHDOH

$[

1RW P

$[ $[

$YHP

) [

^Z [Z [ `

GHFL

)LH [ \ RYDORDUHIL[ úLILH [ [ [Q XQúLUFUHVF WRUGHQXPHUH UHDOH FRQYHUJHQW F WUH [ &RQVLGHU P HYHQLPHQWHOH $[ $

%Q

^Z [

Q

d [Z [Q`

Q

$YHP

$

^Z [Z [`

$[ * % * % *

(YHQLPHQWHOHGLQPHPEUXOGRLVXQWLQFRPSDWLELOHGRX FkWHGRX SULQFRQVWUXF LH DVWIHOF 3 $ 3 $[ 3% 3% 'DU 3 $

) [ 3 $[

) [

3%Q 3 ^Z [Z [Q` 3^Z [Z [Q ` ) [Q ) [Q Q 5HOD LD VHVFULH

) [ ) [ >) [ ) [ @ >) [ ) [ @ GHFL ) [ OLP ) [Q XQGH Qof

) [Q ) [ >) [ ) [ @ >) [Q ) [Q @ VDX ) [ ) [ )LH úLUXO GH QXPHUH UHDOH [ ! [ ! ! [Q ! FRQYHUJHQW OD f úL ILH

^Z [

HYHQLPHQWHOH $[ úL %Q

Q

d [Z [Q` Q (YHQLPHQWHOH %Q

VXQWLQFRPSDWLELOHGRX FkWHGRX úL $[

) [

f Q

f

¦ 3% VDX

%Q GHFL 3 $[

Q

Q

> ) [ ) [ @ >) [ ) [ @ >) [Q ) [Q @

DGLF ) [ 'DU 6 Q

6Q

OLP 6 Q Qof

) [ ) [Q GHFL ) [ ) [ OLP ) [Q LQkQGVHDPDGH Q of

IDSWXOF úLUXO ^ [Q `Q` WLQGHOD f UH]XOW OLP ) [Q Q of

) f

)LH úLUXO FUHVF WRU ^ [Q `Q` GH QXPHUH UHDOH FDUH WLQGH OD f úL ILH HYHQLPHQWHOH

:

^Z [Z d f `

Q $YHP :

'Q f M

Z [ Z [

' M úL 'L ' M

'Q

^Z [

Q

d [Z [Q C`

L z M GHFL 3:

f

¦ 3' M

M

VDX

) [ >) [ ) [ @ >) [Q ) [Q @ GHXQGHUH]XOW OLP ) [Q ) f Qof

5HFLSURFDDFHVWHLWHRUHPHHVWHXUP WRDUHD 7HRUHPD2ULFHIXQF LH ) PRQRWRQ QHGHVFUHVF WRDUHFRQWLQX ODVWkQJDúL FX ) f ) f HVWHIXQF LDGHUHSDUWL LHDXQHLYDULDELOHDOHDWRDUHGHILQLW SHXQFkPSGHSUREDELOLWDWHFRQYHQDELODOHV 7HRUHPD)LH [ RYDULDELO DOHDWRDUHDF UHLIXQF LHGHUHSDUWL LHHVWH ) )LH D úL E GRX QXPHUHUHDOHFX D E $XORFHJDOLW LOH 3D d [ E ) E ) D 3D [ E

) E ) D 3 [ ) E ) D 3 [ ) E ) D 3[

D D 3 [ E 3D [ d E E 3D d [ d E 'HPRQVWUD LH )LH HYHQLPHQWHOH $ ^Z [Z D`

^Z [Z D` ' ^Z [Z E`

&

%

^Z [Z E`

5H]XOW $ % $ * & % $ % * ' úL

3 % $& 3 % $ * %&

3D d [ E

3% 3 $ 3&

3 % * ' $ * &

3 $ 3& 3'

&

3 % * ' $ 3% 3 $ 3' LQkQGVHDPDF 3 $ ) D 3% ) E UH]XOW FHOHSDWUXHJDOLW L 2EVHUYD LH'LQ 3[ [ ) [ ) [ UH]XOW F SXWHPVFULHHJDOLW LOH &

úLVXEIRUPD 3D [ E ) E ) D 3D [ d E

) E ) D ) E ) D

3D d [ d E ([HPSOH 6HFRQVLGHU IXQF LD ) GHILQLW SULQUHOD LLOH

) [

° ®D[ ° ¯

SHQWUX [ SHQWUX d [ d SHQWUX [ !

D FRQVWDQW6HFHUH D 6 VHGHWHUPLQHFRQVWDQWD D DúDvQFkW ) V ILHIXQF LHGHUHSDUWL LH E 6 VHFDOFXOH]H 3 d [ 5 VSXQV D )XQF LD ) HVWHFRQWLQX vQWRDWHSXQFWHOHD[HLUHDOHFXH[FHS LDSXQFWXOXL [ LQkQGVHDPDGHGHILQL LDIXQF LHLGHUHSDUWL LHWUHEXLHFD ) V ILHFRQWLQX ODVWkQJD vQ RULFH SXQFW [ \ úL d ) [ d GHFL vQ [ WUHEXLH V DYHP

d ) ) d GH XQGH UH]XOW d D d 'DF FHUHP FD ) V ILH FRQWLQX vQ [ DWXQFL D E $YHP 3D d [ E ) E ) D GHXQGH 3 d [ ) ) 6 VHGHWHUPLQHFRQVWDQWHOH D úL E DVWIHOvQFkW ) [ D E DUFWJ [ [ \ V ILHRIXQF LHGHUHSDUWL LH6 VHFDOFXOH]H 3 [ 5 VSXQV'LQ OLP ) [ úL OLP ) [ UH]XOW [of

[of

OLP D E DUFWJ [

[of

S S D E

OLP D E DUFWJ [ D E

[of

FRQVLGHUkQGXVH GHWHUPLQDUHD

3 [ ) )

S S d DUFWJ [ d 6H RE LQH D

E

úL S

'HILQL LH)LH [ RYDULDELO DOHDWRDUHDF UHLIXQF LHGHUHSDUWL LHHVWH ) 'DF H[LVW RIXQF LHUHDO I GHILQLW úLLQWHJUDELO SH \ DúDvQFkW

) [

[

³ I X GX

f

DWXQFL ) VHQXPHúWHIXQF LHGHUHSDUWL LHDEVROXWFRQWLQX LDU [ VHQXPHúWHYDULDELO DOHDWRDUH DEVROXW FRQWLQX )XQF LD I VH QXPHúWH GHQVLWDWH GH SUREDELOLWDWH UHSDUWL LH LDUH[SUHVLD I [ G[ VHQXPHúWHOHJHGHSUREDELOLWDWHHOHPHQWDU 'DF ) DUHRGHQVLWDWHGHSUREDELOLWDWH I DWXQFL

I [ ) c[ 5H]XOW GHDLFLF

) [ '[ ) [ '[o '[ OLP

3 [ d [ [ G[

3 [ d [ [ '[ '[ o '[ OLP

I [ G[

'HQVLWDWHDGHSUREDELOLWDWHDUHXUP WRDUHOHSURSULHW L

I [ t SHQWUXRULFH [ \

f

³ I X GX

f

3HQWUXRULFH D E UHDOLDUHORFUHOD LD 3D d [ E

E

³ I [ G[ D

([HPSOH 6HFRQVLGHU IXQF LD

I [

SHQWUX [ ° ®D VLQ [ SHQWUX d [ d S ° SHQWUX [ ! S ¯

6HFHUH D 6 VH GHWHUPLQH FRQVWDQWD UHDO D DVWIHO FD I V ILH GHQVLWDWHD GH SUREDELOLWDWHDXQHLYDULDELOHDOHDWRDUH E 6 VHGHWHUPLQHIXQF LDGHUHSDUWL LHFRUHVSXQ] WRDUH

§ ©

F 6 VHFDOFXOH]H 3¨ d [

S· ¸ ¹

5 VSXQV D 'LQSURSULHW LOHGHQVLW LLGHSUREDELOLWDWHGHGXFHP f

S

³ I [ G[

D ³ VLQ [G[

D

f

GHXQGH D

E

)LH ) IXQF LDGHUHSDUWL LHFRUHVSXQ] WRDUH$YHP ) [ 3HQWUX [ I [ GHFL ) [ 3HQWUX d [ S DYHP

) [

[

S

[

f

S

³ I X GX ³ I X GX ³ I X GX

'HFL

) [

F

[

I X GX ³ I X GX

3HQWUX [ t S DYHP

) [

f

S· § 3¨ d [ ¸ ¹ ©

S

³ I X GX

f

VLQ XGX ³

³

[

FRV [ S

VLQ XGX ³

SHQWUX [ ° ° ® FRV [ SHQWUX d [ S ° °¯ SHQWUX [ t S

VLQ XGX ³

*UDILFXO IXQF LHL I HVWH FHO GLQ ILJXUD LDU DO IXQF LHL ) HVWH FHO GLQ ILJXUD $ULDKDúXUDW GLQILJXUDUHSUH]LQW SUREDELOLWDWHDFHUXW ODSXQFWXOF

)LJXUD

)LJXUD

)LH [ RYDULDELO DOHDWRDUHDF UHLIXQF LHGHUHSDUWL LHUHSDUWL LHXQLIRUP HVWH

) [

SHQWUX [ ° ® [ SHQWUX d [ ° SHQWUX [ t ¯

6 VHFDOFXOH]HGHQVLWDWHDGHUHSDUWL LHDYDULDELOHLDOHDWRDUH K

OQ [

5 VSXQV

GHXQGH

úL

§ · 3K [ 3¨¨ OQ [ ¸¸ © [ ¹

§ · 3¨¨ H [ ¸¸ 3 [ d H [ ©[ ¹

)K [ ® [ ¯ H

SHQWUX [ SHQWUX [ t

SHQWUX [ I K [ ® [ SHQWUX [ t ¯H >@ 3UREDELOLWDWHD FD GXS [ RUH GH IXQF LRQDUH R ODPS HOHFWURQLF V LDV GLQ IXQF LXQH vQ LQWHUYDOXO [ [ G[ HVWH HJDO FX G[ LQGHSHQGHQW GH [ 2 ODPS DOXFUDW RUH6 VHFDOFXOH]HSUREDELOLWDWHDFDHDV LDV GLQIXQF LXQHvQ XUP WRDUHOH RUH 5 VSXQV)LH [ YDULDELODDOHDWRDUHFDUHH[SULP GXUDWDGHIXQF LRQDUHDXQHLO PSLvQRUH úL ILH $ HYHQLPHQWXO ÄODPSD OXFUHD] QX PDL SX LQ GH [ RUH´ LDU % HYHQLPHQWXO ÄODPSDLHVHGLQIXQF LXQHvQLQWHUYDOXO [ [ G[ ´3ULQLSRWH] 3 % $ G[ $YHP

3 $ 3[ t [ 3[ [ ) [ 3% 3 [ d [ [ G[ I [ G[ XQGHDPQRWDWSULQ I GHQVLWDWHDGHSUREDELOLWDWHDOXL [ 'HRDUHFH % $ 3% $ 3% I [ G[ 3 % $ G[ 3 $ 3 $ ) [ 5H]XOW

ª [ º I [ > ) [ @ « ³ I X GX » ¬ ¼

'HULYkQG vQ DPELL PHPEUL vQ UDSRUW FX [ VH RE LQH HFXD LD GLIHUHQ LDO

GI I [ FXVROX LD I [ NH [ [ t N FRQVWDQW 'LQ G[

f

f

I X GX

³

N ³ H [ G[ N

UH]XOW N LDU I [ H 3UREDELOLWDWHDFHUXW YDIL

3

3 d [ 3 d [

[

[ t

[ [ ³ H G[ ³ H G[

³ H [ G[

H H H

H

0RPHQWHOHXQHLYDULDELOHGHWLSFRQWLQXX )LH ^: 6 3` XQ V FkPS GH SUREDELOLWDWH úL [ R YDULDELO DOHDWRDUH D F UHL IXQF LHGHUHSDUWL LHHVWH ) )LH I GHQVLWDWHDGHUHSDUWL LHDYDULDELOHLDOHDWRDUH [ 'HILQL LH6HQXPHúWHYDORDUHPHGLHDYDULDELOHLDOHDWRDUH [ H[SUHVLD

0 [

f

f

f

f

³ [G) [ ³ [I [ G[

'HILQL LH 6H QXPHúWH PRPHQW GH RUGLQXO U U ` DO YDULDELOHL DOHDWRDUH FRQWLQXH [ H[SUHVLD

0 U [ D U [ LDUH[SUHVLD

0 U [ E U [

f

f

f

f

U ³ [ G) [

f

³[

f

U

G) [

³ [ I [ G[

f

U

³ [ I [ G[

f

U

VHQXPHúWHPRPHQWDEVROXWGHRUGLQ U DOYDULDELOHLDOHDWRDUH [ ÌQ DFHODúL PRG vQ FDUH VDX GHILQLW PRPHQWXO FHQWUDW GH RUGLQXO U GLVSHUVLD DEDWHUHD PHGLH S WUDWLF vQ FD]XO YDULDELOHORU DOHDWRDUH GLVFUHWH VH GHILQHVF úL SHQWUX YDULDELOHDOHDWRDUHGHWLSFRQWLQXX3URSULHW LOHYDORULLPHGLLúLDOHGLVSHUVLHLGDWHSHQWUX YDULDELOHDOHDWRDUHGHWLSGLVFUHWVHPHQ LQSHQWUXYDULDELOHDOHDWRDUHGHWLSFRQWLQXX ÌQDSOLFD LLVHvQWkOQHVFúLXUP WRDUHOHFDUDFWHULVWLFL

'HILQL LH6HQXPHVFDVLPHWULH $V úLH[FHV ( QXPHUHOH

P [

$V (

P [

P [

P [

GDF PRPHQWHOHUHVSHFWLYHH[LVW ([HPSOX)LH [ RYDULDELO DOHDWRDUHGHWLSFRQWLQXXFXGHQVLWDWHDGHSUREDELOLWDWH

I [

[ H [ \ 6 VH FDOFXOH]H YDORDUHD PHGLH GLVSHUVLD FRHILFLHQWXO GH

DVLPHWULHúLH[FHVXO 5 VSXQV$YHP

f

[ [H G[ ³ f

0 [

' [

f

[H [ G[ ³ f

f

[ G[ [ H ³f

f

³[ H

[

f

[

G[

G[

'LQFDX]DVLPHWULHLUHSDUWL LHLGDWHUH]XOW $V

P [ ³

³ [H

[ [ H G[

GHFL ( 'HILQL LH6HQXPHúWHPRPHQWFHQWUDWvQ D GHRUGLQXO U DOYDULDELOHLDOHDWRDUH [ PRPHQWXO GH RUGLQXO U DO YDULDELOHL DOHDWRDUH [ D LDU PRPHQWHOH YDULDELOHORU U

DOHDWRDUH [ D VHQXPHVFPRPHQWHDEVROXWHFHQWUDWHvQ D GHRUGLQXO U ([HPSOX >@ )LH R IXQF LH GH UHSDUWL LH ) FX GHULYDWH vQ WRDWH SXQFWHOH GH FRQWLQXLWDWHúLDVWIHOFDSHQWUX L GDWV H[LVWH N ! L DúDvQFkW OLP ) [ [ N

OLP > ) [ @ [

[of

[of

N

6 VHDUDWHF

U P L D L XQGH P LU HVWHPRPHQWXOGHRUGLQXO L FHQWUDWvQ D LDU 0 L D

0 L D

f

D

D

f

L L ³ [ D > ) [ @G[ ³ [ D ) [ G[

5 VSXQV$YHP

L L f f [ D [ D > ) [ @ ³ 0 L D ) c [ G[

L

D

L

D

[ D L ) [ D L

f

D

³

f

[ D L ) c[ G[

L

LQkQGVHDPDGHFRQGL LLOHSUREOHPHLUH]XOW f

[ D L ) c[ G[ P LU D ³ L f L 'HILQL LH 0HGLDQD XQHL YDULDELOH DOHDWRDUH [ HVWH QXP UXO 0 H VDX P[ 0 L D

SHQWUXFDUH

3[ t 0 H t VDX

) 0 H d

d 3[ d 0 H

úL ) 0 H t

'LQGHILQL LHUH]XOW XUP WRDUHOHSURSULHW L 'DF [ HVWH R YDULDELO DOHDWRDUH FX 0 [ LQHJDOLWDWHD 0 H P t V ,QHJDOLWDWHDOXL&HEkúHYQHG

3 [P tV d LQkQGVHDPDGHGHILQL LDPHGLDQHLUH]XOW

P úL '[ V DWXQFL DUH ORF

P V d 0 H d P V 'DF [ úL K VXQWGRX YDULDELOHDOHDWRDUHLQGHSHQGHQWHFDUHDXDFHHDúLIXQF LH GHUHSDUWL LH ) úL O HVWHXQQXP UUHDORDUHFDUHDWXQFLDXORFLQHJDOLW LOH

3[ 0 H t H d 3[ K t H H· § 3 [ 0 H t H d 3 [ K t H d 3¨ [ K t ¸ ¹ © SHQWUXRULFH H ! FX 0 H PHGLDQDYDULDELOHLDOHDWRDUH [

9DULDELOHOH DOHDWRDUH ILLQG LQGHSHQGHQWH úL FX DFHHDúL IXQF LH GH UHSDUWL LH DYHP P[ PK 0 H úL

3 [ K t H

3 [ 0 H P 0 H t H t 3 [ 0 H t H K 0 H d 3 [ 0 H t H 3 K 0 H d

'LQ UH]XOW 3 K 0 H d d

3[ K t H t

GHFL

3[ 0 H t H

3HQWUXGHPRQVWUD LDOXL SULPDLQHJDOLWDWHUH]XOW GLQ úLGHILQL LD PHGLDQHL3HQWUXLQHJDOLWDWHDDGRXDREVHUY PF

3 [ K t H

3

[ O K O t H

d

H· H· § § d 3¨ [ O t ¸ 3¨ K O t ¸ ¹ ¹ © © H· § 3 ¨ [ O t ¸ ¹ ©

'LQ GHILQL LD PHGLDQHL UH]XOW F vQ FD]XO XQHL YDULDELOH DOHDWRDUH [ GH WLS FRQWLQXXPHGLDQDHVWHXQLFGHWHUPLQDW GHHJDOLWDWHD [

³

I [ G[

f

f

³ I [ G[ [

'LQ SXQFW GH YHGHUH JHRPHWULF PHGLDQD HVWH DEVFLVD SXQFWXOXL SULQ FDUH WUHFH SDUDOHOD OD D[D 2\ FDUH vPSDUWH vQ GRX S U L HJDOH DULD OLPLWDW GH FXUED GH HFXD LH

I [ úLD[D 2[ ([HPSOX)LH [ RYDULDELO DOHDWRDUHDF UHLGHQVLWDWHGHSUREDELOLWDWHHVWH

\

S SHQWUX [ VDX [ ! ° ° I [ ® S °VLQ [ SHQWUX d [ d °¯ 6 VHGHWHUPLQHPHGLDQDOXL [ GHXQGH 5 VSXQV'DF [ HVWHGHWLSFRQWLQXXDWXQFL ) 0 H 0

H VLQ [G[ ³ GHFL FRV 0 H

5H]XOW 0 H

FRV [

0H

FRV 0 H

S ILJXUD

)LJXUD

,QHJDOLWDWHD OXL 0DUNRY )LH [ R YDULDELO DOHDWRDUH SR]LWLY D F UHL YDORDUH PHGLHHVWHILQLW 3HQWUXRULFH O ! DYHP

3[ t O0 [ d 1RW P P

P

0 [ úLDYHP

O

f

OP

f

f

OP

OP

³ [G) [ ³ [G) [ ³ [G) [ t OP ³ G) [

OP> ) OP @

O 'HILQL LH 0RGD 0R D XQHL YDULDELOH DOHDWRDUH HVWH YDORDUHD YDULDELOHL

GHXQGH 3 [ OP d

DOHDWRDUHFHDPDLSUREDELO

)XQF LHFDUDFWHULVWLF

$YkQGvQYHGHUHF LQVWUXPHQWXODQDOLWLFGHVWXGLXIXUQL]DWGHIXQF LDGHUHSDUWL LH HVWH GHVWXO GH GLILFLO VD LPSXV LQWURGXFHUHD XQHL QRL P ULPL FDUH V FDUDFWHUL]H]H YDULDELODDOHDWRDUH )LH ^:6 3` XQ V FkPS GH SUREDELOLWDWH [ R YDULDELO DOHDWRDUH D F UHL IXQF LHGHUHSDUWL LHHVWH ) 'HILQL LH 6H QXPHúWH IXQF LH FDUDFWHULVWLF D YDULDELOHL DOHDWRDUH [ DSOLFD LD

M[ \ o ^ GHILQLW GHUHOD LD f

³H

M[ W 0 HLW[

LW[

G) [

f

'DF [ HVWH GH WLS GLVFUHW úL LD YDORULOH [N N , , ` FX SUREDELOLW LOH

SN N, DWXQFL GHYLQH LW[ M[ W ¦ SN H N N ,

'DF [ HVWHGHWLSFRQWLQXXFXGHQVLWDWHDGHUHSDUWL LH I DWXQFL GHYLQH f

M[ W

³ H I [ G[ LW[

f

'DF QXH[LVW SHULFROGHFRQIX]LHYRPQRWD MW 'HRDUHFH HLW[

IXQF LDFDUDFWHULVWLF H[LVW SHQWUXRULFHYDULDELO DOHDWRDUHúL

HVWHGHWHUPLQDW vQPRGXQLFGHIXQF LDGHUHSDUWL LH ([HPSOH 'DF [ HVWH R YDULDELO DOHDWRDUH

§ [ ¨¨ O ¨H ©

"

[

'DF

I [

Q

O O O O H " H Q

MW

Q

f

¦H N

HVWH

° ® °E D ¯

LW[ N

SN

R

"· ¸ 9DULDELODHVWHGHWLSGLVFUHWGHFL "¸¸ ¹ f LW ON HO ¦ HLWN HO H N N

YDULDELO

FX

UHSDUWL LH

f

³ H I [ G[

'DF [ HVWHRYDULDELO DOHDWRDUHQRUPDO FX I [

[

K K [ D H [ \ S

f

K HLW[ H K [ D G[ LQkQG VHDPD F ³ S f

IXQF LD FDUDFWHULVWLF YD IL MW

³H

DYHP

E

HLW[ G[ ³ ED D

LW[

HLWE HLWD ED LW

f

XQLIRUP

)XQF LDFDUDFWHULVWLF YDIL

SHQWUX D d [ d E

f

S

DYHP

SHQWUX [ D VDX [ ! E

MW

3RLVVRQ

G[ RE LQHP

f

MW H

LWD

K

W

9RPGDvQFRQWLQXDUHFkWHYDSURSULHW LDOHIXQF LHLFDUDFWHULVWLFH

M

$YHPHYLGHQW M

f

³ G) [

f

3HQWUXRULFH W \ MW d f

f

f

f

6FULHP MW d

³ G) [

M W MW SHQWUXRULFH W \ f

M W

LW[ ³ H G) [

³H

LW[

f

G) [

f

³H

LW[

f

f

G) [

³H

f

M HVWHXQLIRUPFRQWLQX SH \ $YHP H

LW [

H

LW [

f

f

³ H G) [ ³ H LW [

f

LW [

G) [ d

f

³H

d

LW [

H

LW [

G) [

[ d$

LW [

dH

LW [

H

LW [

G) [ d

³ [ G) [ ³ G) [

[ d$

H

³H

[ !$

d W W LW [

G) [ M W

d [ W W

MW MW

LQkQGVHDPDF H

LW[

LW [

H

[ !$

LW [

'DW H ! DUELWUDU YRP OXD SH $ DúD vQFkW

H

³ G) [ GH vQGDW FH

[ !$

H DYHP MW MW H &DRFRQVHFLQ UH]XOW GHDLFLF SHXQLQWHUYDO VXILFLHQWGHPLFGLQMXUXORULJLQLL M QXVHSRDWHDQXOD W W

'DF K

D[ E D E \ DWXQFL MK W HLWE M[ DW

$YHP MK W

0 HLW D[ E

HLWE 0 HL DW [

HLWE M[ DW

)XQF LDFDUDFWHULVWLF DXQHLVXPHILQLWHGHYDULDELOHDOHDWRDUHLQGHSHQGHQWHHVWH HJDO FXSURGXVXOIXQF LLORUFDUDFWHULVWLFHFRUHVSXQ] WRDUHWHUPHQLORU 3HQWUX Q DYHP LW [ [ LW[ LW[ LW[ L\[ W M [ [

0 H

M[ W M[ W

0 H H

0H

0H

3HQWUX Q ! SURFHG PSULQLQGXF LHDVXSUDOXL Q )LH ) ) ) IXQF LL GH UHSDUWL LH úL M M M IXQF LLOH FDUDFWHULVWLFH FRUHVSXQ] WRDUH'DF )

) ) DWXQFL M MM úLUHFLSURF

)LH )

[Q [NQQ

) ) úL D

>D E@ DúDvQFkW QOLP [MQ [MQ of E

³H D

LW[

G) [

NQ

OLP ¦ H Q of

OLP

Q of

GHXQGHGHGXFHP

Q LW[ M

M

f NQ

³ ¦H

E úLUXOGHGLYL]LXQLDOHLQWHUYDOXOXL

3HQWUXRULFH W DYHP

ª ) [ MQ ) [MQ º ¬ ¼

§ Q · LW ¨¨ [ M \ ¸¸ © ¹

f M

ª ) [ MQ \ ) [MQ \ º HLW\ G) \ ¬ ¼

§ E \ LW[ · ¨ H G) [ ¸HLW\ G) \ H G) [ ³D ³¨ ³ ¸ f © D \ ¹ 7UHFkQGODOLPLW SHQWUX D o f E o f DYHP f § f LW[ ·§ f LW\ · LW[ ¨ ³fH G) [ ¨© ³fH G) [ ¸¸¹¨¨© ³fH G) \ ¸¸¹ DGLF M M M 5HFLSURFGDF M M M GLQFHOHGHPDLVXVUH]XOW F M M HVWHIXQF LD FDUDFWHULVWLF D OXL ) ) GH XQGH ) ) ) IXQF LD GH UHSDUWL LH HVWH XQLF E

f

LW[

GHWHUPLQDW 'HDLFLUH]XOW FDRFRQVHFLQ LPHGLDW F XQSURGXVGHIXQF LLFDUDFWHULVWLFH W

HVWHRIXQF LHFDUDFWHULVWLF M HVWHRIXQF LHFDUDFWHULVWLF

7HRUHPD )LH [ R YDULDELO DOHDWRDUH SHQWUX FDUH H[LVW EQ [ DWXQFL

IXQF LDFDUDFWHULVWLF M[ HVWHGH Q RULGHULYDELO úL M[N

L N D N [ d N d Q 'HPRQVWUD LH 'DF GHULY P IRUPDO GH N RUL N d Q IXQF LD FDUDFWHULVWLF

RE LQHP

f

M[N W L N ³ [ N HLW[ G) [

f

'DU f

³[ H

N LW[

G) [ d

f

f

³[

N

G) [ EN [

f

GHFLLQWHJUDODGLQPHPEUXOGRLH[LVW SHQWUX d N d Q úLGHFLUHOD LD DUHVHQV ) FkQGDLFL W VHRE LQH

M[ L N

N

f

³ [ G) [ N

L N D N [

f

([HPSOH 6 VHGHWHUPLQHIXQF LDFDUDFWHULVWLF DYDULDELOHLDOHDWRDUH [ FDUHXUPHD] OHJHDGH UHSDUWL LHELQRPLQDO úLV VHFDOFXOH]HSULPHOHGRX PRPHQWH

§

· ¸ GHFL T ¸¹

5 VSXQV 'LVWULEX LD OXL [ vQWUR VLQJXU SURE HVWH [ ¨¨ ©S

M[ W

SHLW T 'DF IDFHP Q H[WUDF LL LQGHSHQGHQWH DYHP Q YDULDELOH DOHDWRDUH

[L dL d Q

LQGHSHQGHQWH

MK W M[ W M[ Q W

SH

GH

WLSXO

[

úL

T úL McK W QSLHLW SHLW T Q

LW

MK QSL úL 0 K QS McKc $QDORJ D [ L

Q

¦ [

K

L

Q

L

GHFL

GH XQGH

Q S QST

)LHYDULDELOHOHDOHDWRDUHLQGHSHQGHQWH [ úL [ DOHF URUGHQVLW LGHUHSDUWL LHVXQW

I [ [

I [ [

° ® ° ¯ ° ° °[ ® ° ° [ °¯

SHQWUX [ > @

SHQWUX [ > @

SHQWUX [ > @ SHQWUX [ > @ SHQWUX [ >@

6 VHGHWHUPLQHIXQF LDFDUDFWHULVWLF DYDULDELOHLDOHDWRDUH K

5 VSXQV&RQIRUPSURSULHW LL DYHP MK W

M[ W úL

M[ W GHFL MK W

f

³H

f

LW[

f

LW[ ³ H I[ [ G[

f

I [ [ G[

VLQ W FRV W W

M[ W M[ W XQGH

LW[ H G[ ³

HLW H LW LW

[ [

VLQ W W

[ HLW[ G[ ³ [ HLW[ G[ ³

FRV W W

6 VH GHWHUPLQH IXQF LD FDUDFWHULVWLF úL PRPHQWHOH XQHL YDULDELOH DOHDWRDUH [

QRUPDO 1 PV 5 VSXQV$YHP I [

H V S

[ P V

GHFL [ P

f

LW[ V MW H G[ ³ V S f [P &XVFKLPEDUHDGHYDULDELO X LWV RE LQHP V

LPW H S

MW f X

³

GHRDUHFH H GX

W V f X

³H

GX

H

LPW

W V

f

S

f

$YHP Mc

LP V W H

LPW

W V

LP GHFL 0 [ P $QDORJ RE LQHP W

0 [ P V 0 [ P PV ' [ V HWF 'HILQL LH 2 IXQF LH GH UHSDUWL LH ) HVWH QRUPDOL]DW GDF YDORULOH OXL ) vQ ) [ ) [ SXQFWHOHVDOHGHGLVFRQWLQXLWDWHVXQWHJDOHFX

$P Y ]XW F GDW ILLQG IXQF LD GH UHSDUWL LH D XQHL YDULDELOH DOHDWRDUH SXWHP FRQVWUXLIXQF LDVDFDUDFWHULVWLF 5H]XOWDWXOUHFLSURFHVWHGDWGH )RUPXODGHLQYHUVLXQH)LHYDULDELODDOHDWRDUH [ DF UHLIXQF LHGHUHSDUWL LH HVWH ) úLIXQF LDFDUDFWHULVWLF M 'DF [ úL [ [ [ VXQWSXQFWHGHFRQWLQXLWDWH DOXL ) DWXQFL F

H F o f S ³ F

) [ ) [ OLP

LW[

H LW

LW[

MW GW

5HOD LD DUHORFSHQWUXRULFH [ [ [ [ GDF ) HVWHQRUPDOL]DW 3HQWUXGHPRQVWUD LHYH]L>@ 'LQIRUPXODGHLQYHUVLXQHVHGHGXFHFXXúXULQ 7HRUHPD GH XQLFLWDWH )XQF LD GH UHSDUWL LH HVWH GHWHUPLQDW vQ PRG XQLF GH IXQF LDVDFDUDFWHULVWLF ÌQ LSRWH]D F [ DUH GHQVLWDWH GH UHSDUWL LH GLQ IRUPXOD GH LQYHUVLXQH UH]XOW XUP WRDUHOHFRQVHFLQ H

'DF IXQF LDGHUHSDUWL LH ) HVWHGHULYDELO vQSXQFWXO [ GHULYDWDVD I vQ [ HVWHGDW GHUHOD LD

I [

F

HLWK LW[ OLP OLP H MW GW K o f F o f S ³ LWK F

GDF úLQXPDLGDF PHPEUXOGUHSWH[LVW 'DF IXQF LD FDUDFWHULVWLF M HVWH DEVROXW LQWHJUDELO SH \ DWXQFL IXQF LD GH UHSDUWL LHFRUHVSXQ] WRDUH ) HVWHDEVROXWFRQWLQX GHULYDWDHL I HVWHFRQWLQX úL f

H LW[ MW GW ³ S f

I [

([HPSOH >@ 6 VH GHWHUPLQH IXQF LD GH UHSDUWL LH FRUHVSXQ] WRDUH IXQF LHL FDUDFWHULVWLFH

MW H

W

5 VSXQV)RUPXODGHLQYHUVLXQHVHVFULH f

H LW[ MW GW S ³f LW

) [ )

W

f

f

W

H LW[ H GW S ³f LW W

f

VLQ W[ FRV W[ H GW H GW ³ S f W S ³f LW S

W

f

VLQ W[ ³ W H GW 'HULYkQG vQ UDSRUW FX [ úL LQWHJUkQG SULQ S U L RE LQHP f

W

f

W

c c ) c[ W VLQ W[ H GW úL DQDORJ ) [ W VLQ W[ H GW GH XQGH ³ ³ S[ f S f UH]XOW HFXD LDGLIHUHQ LDO ) cc [ [) c [

,QWHJUkQGDYHP ) c [

&H

[

GHXQGH [

) [ & ³ H

X

GX &

f

f

³H

LQkQGVHDPDF

[

S GLQ ) f UH]XOW &

G[

LDUGLQ

f

GHFL S

) f UH]XOW &

[

X

H GX ³ S f

) [

6 VH GHWHUPLQH GHQVLWDWHD GH UHSDUWL LH D YDULDELOHL DOHDWRDUH D F UHL IXQF LH FDUDFWHULVWLF HVWH MW H 5 VSXQV$YHPFRQIRUPFRQVHFLQ HL W

f

W H H LW[ GW ³ S f

I [

f

f º ª W LW[ W LW[ « ³ H H GW ³ H H GW » S ¬ f ¼ f

H W HLW[ H LW[ GW ³ S

W H FRV W[GW S ³

[ \ S [

,QWHJUkQGSULQS U LRE LQHP I [

5HSDUWL LLSUREDELOLVWLFHFODVLFH 5HSDUWL LLGHWLSGLVFUHW ÌQ PXOWH DSOLFD LL SUDFWLFH DOH WHRULHL SUREDELOLW LORU vQWkOQLP FD]XUL vQ FDUH XQ H[SHULPHQWVDXPDLPXOWHH[SHULPHQWHDQDORDJHVHUHSHW GHXQQXP UGHRULILHFDUHGLQ HOHGXFkQGODUHDOL]DUHDVDXODQHUHDOL]DUHDXQXLDQXPLWHYHQLPHQW&HHDFHLQWHUHVHD] HVWHQXP UXOGHUHDOL] ULDOHHYHQLPHQWXOXLvQWURVHULHGHH[SHULPHQWH([SHULPHQWHOH SRWILHIHFWXDWHvQDFHOHDúLFRQGL LLVDXvQFRQGL LLGLIHULWH 7HRUHPDSDUWLFXODU DH[SHULPHQWHORUUHSHWDWH 6 FRQVLGHU P XUP WRDUHD SUREOHP WUHL IRFXUL LQGHSHQGHQWH VXQW WUDVH DVXSUD XQHL LQWH3UREDELOLWDWHDGHDDWLQJH LQWDSHQWUXILHFDUHGLQHOHHVWH S 6 VHGHWHUPLQH SUREDELOLWDWHDFDGRX GLQFHOHWUHLIRFXULV DWLQJ LQWD )LH $ HYHQLPHQWXOÄGRX GLQFHOHWUHLIRFXULDWLQJ LQWD´úLILH $L L HYHQLPHQWHOHÄIRFXO L DDWLQV LQWD´ÌQDFHVWHFRQGL LL $ VHVFULH

$

$ $

$& * $ $& $ * $& $ $

&HOH WUHL YDULDQWH VXQW LQFRPSDWLELOH LDU HYHQLPHQWHOH FDUH OH FRPSXQ VXQW LQGHSHQGHQWH5H]XOW 3 $ 3 $ 3 $ 3 $& 3 $ 3 $& 3 $ 3 $& 3 $ 3 $

GHXQGH 3 $

S S

'H R PDQLHU DQDORJ VH UH]ROY XUP WRDUHD SUREOHP PDL JHQHUDO VH IDF Q H[SHULPHQWH LQGHSHQGHQWH vQ ILHFDUH GLQ HOH XQ HYHQLPHQW $ VH SRDWH UHDOL]D FX SUREDELOLWDWHD S úL QX VH UHDOL]HD] FX SUREDELOLWDWHD T S 6 VH GHWHUPLQH SUREDELOLWDWHDFDvQFHOH Q H[SHULPHQWHHYHQLPHQWXO $ V VHUHDOL]H]HH[DFWGH P RUL )LH %P HYHQLPHQWXOÄ $ VHUHDOL]HD] H[DFWGH P RULvQFHOH Q H[SHULPHQWH´úL

$L HYHQLPHQWHOHÄ $ VDUHDOL]DWvQH[SHULPHQWXOGHUDQJ L ´ L Q )LHFDUH YDULDQW GH UHDOL]DUH D OXL %P VH FRPSXQH GLQ P DSDUL LL D HYHQLPHQWXOXL $ úL GLQ

Q P QHUHDOL] ULDOHOXL $ GHFL Q P UHDOL] ULDOHOXL $& GHFL $ $ $P $P& $Q& * %P

* $& $ $P $P& $Q& *

&

& QP

* * $ $

$Q P $Q

1XP UXO GH PDQLHUH vQ FDUH SXWHP DOHJH GLQ FHOH Q H[SHULPHQWH P H[SHULPHQWH vQ FDUH VH UHDOL]HD] $ HVWH &QP 7RDWH YDULDQWHOH VXQW LQFRPSDWLELOH H[SHULPHQWHOHVXQWLQGHSHQGHQWHGHFL 3%P 3P Q S P T Q P S P T Q P

GH & QP RUL

GHFL

3P Q

&QP S P T Q P

3UREDELOLW LOH 3P Q DXIRUPDWHUPHQLORUGLQGH]YROWDUHDELQRPXOXL S T Q

'LQDFHDVW FDX] FkPSXOGHHYHQLPHQWHGLQDFHDVW VFKHP SUREDELOL]DWGXS UHJXOD VHQXPHúWHFkPSELQRPLQDOHVWHFODUF HYHQLPHQWHOHHOHPHQWDUHDOHFkPSXOXL DVRFLDW H[SHULPHQWXOXL SRW IL FRQVLGHUDWH FD HOHPHQWH DOH SURGXVXOXL FDUWH]LDQ : Q : u u : $FHDVW VFKHP SUREDELOLVWLF DIRVWFHUFHWDW vQPRGGHRVHELWGH-%HUQRXOOLGH DFHHDVHPDLQXPHúWHúLVFKHPDOXL%HUQRXOOL 6 FDOFXO P YDORDUHD PHGLH úL GLVSHUVLD XQHL YDULDELOH DOHDWRDUH UHSDUWL]DW ELQRPLQDO$YHP Q

0 [

¦ N& N

N Q

SN TQN

3HQWUXDFDOFXODDFHDVW VXP YRPSOHFDGHODHJDOLWDWHD Q

SW T Q ¦ &QN S N W N T Q N SHFDUHRGHULY PvQUDSRUWFX W

QS SW T

Q

N

Q

¦ N& N

N Q

S N W N T Q N

LQkQGVHDPDF S T RE LQHP

'HDLFLSHQWUX W

Q

¦ N& N

5H]XOW

N Q

S N T QN

QS

0 [ QS 3HQWUX D FDOFXOD GLVSHUVLD YD WUHEXL V FDOFXO P PRPHQWXO GH RUGLQXO GRL D YDULDELOHLDOHDWRDUH [ Q

¦N &

0 [

N

'LQ SULQvQPXO LUHFX W RE LQHP

QSW SW T

Q

HJDOLWDWHFDUHGHULYDW vQUDSRUWFX W QHG

QS SW T

Q

'HDLFLSHQWUX W

S N T Q N

Q

¦ N& N

N Q

QQ S W SW T

SNW N TQN

Q

úL S T RE LQHP

0 [ 5H]XOW

N Q

Q

¦N & N

N Q

S N W N T Q N

QS QQ S

' [ 0 [ >0 [ @

QST

0RGD XQHL UHSDUWL LL HVWH YDORDUHD YDULDELOHL DOHDWRDUH FHD PDL ULGLFDW 0RGD vQ FD]XOOHJLLELQRPLDOHHVWHRYDORDUHvQWUHDJ FXSULQV vQWUH QS T úL QS T 'HH[HPSOXSHQWUX Q úL S DYHPGRX YDORULPRGDOH úL ([HPSOH 'RL SDUWHQHUL FX IRU HJDO ER[HD] UXQGH SUREDELOLWDWHD FD RULFDUH GLQ HL V FkúWLJHRUXQG HVWH

6 VHFDOFXOH]HYDORDUHDPHGLHGLVSHUVLDúLDEDWHUHDPHGLH

S WUDWLF DYDULDELOHLDOHDWRDUHFDUHUHSUH]LQW QXP UXOGHUXQGHFkúWLJDWHGHXQXOGLQ SDUWHQHUL 5 VSXQV 9DULDELOD DOHDWRDUH [ DUH UHSDUWL LD ELQRPLDO 3 [

N

§· & ¨ ¸ ©¹ N

$YHP 0 [ ' [ '[ 2 XUQ FRQ LQH ELOH DOEH úL ELOH QHJUH 6H IDF GH H[WUDF LL GLQ XUQ N

SXQkQGGXS ILHFDUHH[WUDF LHELODvQDSRLvQXUQ 6HFHUHRPDUJLQHLQIHULRDU SHQWUX SUREDELOLWDWHD FD QXP UXO GH DSDUL LL D ELOHL DOEH vQ FHOH GH H[WUDF LL V ILH FXSULQVvQWUH úL 5 VSXQV'DF QRW PSULQ [ YDULDELODDOHDWRDUHFDUHUHSUH]LQW QXP UXOGHDSDUL LLDOH ELOHL DOEH [ DUH UHSDUWL LD ELQRPLDO $YHP SUREDELOLWDWHD FD vQWUR H[WUDF LH V

RE LQHP R ELO DOE S

GHFL T

LQHJDOLWDWHDOXL&HEvúHYúLVHRE LQH

0 [ ' [ 6H DSOLF

3 [ 3 [ t

/D FRQWUROXO GH FDOLWDWH HVWH FRQWURODW XQ ORW GH SLHVH 3UREDELOLWDWHD FD OXkQG OD vQWkPSODUHRSLHV GLQORWV ILHGHIHFW HVWH 6XQWFRQWURODWH SLHVHGLQ ORWFDUHVXQWOXDWHSHUkQGúLUHSXVHILHFDUHvQDSRLvQORWGXS FHDIRVWFRQWURODW 6H FHUH D 3UREDELOLWDWHDFDvQWUHFHOH SLHVHFRQWURODWHV DYHPFHOPXOWSDWUXSLHVH GHIHFWH E &HOPDLSUREDELOQXP UGHSLHVHEXQH 5 VSXQV D 3

¦ 3 N N

¦ & N

N

N

N

E > @ >@ 8QJUXSGH HOHYLDXGLD] XQFXUVGH WULPHVWUH/DWHUPLQDUHGDXXQH[DPHQOD FDUHOLVHSXQHILHF UXLDFkWHRvQWUHEDUHGLQPDWHULDILHF UXLWULPHVWUXùWLPF HOHYL FXQRVF vQ vQWUHJLPH PDWHULD SUHGDW HOHYL FXQRVF GLQ PDWHULD SUHGDW vQILHFDUHWULPHVWUX HOHYLFXQRVFFkWH GLQPDWHULH HOHYL HOHYLFkWH úLGRLHOHYLQXFXQRVFQLPLFGLQPDWHULDSUHGDW /DH[DPHQXQ HOHYU VSXQGHELQHODSULPHOHGRX vQWUHE ULúLIDOVODDWUHLD&DUHHVWHSUREDELOLWDWHD FD HO V ILH XQXO GLQWUH HOHYLL FDUH FXQRVF vQWUHDJD PDWHULH GLQvQWUHDJDPDWHULH 5 VSXQV )LH HYHQLPHQWHOH $ FLQFL HOHYL FXQRVF vQWUHDJD PDWHULH $ HOHYL FXQRVF GLQPDWHULH $ HOHYLFXQRVF GLQPDWHULH $ HOHYLFXQRVF

$ HOHYLFXQRVFFkWH GLQPDWHULHúL $ HOHYLQXFXQRVFQLPLFGLQ 3 $ 3 $ 3 $ PDWHULD SUHGDW $YHP 3 $ 3 $ 3 $ )LH HYHQLPHQWXO ; XQ HOHY U VSXQGH ELQH OD GRX vQWUHE UL úL IDOV OD D WUHLD $YHP

3 ; $

§· 3 ; $ & ¨ ¸ © ¹

§· §· 3 ; $ & ¨ ¸ 3 ; $ & ¨ ¸ 3 ; $ © ¹ © ¹

9RPGDvQFRQWLQXDUHGRX GLQFHOHPDLFXQRVFXWHJHQHUDOL] ULDOHVFKHPHL ELQRPLQDOH

§· 3 ; $ & ¨ ¸ © ¹

7HRUHPDJHQHUDO DH[SHULPHQWHORUUHSHWDWH

3UHVXSXQHP F VH IDF Q H[SHULPHQWH LQGHSHQGHQWH vQ ILHFDUH GLQ HOH XQ HYHQLPHQW $ VHSRDWHUHDOL]DFXSUREDELOLWDWHD SL L Q úLQXVHUHDOL]HD] FX

SL 6 VH GHWHUPLQH SUREDELOLWDWHD FD vQ FHOH Q H[SHULPHQWH HYHQLPHQWXO $ V VHSURGXF H[DFWGH P RUL SUREDELOLWDWHD TL

&XQRWD LLOHI FXWHODVFKHPDELQRPLQDO DYHP GHXQGH

3P Q

S S SP TP TQ T S S TQ SQ TT TQ P SQ P SQ

$FHDVW SUREDELOLWDWHHVWHHJDO FXVXPDWXWXURUSURGXVHORUSRVLELOHvQFDUH S LQWU GH P RULFXLQGLFLGLIHUL LLDU T GH Q P RULFXLQGLFLGLIHUL L 2EVHUYkQGF HIHFWXkQGSURGXVXOD Q ELQRDPH SL ] TL L

RE LQH

MQ ]

Q VH

Q

S ] T L

L

L

XQGH ] HVWH XQ SDUDPHWUX RDUHFDUH úL DWXQFL 3P Q HVWH FRHILFLHQWXO OXL ] P GLQ DFHVW SURGXV$FHDVW IXQF LHVHQXPHúWHIXQF LHJHQHUDWRDUHDSUREDELOLW LORU 3P Q $YHP Q

Q

L

P

SL ] TL ¦ 3P Q ] P FX

Q

¦3

P

P Q

(VWHHYLGHQWF WHRUHPDSDUWLFXODU DH[SHULPHQWHORUUHSHWDWHUH]XOW GLQWHRUHPD JHQHUDO SHQWUX S SQ S úL T TQ T ÌQDFHVWFD]IXQF LDJHQHUDWRDUH GHYLQH MQ ]

S] T Q VDX

Q

S] T Q ¦ &QP S P T Q P ] P P

GHXQGHIRUPXOD ÌQ XQHOH H[SHULPHQWH SUDFWLFH VH FHUH SUREDELOLWDWHD GH UHDOL]DUH D HYHQLPHQWXOXL $ GHFHOSX LQ P RULvQFHOH Q H[SHULPHQWH1RWkQGFX &P DFHVW HYHQLPHQWDYHP &P

%P * %P * * %Q GHXQGH 3&P 3P Q 3P Q 3Q Q

VDX

3&P

Q

¦3

N P

N Q

6FKHPDSUREDELOLVWLF GHVFULV VHQXPHúWHVFKHPDOXL3RLVVRQ

([HPSOH /D XQ FRQFXUV GH PDWHPDWLF FDQGLGD L SULPHVF FkWH XQ SOLF FDUH FRQ LQH Q Q ! ELOHWHFXSUREOHPHGHDOJHEU úLJHRPHWULH&HOHWUHLSOLFXULFRQ LQUHVSHFWLY FkWH VXELHFWHGHDOJHEU )LLQGH[DPLQD LFHLWUHLFDQGLGD LH[WUDJILHFDUHFkWH XQ ELOHW GLQ SOLF ([WUDJHUHD I FkQGXVH OD vQWkPSODUH V VH DIOH SUREDELOLWDWHD XUP WRDUHORUHYHQLPHQWH D 7UHLFDQGLGD LV ILHH[DPLQD LODJHRPHWULH E 1LFLXQFDQGLGDWV QXILHH[DPLQDWODJHRPHWULH F &HOSX LQXQFDQGLGDWV ILHH[DPLQDWODDOJHEU 20HWDSDMXGH HDQ 5 VSXQV6HDSOLF VFKHPDOXL3RLVVRQ$YHP

Q ·§ Q ·§ Q· § ¨ ] ¸¨ ] ¸¨ ] ¸ Q ¹© Q Q ¹© Q Q ¹ ©Q ª ] Q ] Q Q ] Q Q Q º¼ Q ¬ Q Q Q 7HUPHQXOOLEHUGLQSROLQRPXO M ] YDIL 3 Q &RHILFLHQWXOOXL ] GLQ M ] HVWH 3 Q 3 3 >@ 8Q DSDUDW VH FRPSXQH GLQ HOHPHQWH ILDELOLWDWHD SUREDELOLWDWHD GH IXQF LRQDUH I U GHIHF LXQH vQWUXQ LQWHUYDO GH WLPS HOHPHQWHORU HVWH S S S S S 'DF QLFL XQXO GLQ HOHPHQWH QX HVWHvQSDQ SUREDELOLWDWHDGHIXQF LRQDUHDDSDUDWXOXLI U GHIHF LXQLHVWHHJDO FX GDF XQXO GLQ FHOH FLQFL HOHPHQWH HVWH vQ SDQ DFHDVW SUREDELOLWDWH HVWH LDU

M ]

D E F

GDF GRX HOHPHQWH VXQW vQ SDQ DSDUDWXO QX SRDWH IXQF LRQD 6 VH GHWHUPLQH SUREDELOLWDWHDFDDSDUDWXOV SRDW HIHFWXDPXQFDSHQWUXFDUHHVWHGHVWLQDW 5 VSXQV)DFHPXUP WRDUHOHLSRWH]H $ QLFLXQHOHPHQWQXHVWHvQSDQ $ XQ HOHPHQWHVWHvQSDQ 3UREDELOLW LOHORUYRUIL 3 $

M ]

3 3 $ 3 &XP

] ] ] [ ]

] GHXQGH 3 $ 3 $ 1RWkQGFX $ HYHQLPHQWXOÄDSDUDWXOHIHFWXHD] PXQFDSHQWUXFDUHHVWHGHVWLQDW´ IRUPXODSUREDELOLW LLWRWDOHQHG 3 $

5HSDUWL LD3RLVVRQGHSDUDPHWUXO 6 SUHVXSXQHP F vQ UHSDUWL LD ELQRPLQDO OX P QS GHWHUPLQ PvQDFHVWFD]YDORULOHSUREDELOLW LORUSHQWUX Q o f 2E LQHP

ª QQ Q N ON § O · Q N º OLP « ¨ ¸ » Qof QN N © Q ¹ ¼» ¬«

OLP 3N Q

Qof

1RWkQG SN

f

¦ SN N

ON O H N

OLP 3N Q DYHP

Qof

ON O H N

SN úL

O FRQVWDQW 6

f

ON N

HO ¦ N

H O HO

GHFL SUREDELOLW LOH GHILQLWH SULQ VXQW

WHUPHQLLXQHLUHSDUWL LL 'HILQL LH 5HSDUWL LD GHWHUPLQDW SULQ SUREDELOLW LOH VH QXPHúWH UHSDUWL LH3RLVVRQGHSDUDPHWUX O LDUYDULDELODDOHDWRDUH

§ [ ¨ O ¨H ©

O O H

" N "· ¸ O O ON O H " H "¸ N ¹

VHQXPHúWHYDULDELO DOHDWRDUH3RLVVRQ 6 FDOFXO PYDORDUHDPHGLHúLGLVSHUVLDYDULDELOHLDOHDWRDUH [ $YHP

0 [ GHFL

O

f

¦N N

O N O H N

f

¦ N N N

O

f

N

f

¦N N

N N

N

ON H

O O f O N O H ¦N H N N N

O

N

O N O N

O HO ¦ GHFL

f

0 [ O

'HDVHPHQHD

0 [

ON OH ¦ OH O H O N N

ON O N H ¦ N N f

' [ O

O O

0RGDHVWHRYDORDUHvQWUHDJ FXSULQV vQWUH P úL P

8QD GLQWUH FHOH PDL LPSRUWDQWH SURSULHW L D UHSDUWL LHL 3RLVVRQ HVWH DFHHD F YDORDUHDPHGLHúLGLVSHUVLDYDULDELOHLDOHDWRDUH [ VXQWHJDOHÌQSUDFWLF GDF PHGLDúL GLVSHUVLD FDOFXODW SH ED]D GDWHORU REVHUYDWH VXQW HJDOH VDX IRDUWH DSURSLDWH SXWHP FRQVLGHUDF UHSDUWL LDWHRUHWLF DYDULDELOHLVWXGLDWHHVWHGHWLS3RLVVRQ 5HSDUWL LD 3RLVVRQ HVWH GHQXPLW OHJHD HYHQLPHQWHORU UDUH GDWRULW SURSULHW LL VDOH GH D DSUR[LPD R UHSDUWL LH ELQRPLDO FkQG QXP UXO H[SHULPHQWHORU Q HVWH IRDUWH PDUHLDUSUREDELOLWDWHDGHDSDUL LHDHYHQLPHQWXOXLFRQVLGHUDWHVWHIRDUWHPLF ([HPSOX 2 PDúLQ IDEULF XQ QXP U PDUH GH SLHVH GLQWUH FDUH XQHOH VXQW GHIHFWH6HIDFREVHUYD LLSH 1 GHHúDQWLRDQHD Q SLHVHILHFDUHDOHVH ODvQWkPSODUH2E LQHPXUP WRDUHGLVWULEX LHDSLHVHORUGHIHFWH 1USLHVHGHIHFWH 1UHúDQWLRQ QL

[L

SHVWH WRWDO

) FkQG LSRWH]D F SURSRU LD SLHVHORU GHIHFWH U PkQH FRQVWDQW QXP UXO ; DO SLHVHORU GHIHFWH vQ ILHFDUH HúDQWLRQ HVWH R YDULDELO DOHDWRDUH ELQRPLDO GH SDUDPHWUX

Q

úL S YDORDUHQHFXQRVFXW 0HGLDGHVHOHF LHHVWH [

SXWHPHVWLPD S

[ Q

¦Q [ L

L L

1

úL

ÌQ DFHVW H[HPSOX SXWHP DSUR[LPD OHJHD ELQRPLDO FX OHJHD 3RLVVRQ SURSRU LD SLHVHORUGHIHFWHILLQGVXILFLHQWGHPLF LDUHIHFWLYXOILHF UXLHúDQWLRQHVWH Q &RPSDUD LD vQWUH IUHFYHQ HOH REVHUYDWH úL SUREDELOLW LOH DMXVWDWH SULQ OHJHD ELQRPLDO úL3RLVVRQUH]XOW GLQWDEHOXO

1XP USLHVH )UHFYHQ DGH GHIHFWH REVHUYD LH

SHVWH 7RWDO

3UREDELOLWDWH 3UREDELOLWDWH OHJH OHJH ELQRPLDO 3RLVVRQ

6FKHPDSROLQRPLDO

2 XUQ FRQ LQH ELOH GH FXORULOH F F FV vQ SURSRU LL FXQRVFXWH GHFL

FXQRDúWHP SUREDELOLWDWHD SL GH DSDUL LH vQWUR H[WUDF LH D XQHL ELOH GH FXORDUHD FL

L V 6HIDF Q H[WUDF LLDFkWHRELO FXFRQGL LDFDODILHFDUHH[WUDF LHXUQDV DLE DFHHDúLFRPSR]L LH)LH $D HYHQLPHQWXOFDvQH[WUDF LLOHHIHFWXDWHV DSDU D L ELOH V GHFL D D D V 3UREDELOLWDWHDDFHVWXLHYHQLPHQWHVWH Q D D 3 $D S S SVD V DD D V $FHDVW SUREDELOLWDWHVHPDLQRWHD] FX 3Q D D V

GHFXORDUHD FL L

([SHULPHQWXO GHVFULV vPSUHXQ FX FkPSXO GH HYHQLPHQWH DVRFLDW SUREDELOL]DW GXS UHJXOD VHQXPHúWHVFKHP SROLQRPLDO &kPSXOSUREDELOL]DWGLQDFHDVW VFKHP VHQXPHúWHFkPSSROLQRPLDO ([HPSOX >@ 8Q PXQFLWRU SURGXFH FX SUREDELOLW LOH úL UHVSHFWLYRSLHV EXQ RSLHV FXXQGHIHFWUHPHGLDELOúLXQUHEXW0XQFLWRUXODSURGXV WUHLSLHVH&DUHHVWHSUREDELOLWDWHDFDvQWUHFHOHWUHLSLHVHV ILHFHOSX LQRSLHV EXQ úL FHOSX LQXQUHEXW" 5 VSXQV3HQWUXFDOFXODUHDDFHVWHLSUREDELOLW LDSOLF PVFKHPDSROLQRPLDO úLDQXPH

3

3 3 3

6FKHPDELOHLQHUHYHQLWH 6HFRQVLGHU RXUQ FXXUP WRDUHDVWUXFWXU D ELOHGHFXORDUHD F D ELOHGH

FXORDUHD F DV ELOHGHFXORDUHD FV 6HIDF Q H[WUDF LLI U DUHSXQHELODH[WUDV vQDSRL vQ XUQ H[SHULHQ D HVWH HFKLYDOHQW FX H[WUDJHUHD D Q ELOH GHRGDW )LH $D HYHQLPHQWXO DOHDWRU ÄDSDUL LD D H[DFW D N N FHORU Q ELOHH[WUDVHXQGH D

V ELOH GH FXORDUHD FN vQ JUXSXO V

D D V d D N d DN ¦ D N

Q $YHPXQFkPS

N

GHHYHQLPHQWHSHFDUHvOYRPSUREDELOL]DGXS GHILQL LDFODVLF DSUREDELOLW LL 1XP UXO FD]XULORU HJDO SRVLELOH GH UHDOL]DUH D HYHQLPHQWXOXL $D HVWH GDW GH

&DQ D V WRDWH SRVLELOLW LOH GH H[WUDF LH D Q ELOH GLQ WRWDOXO GH ELOH DIODWH vQ XUQ D

D

D

1XP UXOFD]XULORUIDYRUDELOHUHDOL] ULLOXL $D HVWHGDWGH &D &D &D VV 'HFL

3 $D 3Q D D V

D

D

&D &D &DDVV &DQ D V

([SHULPHQWXO GHVFULV vPSUHXQ FX FkPSXO GH HYHQLPHQWH DVRFLDW SUREDELOL]DW GXS UHJXODGDW VHQXPHúWHVFKHP KLSHUJHRPHWULF VDXVFKHPDELOHLQHUHYHQLWH ([HPSOH 2XUQ FRQ LQH ELOHGLQWUHFDUH ELOHDOEH QHJUH URúLLúL YHU]L6H H[WUDJ ELOH GLQ XUQ I U D UHSXQH ELOD H[WUDV vQDSRL 6H FHUH SUREDELOLWDWHD FD vQWUHFHOH ELOHH[WUDVHV DYHP D 7UHLELOHDOEHRELO URúLHúLXQDYHUGH E 2ELO DOE GRX QHJUHúLGRX URúLL 5 VSXQV6HDSOLF VFKHPDELOHLQHUHYHQLWH$YHP

& &&& & 3HQWUX FRQWUROXO GH FDOLWDWH DO XQXL ORW GH 1 SLHVH VH H[WUDJ GHRGDW Q SLHVH Q 1 ùWLLQGF vQORWDYHP D SLHVHUHEXWúL E SLHVHEXQH D E 1 V VH D 3

& &&& E 3 &

VFULH WDEORXO GH GLVWULEX LH D YDULDELOHL DOHDWRDUH FDUH UHSUH]LQW QXP UXO GH SLHVH UHEXW GLQWUH FHOH Q H[WUDVH 6 VH FDOFXOH]H YDORDUHD PHGLH úL GLVSHUVLD DFHVWHL YDULDELOH 5 VSXQV9DULDELODDOHDWRDUH [ SRDWHOXDYDORULOH Q FXSUREDELOLW LOH

3[

N

&DN &EQ N N & 1Q

Q GHFL

§ N ¨ N QN [ ¨ &D &E ¨ &Q 1 ©

· ¸ ¸¸ N ¹

Q

$YHP

0 [ GDU

& 1Q

¦ N&DN &EQ N N

Q

¦ &DN&EQ N N

úL

D & 1Q

Q

Q

¦& N

0 [ D

N D

&EQ N

& 1Q & 1Q

Q

¦& N

N D

&EQ N

&DQE

& 1Q

Q D 1

D E T GHFL 0 [ QS 1 1 0 [[ 0 [ GDU 'HDVHPHQHD 0 [

1RW P S

& 1Q 0 [[ GHXQGH

0 [

Q

¦ N N &DN &EQ N N

DD &DQE

D D Q Q D 1 1 1

'LVSHUVLDYDIL

' [

Q

QDE 1 Q 1 1

Q

DD ¦ &DN&QQ N

N

DD & 1Q

QD >DQ 1 Q@ 1 1 QST

1 Q 1

5HSDUWL LLGHWLSFRQWLQXX ÌQFHOHFHXUPHD] QHYRPUHIHULODUHSDUWL LLOHXQLGLPHQVLRQDOHGHWLSFRQWLQXX )LH ^:6 3` XQ V FkPSGHSUREDELOLWDWH PXO LPHDYDULDELOHORUDOHDWRDUH

GHILQLWH SH : úL PXO LPHD IXQF LLORU GH UHSDUWL LH 9RP SUHVXSXQH F SHQWUX RULFH

) H[LVW YDULDELODDOHDWRDUH [ DF UHLIXQF LHGHUHSDUWL LHHVWH )

5HSDUWL LDGHGHQVLWDWHXQLIRUP ÌQ PXOWH SUREOHPH VH vQWkOQHVF YDULDELOH DOHDWRDUH FRQWLQXH DOH F URU YDORUL VXQW vQWUXQDQXPLWLQWHUYDOúLDVWIHOF WRDWHYDORULOHVXQWHFKLSUREDELOHDXDFHHDúLGHQVLWDWH GHSUREDELOLWDWH 'HH[HPSOXODFkQW ULUHDXQXLRELHFWFXREDODQ GHSUHFL]LHúLQHGLVSXQkQGGH JUHXW L PDL PLFL GH XQ JUDP UH]XOWDWXO FkQW ULULL DUDW F JUHXWDWHD RELHFWXOXL HVWH FXSULQV vQWUH N úL N JUDPH 6SXQHP F JUHXWDWHD RELHFWXOXL HVWH N

JUDPH

$GPLWHP F HURDUHD FRPLV [ HVWH R YDULDELO DOHDWRDUH UHSDUWL]DW FX R GHQVLWDWH

§ · ¸ © ¹

XQLIRUP vQLQWHUYDOXO ¨

'HILQL LH 6H QXPHúWH IXQF LH GH UHSDUWL LH XQLIRUP SH >D E@ IXQF LD GH UHSDUWL LHDF UHLGHQVLWDWHGHSUREDELOLWDWHHVWH

I [

\

° ®E D ° ¯

SHQWUX [ >D E@ SHQWUX [ >D E@

)XQF LD GH UHSDUWL LH XQLIRUP YD IL GDW GH DULD FXSULQV vQWUH JUDILFXO FXUEHL

I [ úLD[D 2[ FDUHVHDIO ODVWkQJDOXL [ 'HFL

) [

SHQWUX [ D

° °[D ® °E D ¯°

SHQWUX D d [ E

SHQWUX E d [

LDUJUDILFXOHLHVWHFHOGLQILJXUD

)LJXUD

'HILQL LH 9DULDELOD DOHDWRDUH [ VH QXPHúWH XQLIRUP SH >D E@ GDF DUH

UHSDUWL LHXQLIRUP SH >D E@

'LQFDX]DVLPHWULHLOHJLLXQLIRUPHPHGLDQDOXL [ HVWHHJDO FX E

0 [ ' [

ED

[G[ E D ³D E

§ DE· ¨[ ¸ G[ ³ ED D© ¹

E D

DE $YHP

'LQFDX]DVLPHWULHLFRHILFLHQWXOGHDVLPHWULHHVWHQXO

0 N [ P [

E

[ N G[ ³ ED D

E N D N E D N

E

DE· § ¨[ ¸ G[ ³ ED D© ¹

E D

LDUH[FHVXOYDIL

P [ P [ 6 FDOFXO P DFXP SUREDELOLWDWHD 3D [ E XQGH YDULDELOD DOHDWRDUH [ HVWH UHSDUWL]DW XQLIRUP vQ >D E@ úL >D E@ >D E@ 'LQ SXQFW GH YHGHUH JHRPHWULF (

DFHDVW SUREDELOLWDWHHVWHHJDO FXDULDKDúXUDW GLQILJXUD(VWHHYLGHQWF

3D [ E

ED ED

DGLF SUREDELOLWDWHDFHUXW HVWHHJDO FXUDSRUWXOGLQWUHOXQJLPLOHFHORUGRX LQWHUYDOH

)LJXUD

([HPSOH 6HP VRDU GLDPHWUXOXQXLFHUFúLVHRE LQGLYHUVHUH]XOWDWHFDUHVXQWLQWHUSUHWDWHFD YDORULDOHXQHLYDULDELOHDOHDWRDUH [ 6 VHGHWHUPLQHUHSDUWL LDDULHLFHUFXOXLúWLLQGF

[ DUHRUHSDUWL LHXQLIRUP vQLQWHUYDOXO >D E@ GHOXQJLPH

5 VSXQV$YHP

SHQWUX D [ d E I [ [ ® ¯ SHQWUX [ d D [ ! E S[ 6 UH]XOW [ GHFLSHQWUX D E 'LQDULDFHUFXOXL 6 S

° ° °° [ ® ° S ° ° °¯

§ [· ¸ )6 [ )[ ¨¨ ¸ S © ¹

SHQWUX [

S D

S S D d [ E S SHQWUX E [ SHQWUX

'DF [ úL K VXQW GRX YDULDELOH DOHDWRDUH LQGHSHQGHQWH UHSDUWL]DWH XQLIRUP vQ

[ K

>@ 6 VHGHWHUPLQHGHQVLWDWHDGHUHSDUWL LHDYDULDELOHLDOHDWRDUH ] 5 VSXQV

SHQWUX [ >@ I K [ ® ¯ SHQWUX [ >@ ³ X I[ X IK X[ GX ³ XI[ X[ GX [ ³ XI[ X GX I [ [

I] [ GHXQGH

° ° ® ° °¯ [

I ] [

SHQWUX [ d

SHQWUX [ !

'DF [ [ Q VXQW Q YDULDELOH LQGHSHQGHQWH XQLIRUPH SH >@ V VH DUDWH F YDULDELODDOHDWRDUH ] Q

I ] Q [ XQGH

Q

¦[ N

N

DUHGHQVLWDWHDGHUHSDUWL LH

SHQWUX [ ° ° 4Q N [ SHQWUX d N d [ d N d Q ® ° Q °¯ SHQWUX Q [

4Q N [ [ Q &Q [

Q

&QN [ N N

5 VSXQV9RPUD LRQDSULQUHFXUHQ DVXSUDOXL Q 3HQWUX ]

I ] [

f

³

f

GHFL

I [ ] I ] G[

[

Q

[ [

³ I ] G]

[

SHQWUX [ °[ SHQWUX d [ ° I ] [ ® ° [ [ SHQWUX d [ d °¯ SHQWUX [ ! 3HQWUX ] Q VHREVHUY F I ] [ HVWHQXO vQDIDUDVHJPHQWXOXL > Q@ LDUSH DFHVWVHJPHQW

I ] Q [

[

³ I W GW ] Q

[

/HJHDQRUPDO

/HJHDGHUHSDUWL LHQRUPDO HVWHROHJHOLPLW vQWkOQLW IUHFYHQWvQDSOLFD LLSUDFWLFH 6H SRDWH DU WD F VXPD XQXL QXP U VXILFLHQW GH PDUH GH YDULDELOH DOHDWRDUH LQGHSHQGHQWHXUPkQGROHJHRDUHFDUHSHQWUXVXILFLHQWGHSX LQHUHVWULF LLWLQGHF WUHR OHJHQRUPDO 'HILQL LH6HQXPHúWHIXQF LHGHUHSDUWL LHQRUPDO QRWDW SULQ ) P V IXQF LDGHUHSDUWL LHGHILQLW SULQGHQVLWDWHDGHSUREDELOLWDWH

I [ P V

H V S

[ P V

P úL V ILLQGFRQVWDQWHQXPLWHSDUDPHWULLUHSDUWL LHL *UDILFXOGHQVLW LL I [ P V HVWHFHOGLQILJXUD

)LJXUD

)XQF LDGHUHSDUWL LHHVWH

) [ P V

[

³ I X P V GX f

[

H V S ³f

X P V

GX

)DFHPVFKLPEDUHDGHYDULDELO

) [ P V

S

[P V

³

H

XP V W

GW

f

W úLVHRE LQH

§[P · ¸ )¨ © V ¹

,QWHJUDOD QX SRDWH IL H[SULPDW SULQ IXQF LL HOHPHQWDUH GDU SRDWH IL FDOFXODW FXDMXWRUXOIXQF LLORUVSHFLDOH3HQWUXDVWIHOGHIXQF LLGHVvQWkOQLWHvQSUDFWLF VDX vQWRFPLW WDEHOH 'LQ VH YHGH F HVWH VXILFLHQW V FXQRDúWHP YDORULOH QXPHULFH DOH IXQF LHL ) SHQWUX D GHGXFH YDORULOH QXPHULFH DOH IXQF LHL

) P V 9RPQRWD [

W

H GW ³ S f

) [

9DULDELOD DOHDWRDUH [ VH QXPHúWH QRUPDO 1 PV GDF DUH IXQF LD GH

UHSDUWL LH ) P V 3HQWUX [ YRPFDOFXODFDUDFWHULVWLFLOHQXPHULFHHVHQ LDOHYDORDUHD PHGLHGLVSHUVLDúLPRPHQWHOHFHQWUDWH 3HQWUX

0 [

f

³ [I [ P V G[

f

I FkQGVFKLPEDUHDGHYDULDELO

0 [

[P V

f

[H V S ³f

[ P V

G[

W VHRE LQH

f

V W P H W GW ³ S f

f

f

V P WH W GW H W GW ³ ³ S f S f

6H REVHUY XúRU F SULPD LQWHJUDW HVWH QXO LDU FHD GH D GRXD HVWH LQWHJUDOD (XOHU3RLVVRQ f

W ³ H GW

f

5H]XOW

f

³ H W GW

S

0 [ P

GHFLSDUDPHWUXO P HVWHWRFPDLYDORDUHDPHGLHDOXL [ 'HDVHPHQHD

' [

f

[ P H ³ V S f

[ P V

G[

úLXDFHHDúLVFKLPEDUHGHYDULDELO

V S

' [

f

[P V

W

³W H

W VHRE LQH

V ª W « WH S «¬

GW

f

GHXQGH

º ³ H W GW » f »¼ f

f

f

' [ V

)RUPXOD QHDUDW F FHQWUXOGHGLVSHUVLH P HVWHFHQWUXOGHVLPHWULHDO UHSDUWL LHL 'DF [ P vúL VFKLPE VHPQXO H[SUHVLD U PkQH QHVFKLPEDW 'DF P vúLVFKLPE YDORDUHDFXUEDGHGHQVLWDWHVHGHSODVHD] GHDOXQJXOD[HL 2[ [ I U DúLVFKLPEDIRUPDILJXUD 'HFL P FDUDFWHUL]HD] SR]L LDUHSDUWL LHLSHD[D 2[ 3DUDPHWUXO V FDUDFWHUL]HD] IRUPDFXUEHLGHGHQVLWDWH2UGRQDWDPD[LP DFXUEHL HVWHLQYHUVSURSRU LRQDO FX V 3HQWUX P úL V ! V ! V ILJXUD QHDUDW IRUPDFXUEHLGHGHQVLWDWH ÌQ PXOWH DSOLFD LL SHQWUX FDUDFWHUL]DUHD GLVSHUVLHL OHJLL QRUPDOH VH XWLOL]HD] P VXUDGHSUHFL]LHFDUHHVWHP ULPHD

/

V

)LJXUD

0RPHQWXOFHQWUDWGHRUGLQ N YDIL

PN

f

³ [ P I [ P V G[ N

f

V S

N

f

V S

f

³ [ P

f

N

H

[ P V

N W

³W H

f

,QWHJUkQGSULQS U LDYHP

PN

V S

N

ª W W « W H «¬

N V S GHXQGH

PN

N f

³W

f f

N W

H

f N N W º W H GW » ³f »¼

GW

f

N VP N

)LJXUD

'LQ DFHDVW IRUPXO GH UHFXUHQ RE LQHP P

V P

V P

V

N VN XQGHVDQRWDWSULQ N SURGXVXOWXWXURUQXPHUHORULPSDUHGH

« P N

OD OD N

P V 6 FDOFXO P vQ FRQWLQXDUH SUREDELOLWDWHD 3D d [ E ) E ) D XQGH ) [ HVWHUHSDUWL LDOXL [ LQkQGVHDPDGH UH]XOW ILJXUD §EP·

§ D P · 3D d [ E ) ¨ ¸) ¨ ¸ © V ¹ © V ¹ $VLPHWULDHVWH $V

P V

LDUH[FHVXO (

'HH[HPSOXDYHP

3P d [ P V ) ) # 3P V d [ P V ) ) # 3P V d [ P V ) ) # 3P V d [ P V ) ) # XQGHYDORULOHOXL ) W VXQWGDWHvQWDEHOXOGLQDQH[H

)LJXUD

6HREVHUY F VXPDFHORUWUHLYDORUL DXRSUHFL]LHGH

HVWHDSUR[LPDWLYHJDO FX FHHDFHDUDW F SHQWUXUHSDUWL LDQRUPDO D XQHL YDULDELOH DOHDWRDUH GLVSHUVLD VH OLPLWHD] OD LQWHUYDOXO P r V FHHD FH SHUPLWH FD GD L ILLQG P úL V V VH SRDW LQGLFD LQWHUYDOXO vQ FDUH YDULDELOD

DOHDWRDUH LD WRDWH YDORULOH SRVLELOH FX R SUREDELOLWDWH PDUH VDX SUDFWLF LD WRDWH YDORULOHSRVLELOH$FHDVW PHWRG GHHVWLPD LHVHQXPHúWHvQVWDWLVWLF ÄOHJHDFHORU WUHLVLJPD´YH]LúLSDUDJUDIXO ÌQ DSOLFD LL UHSDUWL LLOH ELQRPLDO úL 3RLVVRQ VH DVLPLOHD] XQHL UHSDUWL LL QRUPDOH 1 GDF SHQWUX UHSDUWL LD ELQRPLQDO Q t úL QS t úL VH LD FD

[ QS DVLPSWRWLFQRUPDO 1 LDU QST SHQWUX UHSDUWL LD 3RLVVRQ GDF O t YDULDELOD DOHDWRDUH ILLQG vQ DFHVW FD] [ O O

YDULDELO DOHDWRDUHYDULDELODQRUPDW

([HPSOH /DXQDWHOLHUVHIDEULF ELOHFXXQGLDPHWUXGH FP'HIHFWHOHGHIDEULFD LH GDX R HURDUH D GLDPHWUXOXL UHSDUWL]DW GXS R OHJH QRUPDO P QX DYHP HURULVLVWHPDWLFH úL V FP/DFRQWUROVXQWGDWHFDUHEXWXULWRDWHELOHOH FDUH WUHF SULQWUXQ LQHO GH GLDPHWUX GH FP úL FHOH FDUH QX SRW WUHFH SULQWUXQ LQHO GH GLDPHWUX GH FP 6 VH GHWHUPLQH SUREDELOLWDWHD FD R ELO OXDW ODvQWkPSODUHV ILHUHIX]DW 5 VSXQV )LH HYHQLPHQWXO $ ELOD HVWH UHIX]DW $WXQFL $ $ * $ XQGH $ HVWHHYHQLPHQWXOFHFRUHVSXQGHFD]XOXLFkQGGLDPHWUXO G LDU $ SHQWUX G ! 9RPFDOFXOD

3 G

3 $& XQGH PG

3 G PG

HVWHGLDPHWUXOQRUPDO$YHP

3 $& GHFL

§ ·

) ¨ ¸ ) # # © ¹

3 $ # GHDSDUDWHGHWLSXO $ úL GHDSDUDWHGHWLSXO % FXDFHHDúLGHVWLQD LH VXQW vQ VHUYLFLX (OH WUHEXLH UHSDUDWH GXS H[SORDWDUH FX SUREDELOLW LOH UHVSHFWLY 6HFHUHV VHGHWHUPLQH

D SUREDELOLWDWHD FD QXP UXO GH DSDUDWH FH WUHEXLH UHSDUDWH V ILH FXSULQV vQWUH úL E QXP UXO GH UHSDUD LL Q FH WUHEXLH HIHFWXDWH vQ DWHOLHU SHQWUX FD SUREDELOLWDWHD S DQXP UXOXLGHDSDUDWHvQUHSDUD LHV ILH 5 VSXQV D )LH HYHQLPHQWXO $ DSDUDWXO WUHEXLH UHSDUDW 1XP UXO GH DSDUD LL D HYHQLPHQWXOXL $ HVWHRYDULDELO DOHDWRDUHUHSDUWL]DW QRUPDOFX 0 [

' [ 3 d [ d # 3 [ 3 [

E 3[ Q

§ · ) ¨ ¸ © ¹ § Q · ) ¨ ¸ 'LQ WDEHOH DYHP ) # GHFL © ¹

Q GHXQGHUH]XOW Q #

0HGLDQDXQHLYDULDELOHDOHDWRDUHUHSDUWL]DW QRUPDOHVWHQXP UXOHJDOFXMXP WDWH GLQOXQJLPHDXQXLLQWHUYDOGHSHD[DDEVFLVHORUVLPHWULFvQUDSRUWFXSXQFWXO P úLFDUH HVWH ED]D ILJXULL GH DULH HJDO FX MXP WDWH GLQ DULD P UJLQLW GH D[D 2[ úL FXUED GH UHSDUWL LHILJXUD

)LJXUD

'DF [ HVWHRYDULDELO DOHDWRDUHUHSDUWL]DW QRUPDOGLQGHILQL LHUH]XOW F

3 [ P 0 H

GHFL GLQ LQkQG VHDPD GH VLPHWULD GRPHQLXOXL vQ UDSRUW FX FHQWUXO GH GLVSHUVLHUH]XOW

GHXQGH

§0 · 3 [ P 0 H ) ¨ H ¸ © V ¹ §0 · ) ¨ H ¸ © V ¹

LDUGLQWDEHOHUH]XOW

0H V

VDX 0 H

V

'HFLFXQRVFkQG V SXWHPGHWHUPLQDLPHGLDWYDORDUHDPHGLDQHL 'DF SHQWUX FDUDFWHUL]DUHD GLVSHUVLHL XWLOL] P PHGLDQD GHQVLWDWHD GH SUREDELOLWDWHDUHSDUWL LHLQRUPDOHVHVFULH

I [ P V XQGH 0 H

U ( S

H

U [ P 0 H

UV

5HSDUWL LDORJQRUPDO

6SXQHP F YDULDELOD DOHDWRDUH [ XUPHD] R UHSDUWL LH ORJQRUPDO GDF GHQVLWDWHDVDGHSUREDELOLWDWHHVWH

I [

V[ S

H

OQ [ D V

[ !

FX D úL V YDORDUHDPHGLHUHVSHFWLYGLVSHUVLDORJDULWPXOXLOXL [

OQ [ D HD HVWH UHSDUWL]DW V

'DF FRQVLGHU P YDULDELOD DOHDWRDUH K

1

$YHP f

f

OQ [ D

V 0 [ ³ [I [ G[ H G[ ³ V S OQ [ D 'DF VHIDFHVFKLPEDUHDGHYDULDELO X UH]XOW V

0 [ H ' [

f

D

V

³ [ 0 [ I [ G[

H

§ · D V ¨¨ H V ¸¸ © ¹

,PSRUWDQ DDFHVWHLUHSDUWL LLFRQVW vQXUP WRDUHOH 'DF [ I [ FHHD FH HVWH FRQYHQDELO vQ FD]XO YDULDELOHL DOHDWRDUH WLPSUHSDUWL LDQRUPDO QXDUHDFHDVW SURSULHWDWH 'DF [ [ Q VXQW YDULDELOH DOHDWRDUH ORJQRUPDOH LQGHSHQGHQWH SURGXVXO

[[ Q HVWH R YDULDELO DOHDWRDUH ORJQRUPDO ÌQWUDGHY U GDF [ HVWH ORJQRUPDO DWXQFL,Q [ HVWHQRUPDO úLDFHVWUH]XOWDWGHFXUJHGLQSURSULHWDWHD

GHDGLWLYLWDWHDYDULDELOHORUDOHDWRDUHLQGHSHQGHQWH

5HSDUWL LDH[SRQHQ LDO QHJDWLY 'HILQL LH 6SXQHP F YDULDELOD DOHDWRDUH [ XUPHD] R UHSDUWL LH H[SRQHQ LDO QHJDWLY GDF DUHGHQVLWDWHDGHSUREDELOLWDWH I [ OH O[ O ! d [ f $YHP

H O[ ) [ ® ¯

SHQWUX [ ! SHQWUX [ d

([HPSOX >@ 'HQVLWDWHD GH UHSDUWL LH D YLH LL XQHL O PSL GLQWUXQ DSDUDW GH UDGLR FX O PSL HVWH OH OW W ! GDW vQ DQL úL O

6 VH GHWHUPLQH

SUREDELOLWDWHDFDvQPDLSX LQGH DQLQLFLRODPS V QXPDLILHVFKLPEDW 5 VSXQV 9LH LOH PHGLL DOH O PSLORU VXQW FRQVLGHUDWH HYHQLPHQWH LQGHSHQGHQWH 3UREDELOLWDWHDFDYLD DPHGLHDXQHLO PSLV ILHPDLPDUHGH DQLHVWH f

³ OH

S

OW

H O

GW

LDUSUREDELOLWDWHDF XWDW YDIL 3 S 5HSDUWL LDF )LH [ [ [Y Y YDULDELOH DOHDWRDUH QRUPDOH QRUPDWH LQGHSHQGHQWH

[L 1 6XPDS WUDWHORUDFHVWRUYDULDELOHDOHDWRDUHHVWHRYDULDELO DOHDWRDUH QRWDW F [ [ [Y $FHDVW YDULDELO DOHDWRDUHDUHGHQVLWDWHDGHUHSDUWL LH

I [

Y

§Y· *¨ ¸ ©¹

[

Y

H

[

[ >f

6SXQHPF DFHDVW GHQVLWDWHGHUHSDUWL LHGHILQHúWHUHSDUWL LD F FX Y JUDGH GH OLEHUWDWH vQ HOHJkQG SULQ DFHDVWD QXP UXO YDULDELOHORU LQGHSHQGHQWH D F URU Y

§Y· ©¹

YDULD LHQXVXIHU QLFLRUHVWULF LH *¨ ¸ HVWHRFRQVWDQW DOHDV GHDúDPDQLHU f

vQFkW

³ I [ G[

5HDPLQWLP F *Q

f

³[

Q [

H G[ HVWH IXQF LD JDPD D OXL (XOHU FX Q XQ

SDUDPHWUXSR]LWLY &XUED GHQVLW LL GH UHSDUWL LH QX HVWHVLPHWULF ILJXUD GDUHDWLQGHV GHYLQ VLPHWULF GDF QXP UXOJUDGHORUGHOLEHUWDWH Y FUHúWHSHVWH

)LJXUD

9DORDUHDPHGLHDXQHLYDULDELOHDOHDWRDUH [ UHSDUWL]DW F HVWH 0 [ ÌQWUDGHY U

0 [

f

Y

[

³ [ [ H G[ §Y· *¨ ¸ ©¹ [ úLDYHP )DFHPVFKLPEDUHDGHYDULDELO W Y §Y· *¨ ¸ f Y ©¹ Y W 0 [ W H GW ³ §Y· §Y· *¨ ¸ *¨ ¸ ©¹ ©¹ Y

Y

$QDORJVHDUDW F GLVSHUVLDHVWH

' [ Y

9RPGDRSURSULHWDWHGHRVHELWGHXWLO vQVWDWLVWLFDPDWHPDWLF úLDQXPH )LH [ [ [ Q XQúLUGHYDULDELOHLQGHSHQGHQWHFDUHSRWOXDILHFDUHYDORULOH P

D D DP FX SUREDELOLW LOH S S SP SL t ¦ SL

'DF QRW P FX

L

P

D L L P QXP UXO GH FkWH RUL D IRVW OXDW YDORDUHD DL ¦ D L YDULDELOD

D QS D QS D P QSP QS

Q DWXQFL

L

QS

QSP

XUPHD] RUHSDUWL LH F FX P JUDGHGHOLEHUWDWH 5HSDUWL LD F GHSLQGH QXPDL GH SDUDPHWUXO Y QXP UXO JUDGHORU GH OLEHUWDWH 7DEHOXO GLQ DQH[ QH G SHQWUX ILHFDUH YDORDUH D OXL Y d YDORULOH SUREDELOLW LORUFDV DYHPSHQWUX F RYDORDUHPDLPLF GHFkWXQQXP UGDW F

3

3F F

F

Y

§Y· *¨ ¸ ©¹

³[

Y [

H G[

úLFDUHUHSUH]LQW DULDQHKDúXUDW GLQILJXUD

)LJXUD

([HPSOX3HQWUX Y

3 F 3 F t

VDX 3 F t

5HSDUWL LD6WXGHQW )LH [ [ [ Q YDULDELOH DOHDWRDUH QRUPDOH 1 V LQGHSHQGHQWH 9DULDELOD

W

[

Q [L ¦ QL XQGH [ HVWHRYDULDELO DOHDWRDUH 1 V LQGHSHQGHQW GHúLUXO [L d L d Q HVWHR

YDULDELO DOHDWRDUHFRQWLQX FXGHQVLWDWHDGHUHSDUWL LH

I [

§ V · V *¨ ¸ © ¹§ [ · ¨ ¸¸ [ ff V ¹ VS *§ V · ¨© ¨ ¸ ©¹

$FHDVWD HVWH GHQVLWDWHD UHSDUWL LHL 6WXGHQW GXS SVHXGRQLPXOXL PDWHPDWLFLDQXOXL:*RVVHW FX V Q JUDGHGHOLEHUWDWH &XUEDWHRUHWLF DDFHVWHLGHQVLW LHVWHFHDGLQILJXUD

)LJXUD

(D HVWH DVHP Q WRDUH FX FXUED GHQVLW LL QRUPDOH GDU GLIHULW 'DF V o f UHSDUWL LDYDULDELOHL6WXGHQWWLQGHVSUHIXQF LD/DSODFH ) Q )XQF LDGHUHSDUWL LH6WXGHQWHVWH

) [

[

³ I W GW

f

2EVHUY PF GHQVLWDWHD QXGHSLQGHGH V FHHDFHHVWHIRDUWHXWLOvQ DSOLFD LLSUDFWLFH 6LVWHPHGHYDULDELOHDOHDWRDUH )LH [ [ Q Q YDULDELOH DOHDWRDUH GHILQLWH SH V FkPSXO GH SUREDELOLWDWH

^:6 3`

'HILQL LH 6LVWHPXO [ [ Q VH QXPHúWH YDULDELO DOHDWRDUH Q GLPHQVLRQDO VDXYHFWRUDOHDWRUFX Q GLPHQVLXQL ([HPSOH 3XQFWXOGHH[SOR]LHDOXQXLREX]ODGLVWDQ HVWHGHWHUPLQDWSULQWUXQDQVDPEOXGH WUHLYDULDELOHDOHDWRDUH /DWLUDQVDPEOXOGH Q DWLQJHULDSXQFWHORUFDUHDWLQJ LQWDvQSODQSRDWHILFRQVLGHUDW FDXQVLVWHPGH Q YDULDELOHDOHDWRDUH ÌQJHQHUDOSXWHPLQWHUSUHWDYDULDELOHOHDOHDWRDUH Q GLPHQVLRQDOHFDSXQFWH DOHDWRULLvQWUXQVSD LXHXFOLGLDQFX Q GLPHQVLXQL3HOkQJ DFHDVW LPDJLQHVHXWLOL]HD] SHQWUXLQWHUSUHWDUHDJHRPHWULF DXQXLVLVWHPGH Q YDULDELOHDOHDWRDUHXQYHFWRUDOHDWRU vQVSD LXOHXFOLGLDQFX Q GLPHQVLXQL

6LVWHPHGHGRX YDULDELOHDOHDWRDUH

[ K RYDULDELO DOHDWRDUHFX GLPHQVLXQL 'HILQL LH )XQF LD ) [ \ 3 ^Z [Z [ KZ \` FX [ \ \ VH

)LH ]

QXPHúWHIXQF LHGHUHSDUWL LHDYDULDELOHLDOHDWRDUH ]

,QWHUSUHWkQGVLVWHPXO [ K FDXQSXQFWDOHDWRUIXQF LDGHUHSDUWL LH ) [ \ QXHVWH

DOWFHYDGHFkWSUREDELOLWDWHDFDSXQFWXODOHDWRU [ K V VHJ VHDVF vQS WUDWXOLQILQLWFXYkUIXOvQ

SXQFWXO [ \ GLQILJXUD1RWkQGFX )[ [ úL )K \ IXQF LLOHGHUHSDUWL LHDOHYDULDELOHORU

DOHDWRDUH [ úL K vQDFHHDúLLQWHUSUHWDUH )[ [ UHSUH]LQW SRVLELOLWDWHDFDSXQFWXODOHDWRUV VH DIOHvQVHPLSODQXOOLPLWDWGHGUHDSWDSDUDOHO FX 2\ FHWUHFHSULQSXQFWXOGHDEVFLV [ ODGUHDSWD GUHSWHLLDU )K \ UHSUH]LQW SUREDELOLWDWHDFDSXQFWXODOHDWRUV VHJ VHDVF vQVHPLSODQXO

VLWXDWVXEGUHDSWDSDUDOHO FX 2[ FHWUHFHSULQSXQFWXOGHRUGRQDW \

)LJXUD

9RP GD FkWHYD SURSULHW L DQDORJH FHORU GDWH SHQWUX IXQF LLOH GH UHSDUWL LH XQLGLPHQVLRQDOH ) HVWHQHGHVFUHVF WRDUHvQUDSRUWFXILHFDUHDUJXPHQW ) HVWHFRQWLQX ODVWkQJDvQUDSRUWFXILHFDUHDUJXPHQW ) [f ) f [ ) ff ) [f

)[ [ ) f \ )K \

) ff

ÌQFRQWLQXDUHYRPQRWDVLPEROLF [ K ' HYHQLPHQWXOÄSXQFWXODOHDWRU [ K VHJ VHúWHvQGRPHQLXO ' ´3UREDELOLWDWHDDFHVWXLHYHQLPHQWVHH[SULP VLPSOXGDF ' HVWHXQGUHSWXQJKLDOHF UXLODWXULVXQWSDUDOHOHFXD[HOHGHFRRUGRQDWH)LHGUHSWXQJKLXO ' GH YkUIXUL $D F %E F & E G 'D G ÌQ DFHVW FD] HYHQLPHQWXO

[ K ' HVWHHFKLYDOHQWFX ^D d [ E` ^F d K G `GHFL 3[ K ' ) E G ) D G ) E F ) D F

'DF H[LVW R IXQF LH UHDO I GHILQLW úL LQWHJUDELO SH \ DúD vQFkW

) [ \

[

\

³ ³ I X Y GXGY DWXQFL

I VH QXPHúWH GHQVLWDWHD GH SUREDELOLWDWH

f f

UHSDUWL LH DYDULDELOHLDOHDWRDUHFXGLPHQVLXQL ]

)LH [ K GRX YDULDELOHDOHDWRDUHGHWLSFRQWLQXXúL [ K LQWHUSUHWDWFDXQSXQFW

DOHDWRUvQSODQ)LH \ ' GUHSWXQJKLXOGHODWXUL '[ úL '\ DYHP

3 [ K \ '

$YHP

OLP

) [ '[ \ '\ ) [ '[ \ ) [ \ '\ ) [ \

3 [ K \ '

w ) [ \

'['\

w[w\

'[ o '\ o

1RW PDFHDVW GHULYDW SULQ I [ \

w ) [ \ w[w\

I [ \

HDILLQGWRFPDLGHQVLWDWHDGHSUREDELOLWDWHDYDULDELOHLDOHDWRDUH ] $YHP 3[ K ' I [ \ G[G\

³³ '

'HQVLWDWHDGHUHSDUWL LHDOXL ] HVWHQHQHJDWLY LDU f f

³ ³ I [ \ G[G\

f f

([HPSOH )LHYDULDELODDOHDWRDUH ] [ K FX [ K YDULDELOHDOHDWRDUHLQGHSHQGHQWHDF UHL GHQVLWDWHGHSUREDELOLWDWHHVWH

I [ \

[ \ \ S [ \

6 VHGHWHUPLQH D )XQF LDGHUHSDUWL LHFRUHVSXQ] WRDUH E 3[ K ' XQGH ' HVWHS WUDWXOFRQVWUXLWSHVHJPHQWHOH >@ úL >@

5 VSXQV

) [ \ D

[

\

GXGY ³ ³ S f f X Y

[

\

GX GY ³ ³ S f X f Y

·§ · § ¨ DUFWJ [ ¸¨ DUFWJ \ ¸ ¹© S ¹ ©S

E 3[ K '

S

GXGY

³ ³ X Y

6XSUDID DGHUHSDUWL LHDXQXLVLVWHPGHYDULDELOHDOHDWRDUH [ K HVWHXQFRQFLUFXODU GUHSWFXED]DXQFHUFGHUD] 5 úLFXFHQWUXOvQRULJLQHDVLVWHPXOXLGHFRRUGRQDWH 6 VHGHWHUPLQH D 'HQVLWDWHDGHSUREDELOLWDWHDVLVWHPXOXL E 3UREDELOLWDWHDFDXQSXQFWDOHDWRUV VHJ VHDVF vQLQWHULRUXOXQXLFHUFGHUD] D D 5 ILJXUD

)LJXUD

5 VSXQV D ([SUHVLDGHQVLW LLGHSUREDELOLWDWHvQLQWHULRUXOFHUFXOXL & QRWkQGFX K vQ O LPHD FRQXOXLILJXUD HVWH I [ \

K 5 [ \ 5

$OHJHPSH K DúDvQFkWYROXPXOFRQXOXLV ILHHJDOFXXQLWDWHD K

I [ \

5 [ \ S5

GHFL S5

)LJXUD

E 3[ K &

³³ I [ \ G[G\ 7UHFkQGvQFRRUGRQDWHSRODUH &

[ U VLQ T d U d D d T d S ® ¯ \ U FRV T

VHRE LQH

3[ K &

D S

D

³ ³ S5 5 U UGUGT

5 U UGU 5 ³

§D· §D· ¨ ¸ ¨ ¸ ©5¹ ©5¹ )LH VLVWHPXO GH YDULDELOH DOHDWRDUH [ K D F UXL GHQVLWDWH GH SUREDELOLWDWH HVWH I [ \ úLILH [ [ K úL [ [ K 6 VHGHWHUPLQHGHQVLWDWHDGHSUREDELOLWDWH DOXL [ úL [ 5 VSXQV1HYRPIL[DRYDORDUHDOXL ] úLYRPFRQVWUXLvQSODQXO [2\ FXUEDGHHFXD LH [\ ] KLSHUEROD FDUH DUH FD DVLPSWRWH D[HOH GH FRRUGRQDWH 'RPHQLXO ' HVWH FHO KDúXUDWGLQILJXUD )XQF LDGHUHSDUWL LHDOXL [ VHVFULH

)[ ]

] f [

f

³³ I [ \ G[G\ ³ ³ I [ \ G[G\ ³ ³ I [ \ G[G\ f ] [

'

f

'HULYkQGDFHDVW H[SUHVLHvQUDSRUWFX ] RE LQHP

I [ ]

§ ]· ³ f [ I ¨© [ [ ¸¹G[

f

§

]·

³ [ I ¨© [ [ ¸¹G[

)LJXUD

3HQWUXGHWHUPLQDUHDGHQVLW LLGHSUREDELOLWDWHDOXL [ YRPWUDVDvQSODQXO [2\ GUHDSWDGHHFXD LH [ \ ] ILJXUD 'RPHQLXO ' HVWHFHOKDúXUDW

)LJXUD

$YHP

)[ ]

³³ I [ \ G[G\ '

f ] [

³ ³ I [ \ G[G\

f f

§ · ³f ¨¨© ³f I [ \ G\ ¸¸¹G[

f

][

'HULYkQG DFHDVW H[SUHVLH vQ UDSRUW FX ] FDUH ILJXUHD] OD OLPLWD VXSHULRDU D LQWHJUDOHLDGRXD RE LQHP

I [ [

f

³ I [ ] [ G[

f

'LQFDX]DVLPHWULHLVXPHL [ K DFHDVW IRUPXO VHSRDWHVFULH f

I[ [

³ I ] \ \ G\

f

ÌQ DSOLFD LL SUDFWLFH FD]XO vQ FDUH [ úL K VXQW LQGHSHQGHQWH HVWH IRDUWH LPSRUWDQW )LH [ úL K GRX YDULDELOHDOHDWRDUHLQGHSHQGHQWHFXGHQVLW LOHGHSUREDELOLWDWH

I [ [ úL I K [ $YHP I [ \

I [ [ I K \

6 GHWHUPLQ PGHQVLWDWHDGHSUREDELOLWDWHDYDULDELOHLDOHDWRDUH ] DFHVWFD] úL VHVFULX

I ] ] I ] ]

[ K ÌQ

f

³ I [ I ] [ G[

³ I ] \ I \ G\

[

K

f f

[

K

f

3HQWUXGHVHPQDUHDFRPSXQHULLFHORUGRX OHJLGHSUREDELOLWDWHXWLOL] PQRWD LD VLPEROLF I] I[ IK

XQGH HVWHVLPEROXOGHFRPSXQHUHFRQYROX LH ([HPSOH )LH YDULDELOHOH DOHDWRDUH [ úL K LQGHSHQGHQWH FX GHQVLW LOH GH SUREDELOLWDWH XQLIRUPHvQ >D E@

I [ [

I K [

SHQWUX [ >D E@

° ® °E D ¯

SHQWUX [ >D E@

6 VHGHWHUPLQHGHQVLWDWHDGHUHSDUWL LHDYDULDELOHLDOHDWRDUH ] 5 VSXQV$YHP E

I ] ]

³

E

D

úL ] D

³ I ] [ G[ ³ I W GW D d ] d E K

K

D

] E

'DF ] E D DWXQFL ] D E úL ] D

D

] D

³ I W GW ³ I W GW ³ I W GW K

] E

K

] E

[ K

I K ] [ G[ E D ³D

I [ [ I K ] [ G[

E

K

D

] D ED

'DF ] E ! D DWXQFL ] D ! E úL ] D

E

] D

E ] ED

³ I W GW ³ I W GW ³ I W GW K

K

] E

K

] E

E

5H]XOW

SHQWUX ] d D

° ° ] D °° E D ® ° E D ° E D ° °¯

I ] ]

SHQWUX D ] d D E

SHQWUX D E ] d E SHQWUX ] ! E

$FHDVW GHQVLWDWHGHSUREDELOLWDWHVHQXPHúWHOHJHDGHUHSDUWL LHDOXL6LPSVRQ )LHYDULDELOHOHDOHDWRDUH [ úL K LQGHSHQGHQWHFXGHQVLW LOHGHSUREDELOLWDWH

SHQWUX [ d I K [ ® [ SHQWUX [ ! ¯H [ [ K úL ] VXQWLQGHSHQGHQWH K I [ [

6 VHDUDWHF ] 5 VSXQV$YHP

) X Y

3 ] X ] Y

XY Y X ]

³ ³H

³³

[ \ X °[ ® Y °¯ \ XY Y

³

[ \

H G[G\

[ Y

)] [

I[ X IK Y GXGY

§ [§¨ Y ·¸ X · ¨ H © ¹ H ¸ G[ ¨ ¸ © ¹

³³ I[ X IK Y GXGY

[ \ ] ]

³ H H GX X

X]

] ] X

³ ³H

Y ª X H X º¼ Y ¬

X Y

H GXGY

] H ]

)] [ 5H]XOW F ) X Y

ff

³³ I X I Y GXGY ³ ³ H [

K

[ ] \

)] X )] Y

X ]

X Y

H GXGY

] ]

&DUDFWHULVWLFLQXPHULFHDOHVLVWHPHORUGHGRX YDULDELOH DOHDWRDUH&RYDULDQ &RHILFLHQWGHFRUHOD LH )LHYDULDELODDOHDWRDUHFXGRX GLPHQVLXQL ] [ K

0 [ N KV PRPHQWLQL LDOGHRUGLQ N V DOVLVWHPXOXL

'HILQL LH9RPQXPL D N V

[ K 9RP QXPL PRPHQW FHQWUDW GH RUGLQXO N V DO VLVWHPXOXL [ K QXP UXO N V P N V 0 >[ 0 [ @ >K 0 K @ $YHP f f

³ ³[

DN V

N

\ V I [ \ G[G\

f f

PN V

f f

³ ³ [ 0 [ \ 0 K I [ \ G[G\ N

V

f f

IRUPXOHFDUHvQFD]XOYDULDELOHORUDOHDWRDUHGLVFUHWHGHYLQ DN V [LN \ VM SLM

¦¦

PN V

¦¦ [ L

M

L

L

M

0 [ \ M 0 K SLM

$YHP

D D

N

V

0 [ K 0 [K

0 [

0 K

8QUROLPSRUWDQWvQWHRULDVLVWHPHORUGHYDULDELOHDOHDWRDUHvODUHFRYDULDQ D 'HILQL LH1XPLPFRUHOD LHVDXFRYDULDQ DYDULDELOHORUDOHDWRDUH [ úL K YDORDUHD FRY[ K 0 >[ 0 [ @ >K 0 K @ (IHFWXkQGFDOFXOXOúL LQkQGVHDPDGHSURSULHW LOHYDORULLPHGLLUH]XOW FRY[ K 0 [K 0 [ 0 K &RYDULDQ D HVWH R FDUDFWHULVWLF D VLVWHPXOXL FDUH GHVFULH SH OkQJ GLVSHUVLH OHJ WXUDGLQWUHHOH6HDUDW FXXúXULQ F GDF [ úL K VXQWLQGHSHQGHQWHFRYDULDQ DORU HVWHQXO YH]L 3HQWUX FDUDFWHUL]DUHD OHJ WXULL GLQWUH YDULDELOHOH DOHDWRDUH [ úL K YRP XWLOL]D FRHILFLHQWXOGHFRUHOD LH 'HILQL LH6HQXPHúWHFRHILFLHQWGHFRUHOD LHDOYDULDELOHORUDOHDWRDUH [ úL K UDSRUWXO

FRY[ K '[ 'K (VWHHYLGHQWF GDF [ úL K VXQWLQGHSHQGHQWH U[ K U[ K

'RX YDULDELOHDOHDWRDUHVXQWQHFRUHODWHGDF U[ K

5H]XOW F GRX YDULDELOH DOHDWRDUH LQGHSHQGHQWH VXQW QHFRUHODWH 5HFLSURFD DFHVWHLDILUPD LLQXHVWHDGHY UDW ([HPSOX )LH : ^Z Z Z Z ` XQGH ZL L VXQW SXQFWH GLQ

SODQGHFRRUGRQDWH Z Z Z N Z 'HILQLPSH : YDULDELOHOH DOHDWRDUH

úL

· ¸ S ¸¹

§ K ¨¨ © S S

N· ¸ S ¸¹

S

$YHP 0 [ S úL 0 K

3ZL ¦ SL

XQGH SL

§ [ ¨¨ © S S S

L

S S NS S

3HQWUXYDULDELODDOHDWRDUH [K

N · § ¸¸ [K ¨¨ © S S S S ¹ DOHJHPSH N DúDvQFkW 0 [K 0 [ 0 K GHFL S S S S NS S GHXQGHUH]XOW

S S S

N

GHFL [ úL K VXQWQHFRUHODWH 6 DU W PF QXVXQWLQGHSHQGHQWH$YHP

S S S

3[ K 3 Z S 3[ S S S 3K S S

$OHJkQGQXPHUHOH SL DúDvQFkW SL ! L

¦ SL

úL

L

S z S S S S S UH]XOW F

3[

K z 3 [

GHFL [ úL K QXVXQWLQGHSHQGHQWH

3K

3URSULHW LDOHFRHILFLHQWXOXLGHFRUHOD LH )LH ' [ ' K z DWXQFL U[ K GDF úLQXPDLGDF YDULDELOHOH [ úL K VXQW QHFRUHODWH 'HPRQVWUD LDHVWHLPHGLDW LQkQGVHDPDGHGHILQL LLOHGDWH 3HQWUXRULFHGRX YDULDELOHDOHDWRDUHDYHP U[K d $SOLFkQGLQHJDOLWDWHDOXL6FKZDUW]DYHP

0 >[ 0 [ @ >K 0 K @ d

d 0 >[ 0 [ @ 0 >K 0 K @

'[ 'K

GHXQGHUH]XOW SURSULHWDWHDHQXQ DW 'DF U[K DWXQFLvQWUH [ úL K H[LVW RGHSHQGHQ OLQLDU )LH D E \ DUELWUDUHúL

J D E

/X PDLFL D

0 D>[ 0 [ @ E>K 0 K @

D ' [ DE FRY[ K E ' K t U[ K 'K E '[ úL LQHPVHDPDF U[K 2E LQHP

0 'K [ 0 [ '[ K 0 K

GHFL

'K [ 0 [ '[ K 0 K

'HILQL LH 6H QXPHVF GUHSWH GH UHJUHVLH DOH YDULDELOHORU DOHDWRDUH [ úL K GUHSWHOH

[ 0 [ \ 0 K FRY[ K ' [ ' K \ 0 K [ 0 [ FRY[ K ' K ' [ $FHVWH GUHSWH WUHF SULQ SXQFWXO 0 [ 0 K úL DX QXPHURDVH DSOLFD LL vQ

VWDWLVWLFDPDWHPDWLF ([HPSOH

§ · § · ¸ úL K ¨ ¸ 6HFHUHV VH ¨ ¸ ¨ ¸ © ¹ © ¹

6HFRQVLGHU YDULDELOHOHDOHDWRDUH [ ¨ FDOFXOH]H D 3[

K 3[ K 3[ K GDF 3[ K O E &RHILFLHQWXOGHFRUHOD LHvQIXQF LHGH O F 9DORULOHOXL O SHQWUXFDUH [ úL K VXQWLQGHSHQGHQWH

5 VSXQV D $YHP

GH

XQGH

[

K

3[ K 3[ K 3[ K 3[ K 3[ K 3[ K 3[ K O 3[ O GHFL [

K

O

O

3[

[L

0 [K

¦[ \ 3 [ L M

L

M

O O

3[ 3K 3[ K

3K

O

úL

\L

[L K

\M

· § · § · § O ¨ O ¸ ¨ O ¸ ¨ O ¸ ¹ © ¹ © ¹ ©

O

O WUHEXLHDVWIHODOHVvQFkWWRDWHSUREDELOLW LOHV ILHFXSULQVHvQWUH úL GHFL d O d d O d d O d d O d GHXQGH d O d FHHDFHLPSOLF 0 [K d E U[ K $YHP

0 [K 0 [ 0 K '[ 'K

0 [ 0 K ' [ ' K

GHFL

O

U[ K 'HRDUHFH

d O d UH]XOW

U[ K d

[ úL K VXQWLQGHSHQGHQWH >@6HFRQVLGHU YDULDELODDOHDWRDUH [ K FXGLVWULEX LDGLQWDEHOXOXUP WRU [N 3K \N \N F 3HQWUX O

3[

[N

6 VHGHWHUPLQHGUHSWHOHGHUHJUHVLH 5 VSXQV

0 [

¦ [ 3[

[N

0 K

¦ \ 3K

\N

'[ 'K U[ K

N

N

N

N

'UHDSWDGHUHJUHVLHDOXL [ DVXSUDOXL K HVWH úLvQFD]XOQRVWUX

\ [ 'UHDSWDGHUHJUHVLHDOXL K DVXSUDOXL [ YDIL \ [

7HRULDVHOHF LHL *HQHUDOLW L

6WDWLVWLFDPDWHPDWLF VHIXQGDPHQWHD] FXDMXWRUXOWHRULHLSUREDELOLW LORUDYkQG FD RELHFW VLVWHPDWL]DUHD SUHOXFUDUHD úL XWLOL]DUHD GDWHORU VWDWLVWLFH GH REVHUYD LH vQ YHGHUHD VWXGLHULL SH FDOH LQGXFWLY D IHQRPHQHORU DOHDWRDUH GH PDV 6WXGLHUHD FRQFRUGDQ HL GLQWUH PRGHODUHD PDWHPDWLF D XQRU IHQRPHQH DOHDWRDUH GH PDV úL IHQRPHQHOH vQVHúL HVWH FDUDFWHUL]DW GH DSDUL LD FRQFHSWXOXL IXQGDPHQWDO GH VHOHF LH FRQFHSWFDUHVW ODED]DvQWUHJXOXLHGLILFLXDOVWDWLVWLFLLPDWHPDWLFH&HUFHWDUHDVWDWLVWLF SRUQHúWHGHODRFROHFWLYLWDWHQXPLW úLSRSXOD LHIRUPDW GLQHOHPHQWHVDXLQGLYL]LFDUH VHGLIHUHQ LD] SULQGLYHUVHDWULEXWH3HQWUXVWXGLXOXQHLSRSXOD LLvQVWDWLVWLFDPDWHPDWLF VHXWLOL]HD] GLIHULWHYDORULWLSLFHYDORDUHDPHGLHGLVSHUVLHPRPHQWHHWF FDUHGHSLQG GHSRSXOD LDUHVSHFWLY ÌQSUDFWLF VHSRDWHH[DPLQDQXPDLXQQXP UOLPLWDWGHHOHPHQWHGLQSRSXOD LH VSHUkQGF LQIRUPD LDSULPLW SHDFHDVW FDOHHVWHvQP VXU V QHVSXQ FXVXILFLHQW SUHFL]LH FHHD FH GRULP V FXQRDúWHP GHVSUH vQWUHDJD SRSXOD LH 'HFL H QRUPDO V QH vQWUHE PFHSXWHPVSXQHGHVSUHRSRSXOD LHGLQFDUHSXWHPH[DPLQDQXPDLXQQXP U OLPLWDWGHHOHPHQWH"$FHDVW SUREOHP VW ODRULJLQHDWHRULHLVHOHF LHL 6HOHF LL )LHXQH[SHULPHQWDOHDWRUF UXLDvLDWDú PYDULDELODDOHDWRDUHFDUDFWHULVWLFD [ 'DF UHSHW PH[SHULPHQWXOGH Q RULvQPRGLQGHSHQGHQWRE LQHPXQúLUGHYDORULGHREVHUYD LHDOH YDULDELOHLDOHDWRDUH [ QRWDWH [ [Q 'HILQL LH 0XO LPHD YDORULORU GH REVHUYD LH DOH YDULDELOHL DOHDWRDUH [ DYkQG IXQF LD GH UHSDUWL LH ) VH QXPHúWH VHOHF LH GH YROXP Q HIHFWXDW DVXSUD YDULDELOHL DOHDWRDUH [ PDLSUHFLVDVXSUDYDORULORUYDULDELOHL [ FXIXQF LDGHUHSDUWL LH ) &RQFHSWXO GH VHOHF LH VH SRDWH H[WLQGH vQ FD]XO YDULDELOHORU DOHDWRDUH U GLPHQVLRQDOHÌQDFHVWFD]ILHFDUHPHPEUXGLQSRSXOD LDH[DPLQDW YDILFDUDFWHUL]DW GH U QXPHUHGHFLRULFHúLUGHYDORULREVHUYDWHDXQHLYDULDELOHDOHDWRDUH U GLPHQVLRQDOH SRDWHILLQWHUSUHWDWFDRVHOHF LHGLQWURSRSXOD LH U GLPHQVLRQDO 6HOHF LDSRDWHILFXvQWRDUFHUHVDXI U vQWRDUFHUHvQSULPXOFD]HOHPHQWXOH[WUDV GLQ SRSXOD LH HVWH UHLQWURGXV OD ORF vQDLQWH GH DOHJHUHD HOHPHQWXOXL XUP WRU LDU vQ DO GRLOHDFD]HOHPHQWHOHDOHVHQXVHPDLUHLQWURGXFvQSRSXOD LDJHQHUDO 'DF YROXPXO SRSXOD LHL JHQHUDOH HVWH VXILFLHQW GH PDUH LDU YROXPXO VHOHF LHL VXILFLHQW GH PLF GHRVHELUHD GLQWUH FHOH GRX WLSXUL GH VHOHF LH HVWH IRDUWH PLF LDU vQ DSOLFD LLSUDFWLFHRVHOHF LHI U vQWRDUFHUHHVWHFRQVLGHUDW FDVHOHF LHFXvQWRDUFHUH 9RP VSXQH F R VHOHF LH HVWH UHSUH]HQWDWLY GDF WRDWH YDORULOH GH VHOHF LH [ [Q DXDFHHDúLSUREDELOLWDWHGHDLQWUDvQFRPSRQHQ DHL

)XQF LDGHUHSDUWL LHGHVHOHF LH

)LHRYDULDELO DOHDWRDUH [ FXIXQF LDGHUHSDUWL LH ) 6 SUHVXSXQHPF DYHPR VHOHF LH [ [Q GHYROXP Q HIHFWXDW DVXSUDOXL [ 'HILQL LH'DF Q[ UHSUH]LQW QXP UXOREVHUYD LLORUvQFDUHDDS UXWRYDORDUHD FDUDFWHULVWLFLL [ PDLPLF GHFkW [ YRPQXPLIXQF LHGHUHSDUWL LHGHVHOHF LHIXQF LD GHILQLW SULQUHOD LD

)Q [

Q[ Q

([HPSOX 6H HIHFWXHD] R VHOHF LH GH YROXP Q

DVXSUD XQHL YDULDELOH DOHDWRDUH [ FDUH QH IXUQL]HD] YDORULOH FX IUHFYHQ HOH úL )XQF LDGHUHSDUWL LHYDIL

) [

° °° ® ° ° °¯

SHQWUX [ SHQWUX d [ SHQWUX d [ SHQWUX d [ SHQWUX [ t

/HJ WXUDGLQWUHIXQF LDGHUHSDUWL LHWHRUHWLF úLIXQF LDGHUHSDUWL LHGHVHOHF LHHVWH GDW GHXUP WRDUHDWHRUHP DOXL9,*OLYHQNRFDUHQHIXUQL]HD] úLMXVWLILFDUHDWHRUHWLF DXWLOL] ULLPHWRGHLVHOHF LHL 7HRUHP 'DF YROXPXOVHOHF LHL Q o f P ULPHD

GQ

VXS )Q [ ) [

f [ f

FRQYHUJHvQSUREDELOLWDWHF WUH]HUR &XDOWHFXYLQWHSHQWUX Q o f IUHFYHQ DUHODWLY DHYHQLPHQWXOXL Z [Z [

^

`

DGLF )Q [ FRQYHUJH vQ SUREDELOLWDWH F WUH SUREDELOLWDWHD DFHVWXL HYHQLPHQW DGLF

) [

3HQWUX Q VXILFLHQW GH PDUH IXQF LD GH UHSDUWL LH GH VHOHF LH QH G R LPDJLQH VXILFLHQWGHSUHFLV GHVSUHIXQF LDGHUHSDUWL LHWHRUHWLF

9DORULWLSLFHGHVHOHF LH

6 H[DPLQ P VHOHF LD VXE XUP WRUXO DVSHFW HIHFWX P R VHOHF LH GH YROXP Q DVXSUDXQHLYDULDELOHDOHDWRDUHFDUHDUHIXQF LDGHUHSDUWL LH ) GHFLHIHFWX P Q UHSHW UL DOHXQXLDQXPLWH[SHULPHQWF UXLDvLHVWHDWDúDW YDULDELODDOHDWRDUH [ $FHVWúLUGH Q UHSHW ULIRUPHD] XQH[SHULPHQWFRPSXVUHIHULWRUODYDULDELOHOHDOHDWRDUHLQGHSHQGHQWH [ [Q XQGH [L FRUHVSXQGH FHOHL GH D L D UHSHW UL D H[SHULPHQWXOXL 9DORULOH GH VHOHF LH [ [Q FRQGXF OD R YDULDELO DOHDWRDUH Q GLPHQVLRQDO [ [Q XQGH

[L d L d Q VXQW YDULDELOH DOHDWRDUH LQGHSHQGHQWH DYkQG ILHFDUH DFHHDúL IXQF LH GH UHSDUWL LH9DORULOHYDULDELOHORU [ [Q REVHUYDWHvQWURVHOHF LHIRUPHD] RYDORDUHGH REVHUYD LHDYDULDELOHLDOHDWRDUH Q GLPHQVLRQDOH [ [Q 'DF YDORULOH GH VHOHF LH VXQW FRQFHSXWH FD YDULDELOH DOHDWRDUH RULFH IXQF LH GH DFHVWH YDORUL ± RULFH IXQF LH GH VHOHF LH ± HVWH R YDULDELO DOHDWRDUH D F UHL IXQF LH GH UHSDUWL LHHVWHXQLFGHWHUPLQDW GHIXQF LDGHUHSDUWL LH ) DYDULDELOHLDOHDWRDUH [ FDUHD JHQHUDWVHOHF LD 9RPGDvQFRQWLQXDUHFkWHYDIXQF LLGHVHOHF LH 0RPHQWHGHVHOHF LH 1XPLPPRPHQWGHVHOHF LHGHRUGLQXO U YDULDELODDOHDWRDUH

Q U ¦ [L QL

DU

ÌQSDUWLFXODUYDORDUHDPHGLHGHVHOHF LHHVWH

Q ¦ [L QL 0RPHQWXOFHQWUDWGHVHOHF LHGHRUGLQXO U HVWH Q [L [ U PU ¦ QL [

D

5H]XOW GHDLFLGLVSHUVLDGHVHOHF LH

V

Q [L [ ¦ QL

U U [ PU U `

6HSRDWHYHULILFDFXXúXULQ H[LVWHQ DUHOD LHL

DU

PU U[ PU

FXFRQYHQ LDFD P

'HDLFLUH]XOW

P

P

V

P

D DD D

P

D D D D D D

D [

ÌQ SUDFWLF FDOFXOXO PRPHQWHORU GH VHOHF LH VH IDFH XQHRUL SHQWUX REVHUYD LL JUXSDWHWRDWHYDORULOHGLQWUXQLQWHUYDOvQORFXLQGXVHFXPLMORFXOLQWHUYDOXOXL8QDVWIHO GHFDOFXOHVWHDIHFWDWGHHURULLDUFRUHF LLOHDGXVHPRPHQWHORUFHQWUDWHEUXWH PUc SHQWUXD RE LQHPRPHQWHOHFHQWUDWHDMXVWDWHVXQWFXQRVFXWHVXEQXPHOHGHFRUHF LLOHOXL6KHSSDUG

P P

F Pc Pc

P Pc Pc F F

XQGH F HVWHP ULPHDLQWHUYDOHORUGHJUXSDUH 7HRUHP 'DF UHSDUWL LDWHRUHWLF DUHPHGLD P úLGLVSHUVLD V DWXQFL

V PHGLDGHVHOHF LHDUHYDORDUHDPHGLH P úLGLVSHUVLD Q 'HPRQVWUD LH$YHP

0 [

§ Q · 0 ¨ ¦ [ ¸ Q ©L ¹

Q ¦ 0 [L P QL

§ ª Q º ·¸ §¨ ª Q º ·¸ ¨ [ P » ¸ 0 « ¦ [L P» 0 0 >[ P@ ¨¬Q L ¸ Q ¨ «¬¦ L ¼ ¹ ¼ © ¹ © § Q V · 0 ¨ ¦ [L P ¸ Q ©L ¹ Q 5H]XOW GH DLFL úL GLQ LQHJDOLWDWHD OXL &HEvúHY F [ FRQYHUJH vQ SUREDELOLWDWHD F WUH P

0RPHQWHOHFHQWUDWH P N [ DOHPHGLHLGHVHOHF LHYRUIL

P [

º ·¸ §¨ ª Q 0 >[ P@ 0 ¦ [L P » Q ¨© «¬ L ¼ ¸¹ Q P 0 >[L P@ ¦ Q L Q

§ª Q º · 0 > [ P@ 0 ¨ ¦ [L P » ¸ Q ¨© «¬ L ¼ ¸¹ Q 0 > [L P @ ¦ 0 > [L P @ ª¬ [ M P º¼ ¦ Q L Q dL M d Q

P [

P P P Q Q

P P § · 2¨ ¸ Q ©Q ¹

P [ 0 >[ P@

ÌQJHQHUDO

N P N

§ · 2¨ N ¸ NQ ©Q ¹ N P N P 2§ · ¨ N ¸ N N Q N ©Q ¹

P N [ P N [

N

N

([HPSOH 6 VHDUDWHF GDF [ HVWHRYDULDELO DOHDWRDUHQRUPDO 1 PV DWXQFLUHSDUWL LD PHGLHLGHVHOHF LH [ HVWHGHDVHPHQHDQRUPDO 5 VSXQV)LH Q QXP UXOSUREHORUúL [ PHGLDGHVHOHF LH$YHP

M [ W 0 H 1RW P X

0H

LX[ N

H

PXL

LW[

W GHFL M [ X Q V X

GHFL M [ X

Q

§ L W ¦ [N ¨ Q 0 ¨H N ¨ © Q

0 H

· ¸ ¸¸ ¹

§ L QW [N 0 ¨¨ H N © Q

LX[ N

· ¸ ¸ ¹

'H OD OHJHD QRUPDO úWLP F

N

H

QPXL

QV X

VDX M [ W

§

H

PWL

V W Q

$FHDVWD HVWH

V ·

IXQF LD FDUDFWHULVWLF D XQHL UHSDUWL LL QRUPDOH 1 ¨¨ P ¸¸ GHFL IXQF LD GH UHSDUWL LH Q ¹ © FRUHVSXQ] WRDUHHVWHQRUPDO

)LH [ RYDULDELO DOHDWRDUHFXRUHSDUWL LH3RLVVRQGHSDUDPHWUX O 6 VHGHWHUPLQH UHSDUWL LDPHGLHLGHVHOHF LH 5 VSXQV9RPXWLOL]DWRWPHWRGDIXQF LHLFDUDFWHULVWLFH$YHP

¦ 0 §¨¨ H

M [ W 0 HLW[ W M [ X Q

VDX FX QRWD LD X

M [ W H

Q

W Q

Q

¦ 0 H LX[

Q

©

N

H

· ¸ ¸ ¹

W L [N Q

QX

GH XQGH UHYHQLQG OD YDULDELOD W

N

W

H $PRE LQXWIXQF LDFDUDFWHULVWLF DUHSDUWL LHL&DXFK\GHFL [ HVWHR

YDULDELO DOHDWRDUHUHSDUWL]DW &DXFK\ 7HRUHP 0RPHQWHOHFHQWUDWHDOHYDULDELOHL UHSDUWL LHLQRUPDOHFkQG Q o f 'HPRQVWUD LH$YHP N §ª º · ¨« ¸ [ P» ¸ ¨ » 0 « ¨ « V » ¸ ¨¨ « » ¸¸ ©¬ Q ¼ ¹ N §ª º · ¨« ¸ [ P» ¸ ¨ » 0 « ¨ « V » ¸ ¨¨ « » ¸¸ ©¬ Q ¼ ¹

QN 0 [ P N

V

Q

N

N

V N

N

Q N P N [ N

P

P N [

[ P WLQGF WUHPRPHQWHOH V Q

N

N 2 § ·

N

N

N N

¨ ¸ ©Q¹

P

§· 2 ¨ ¸ QP ©Q¹

7HRUHP 9DORDUHDPHGLHúLGLVSHUVLDPRPHQWXOXLGHVHOHF LHGHRUGLQ U

D U D U DU VXQWUHVSHFWLY D U úL Q 'HPRQVWUD LH$YHP

§ Q · 0 DU 0 ¨ ¦ [LU ¸ ©Q L ¹ ' DU

Q ¦ 0 [LU QL

D U

º ·¸ §¨ ª Q U 0 >DU D U @ 0 ¦ [L D U » Q ¨© «¬ L ¼ ¸¹ Q DU DU 0 [LU D U ¦ Q L Q

5H]XOW GHDLFLF DU FRQYHUJHvQSUREDELOLWDWHF WUH D U 7HRUHP $YHPUHOD LD

'HPRQVWUD LH'LQ

§· 0 PU P U 2¨ ¸ ©Q¹

[L [ U

5H]XOW

PU

[LU &U [ [LU &U [ [LU

DU &U [ DU &U [ DU

,QHJDOLWDWHDOXL6FKZDU]QHG

§· ¸ GHFL 0 [ D HVWHFHO 0 [ 2¨ Q

0 [ V DU V d 0 [ V 0 DU V

Q V V D U V D U V U V V Q Q © ¹ PXOWGHRUGLQXOOXL V d V d U Q 3UHVXSXQHP P FHHDFHQXUHVWUkQJHJHQHUDOLWDWHDGHRDUHFH PU HVWHLQYDULDQW §· ODRVFKLPEDUHDRULJLQLL5H]XOW D N P N d N d U GHFL 0 PU P U 2¨ ¸ ©Q¹

GDU 0 DU V

$QDORJVHSRDWHGHPRQVWUDF

' PU

P U P U UP U P U U P U P U § · 2¨ ¸ Q ©Q ¹

7HRULDHVWLPD LHL 6 FRQVLGHU PF DYHPRVHOHF LHGLQWURSRSXOD LHGDW DF UHLIXQF LHGHUHSDUWL LHL WHRUHWLF DUH R IRUP PDWHPDWLF FXQRVFXW vQ FDUH LQWU DQXPL L SDUDPHWUL FX YDORUL QHFXQRVFXWH ([LVW R LQILQLWDWH GH IXQF LL GH VHOHF LH VWDWLVWLFL FDUH SRW IL SURSXVH FD HVWLPD LLSHQWUXSDUDPHWULLQHFXQRVFX LGDUWUHEXLHDOHVHDFHOHDFDUHGDXFHDPDLEXQ DSUR[LPDUHDSDUDPHWULORU 'HH[HPSOXV SUHVXSXQHPF VWXGLLQGXQIHQRPHQDMXQJHPODFRQFOX]LDF

UHSDUWL LDOXLHVWHQRUPDO 1 PV GHFL I [

H V S

[ P V

3HQWUX DSOLFD LL SUDFWLFH WUHEXLH V GHWHUPLQ P YDORULOH QXPHULFH DOH FHORU GRL SDUDPHWUL P úL V

5HSDUWL LD H[SULPDW SULQWUR IXQF LH GDW vQ FDUH LQWU DQXPL L SDUDPHWUL QHFXQRVFX LVHVSXQHF HVWHROHJHGHUHSDUWL LHVSHFLILFDW 'DF FXQRDúWHP YDORULOH QXPHULFH DOH SDUDPHWULORU DYHP R OHJH GH UHSDUWL LH FRPSOHWVSHFLILFDW 2OHJHGHUHSDUWL LHQHVSHFLILFDW FRUHVSXQGHXQHLOHJLGHUHSDUWL LH QHFXQRVFXWH 'HWHUPLQDUHD YDORULORU SDUDPHWULORU XQHL UHSDUWL LL VSHFLILFDWH VH IDFH FX DMXWRUXO XQHLVHOHF LLGHYROXP Q FDUHFRQGXFHODYDORULOH [ [Q OHJDWHGHYDULDELODVWXGLDW ÌQFHOHFHXUPHD] QHYRPRFXSDGHUHSDUWL LLVSHFLILFDWHFDUHGHSLQGGHXQVLQJXU SDUDPHWUX'HFLIXQF LDGHUHSDUWL LHWHRUHWLF FRQ LQHXQVLQJXUSDUDPHWUXQHFXQRVFXW T 2VHOHF LHGHYROXP Q GLQFROHFWLYLWDWHQHDGDWHVWLPD LD T DOW VHOHF LHGHYROXP

Q QHG HVWLPD LD T HWF5HSHWkQGSURFHGHXORE LQHPHVWLPD LLOH T T U 2HVWLPD LH T DOXL T SRDWHILSULYLW FDRYDULDELO DOHDWRDUHFXYDORULOHSRVLELOH T T U

(VWLPD LLFRQVLVWHQWHFRUHFWHúLDEVROXWFRUHFWH QHGHSODVDWHGHSODVDWH )LH T XQ SDUDPHWUX DO FROHFWLYLW LL JHQHUDOH PHGLH GLVSHUVLH PHGLDQ HWF úL T [ [Q RIXQF LHGHVHOHF LH

'HILQL LH 'DF T [ [Q FRQYHUJH vQ SUREDELOLWDWH F WUH SDUDPHWUXO T

VSXQHPF T HVWHRHVWLPD LHFRQVLVWHQW DOXL T 'HILQL LH'DF 0 T [ [Q T OLP ' T [ [Q

Q of

VSXQHPF T [ [Q HVWHRHVWLPD LHFRUHFW DSDUDPHWUXOXL T 'DF 0 T [ [Q T 2 OLP ' T [ [Q

Q of

VSXQHPF T [ [Q HVWHRHVWLPD LHDEVROXW FRUHFW DSDUDPHWUXOXL T 7HRUHPD 0RPHQWHOH GH VHOHF LH VXQW HVWLPD LL DEVROXW FRUHFWH DOH PRPHQWHORUWHRUHWLFH 'HPRQVWUD LH$YHP

0 D U

§ Q · 0 ¨ ¦ [LU ¸ ©Q L ¹

Q 0 [LU ¦ Q L

D U D U GHFL Q OLP ' D U

ÌQWHRUHPDDPDU WDWF ' D U Q of

DU

7HRUHPD'LVSHUVLDGHVHOHF LHHVWHRHVWLPD LHFRQVLVWHQW SHQWUXGLVSHUVLD WHRUHWLF

Q ¦ [L FRQYHUJH vQ QL Q S SUREDELOLWDWH F WUH PRPHQWXO WHRUHWLF GH RUGLQXO GRL GHFL ¦ [L o D úL QL S [ o D DVWIHOF Q Q S [L [ ¦ [L [ o D D V ¦ QL Q L Q [L [ HVWH R HVWLPD LH FRQVLVWHQW 6H DUDW FX XúXULQ F a V ¦ Q L 'HPRQVWUD LH 'LQ OHJHD QXPHUHORU PDUL UH]XOW F

DEVROXWFRUHFW SHQWUXGLVSHUVLDWHRUHWLF ([HPSOX )LH R VFKHP GH WLS %HUQRXOOL FX GRX VW UL ÌQ Q REVHUYD LL LQGHSHQGHQWHHYHQLPHQWXO $ DSDUHFXSUREDELOLWDWHD S GH D RUL d D d Q 6 VH HVWLPH]H S úL S FXDMXWRUXOOXL D 5 VSXQV 9HULILF P GDF

D §D· HVWH R HVWLPD LH D OXL S $YHP 0 ¨ ¸ Q ©Q¹

S

D ST GHFL HVWHRHVWLPD LHDEVROXWFRUHFW DOXL S Q Q QST S § D · § D · 'H DVHPHQHD DYHP 0 ¨ ' ¨ GHFL ¸ ¸ S Q © Q ¹ Q © Q ¹ D D S o S GDU QXHVWHRHVWLPD LHDEVROXWFRUHFW DOXL S HVWHQXPDLR Q Q

§D· ' ¨ ¸ ©Q¹

HVWLPD LHFRUHFW

D HVWHRHVWLPD LHDEVROXWFRUHFW SHQWUX S HVWHQDWXUDOV vQFHUF PV Q § D · ST D 0 ¨¨ ¸¸ S SH S SULQ $YHP úL Q Q ©Q ¹

'HRDUHFH HVWLP P

§ D · ' ¨¨ ¸¸ ©Q ¹

S T D § · 2¨ ¸ GHFL HVWHRHVWLPD LHFRUHFW SHQWUX S 3HQWUXD Q Q ©Q ¹

GHWHUPLQDRHVWLPD LHDEVROXWFRUHFW REVHUY PF

§ D · 0 ¨¨ ¸¸ ©Q ¹

S

ST Q

Q S S Q Q

§D· 0¨ ¸ ©Q ¹

§ D D · S GHFL 0 ¨¨ ¸¸ Q ¹ Q ©Q

Q S VDX Q

§ D D · Q 0 ¨¨ ¸¸ Q © Q Q ¹ § D D · ¸¸ GHXQGH 0 ¨¨ © QQ ¹

§ D D · ¸¸ S '¨¨ © QQ ¹ RHVWLPD LHDEVROXWFRUHFW DOXL S

S

S T D D §· 2¨ ¸ GHFL HVWH Q QQ ©Q¹

2 HVWLPD LH DEVROXW FRUHFW SHQWUX V HVWH

Q V XQGH V HVWH GLVSHUVLD GH Q

VHOHF LH 'HILQL LH2HVWLPD LH T HVWHQHGHSODVDW GDF 0 T RHVWLPD LHGHSODVDW

ÌQFD]FRQWUDUDYHP

D HVWHRHVWLPD LHDEVROXWFRUHFW DOXL S 6 Q WUHFHPODHVWLPDUHDGLVSHUVLHL ' [ [ ILLQGYDULDELODDOHDWRDUHEHUQRXOOLDQ FDUHLD YDORULOH úL FX SUREDELOLW LOH S úL T S 'LVSHUVLD GH VHOHF LH HVWH Q [L [ $YHP V ¦ Q L Q 0 V ' [ ' [ ' [ Q Q GHFL V HVWHRHVWLPD LHGHSODVDW 9RPOXDFDHVWLPD LHDGLVSHUVLHL ' [ GLVSHUVLDGH ÌQH[HPSOXODQWHULRUDPY ]XWF

VHOHF LHPRGLILFDW

a V

V SHQWUXFDUH 0 a

Q V Q ' [

Q [L [ ¦ Q L

)XQF LLGHHVWLPD LHHILFLHQWH0HWRGDYHURVLPLOLW LLPD[LPH 'H PXOWH RUL R HVWLPD LH QHGHSODVDW QX QH G FHD PDL EXQ DSUR[LPDUH D SDUDPHWUXOXLGHHVWLPDW9DORULOHSRVLELOHDOHHVWLPD LHLOXL T SRWILPXOWvPSU úWLDWHvQ MXUXO YDORULL PHGLL GDF ' T HVWH PDUH LDU HVWLPD LD FDOFXODW GH R VHOHF LH GDW

SRDWH IL vQGHS UWDW GH YDORDUHD PHGLH D OXL T GHFL VH IDFH R HURDUH DOHJkQG T FD HVWLPD LHSHQWUX T 'DF T HVWHRHVWLPD LHDEVROXWFRUHFW SHQWUXSDUDPHWUXO T ! úL 0 T f DWXQFLLQHJDOLWDWHDOXL&HEvúHY

3 T T t H

' T H

G XQ FULWHULX SHQWUX DOHJHUHD HVWLPD LLORU úL DQXPH DOHJHP DFHD HVWLPD LH FDUH DUH GLVSHUVLDPLQLP )LH I [ T R IDPLOLH GH GHQVLW L GH SUREDELOLWDWH DOH XQHL UHSDUWL LL VSHFLILFDWH

FRQWLQXHFX T SDUDPHWUXOUHDOQHFXQRVFXW9RPDGPLWHFRQWLQXLWDWHDIXQF LLORU I [ T úLH[LVWHQ DGHULYDWHORUDFHVWRUIXQF LLvQUDSRUWFX T SkQ ODRUGLQHOHQHFHVDUHFDOFXOHORU 7HRUHPD 5DR&UDPHU 'DF T [ [Q HVWH R HVWLPD LH DEVROXW FRUHFW DSDUDPHWUXOXL T DWXQFL

' T [ [Q t

§ ª w OQ I [ T º · ¸ Q0 ¨ « »¼ ¸ ¨¬ w T ¹ ©

(JDOLWDWHDDUHORFGDF úLQXPDLGDF H[LVW RFRQVWDQW N FHGHSLQGHGH Q úL T DúDvQFkWDSURDSHVLJXU Q

¦ L

w OQ I [L T wT

N T [ [Q T

3HQWUXGHPRQVWUD LHYH]L>@S 'HILQL LH2HVWLPD LHDEVROXWFRUHFW T [ [Q DSDUDPHWUXOXL T VHQXPHúWH HILFLHQW GDF DUHGLVSHUVLDPLQLP 'DF T HVWHRIXQF LHGHHVWLPD LHDEVROXWFRUHFW UDSRUWXO

§ ª w OQ I [ T º · ¸ Q0 ¨ « »¼ ¸ ¨¬ w T © ¹

' T

HQ T

VHQXPHúWHHILFLHQ DOXL T 6HREVHUY F d HQ T d 'DF HQ T

HVWLPD LDHVWHHILFLHQW

([HPSOX&DUDFWHULVWLFD [ DHOHPHQWHORUXQHLSRSXOD LLDUHRUHSDUWL LHQRUPDO

1 P V FX P FXQRVFXW úL V QHFXQRVFXW &RQVLGHU P FD HVWLPD LH D DFHVWXL S Q ¦ [N P XQGH YDULDELOHOH DOHDWRDUH [L d L d Q VXQW N LQGHSHQGHQWHúLDXDFHHDúLUHSDUWL LHFD [ 6 VHGHWHUPLQHHILFLHQ DOXL T SDUDPHWUX T

Q

5 VSXQV$YHP

0 [ P

V S

f

³ [ PH

f

[ P V

G[

V

S

S Q S 0 [N P V V ¦ N S S ' T V Q GHFL T HVWH R HVWLPD LH DEVROXW FRUHFW D OXL V (ILFLHQ D VD HVWH V Q H # GHFL T QXHVWHFHOPDLHILFLHQWHVWLPDWRU S S V Q 7HRUHPD'RX HVWLPD LLHILFLHQWHDOHSDUDPHWUXOXL T VXQWHJDOHDSURDSH

0 T

Q

VLJXU 'HPRQVWUD LH )LH T úL T GRX HVWLPD LL HILFLHQWH DOH OXL T DWXQFL

0 T

0 T ' T

$YHP

N0 T N 0 T GHFL T HVWHRHVWLPD LHDEVROXWFRUHFW DOXL T 0 T

T T

T T

T

0 T T T T ' T ' T

'DF U

UT T

NT N T

N ' T UN N ' T ' T U ' T

GDU U

0 T 0 T

' T

NT N T

' T &RQVLGHU PHVWLPD LD T

T DYHP 0 T

DWXQFL ' T ' T GHFL T QX HVWH VXILFLHQW 5H]XOW

LDUGLQ ' T

'

T

GHFL T

T DSURDSH

SHVWHWRW )LH UHSDUWL LD GH WLS FRQWLQXX I [ T XQGH T SRDWH OXD RULFH YDORDUH GLQWUXQ LQWHUYDO , 9DORULOHGHVHOHF LH [ [Q RE LQXWHvQXUPDD Q H[WUDF LLLQGHSHQGHQWH GLQSRSXOD LHVXQWYDULDELOHDOHDWRDUHLQGHSHQGHQWHFXDFHHDúLGHQVLWDWHGHSUREDELOLWDWH I [ T )LHFDUH VHOHF LH [ [Q R FRQVLGHU P FD XQ SXQFW vQ VSD LXO GH VHOHF LH

Q GLPHQVLRQDO \ Q LDUSUREDELOLWDWHDHOHPHQWDU DYHFWRUXOXL [ [Q HVWH 3 [ [Q T G[ G[Q

I [ T I [Q T G[ G[Q

Q

'HILQL LH)XQF LD 3 \ u , o \ VHQXPHúWHIXQF LHGHYHURVLPLOLWDWH

'HILQL LH(VWLPD LD TÖ [ [Q VHQXPHúWHHVWLPD LHGHYHURVLPLOLWDWHGDF TÖ HVWHXQSXQFWGHPD[LPSHQWUXIXQF LDGHYHURVLPLOLWDWH

5H]XOW F TÖ HVWHRVROX LHDHFXD LHL

w OQ 3 [ [Q T wT

Q

¦ L

w OQ I [L T wT

(FXD LD VHQXPHúWHHFXD LHGHYHURVLPLOLWDWH 7HRUHPD 2ULFH HVWLPD LH HILFLHQW D SDUDPHWUXOXL T HVWH R HVWLPD LH GH YHURVLPLOLWDWHPD[LP 'HPRQVWUD LH'DF T HVWHRHVWLPD LHHILFLHQW DWXQFLLQHJDOLWDWHD GHYLQH HJDOLWDWH úL GHFL

Q

¦ L

w OQ I [L T wT

N TÖ T 'HFL TÖ HVWH R VROX LH D HFXD LHL GH

YHURVLPLOLWDWH 9RP GD vQ FRQWLQXDUH FkWHYD H[HPSOH SULYLQG SUREOHPD HVWLPD LHL SHQWUX XQHOH IDPLOLLGHUHSDUWL LLFXQRVFXWH ([HPSOH 5HSDUWL LDGHWLS%HUQRXOOL$PY ]XWF

D HVWHRHVWLPD LHDEVROXWFRUHFW SHQWUX Q

SUREDELOLWDWHD S 6 DU W PF HDHVWHúLRHVWLPD LHHILFLHQW

5 VSXQV'LQWHRUHPDVHúWLHF SHQWUXRULFHHVWLPD LHDEVROXWFRUHFW T DYHP LQHJDOLWDWHD

' T t XQGH S S

S S S S § w OQ SL wS ©

· ¸¸ SL ¹

§ w OQ SL Q¦ ¨¨ wS L © Q

· ¸¸ SL S ¹

S S S L ST D GHFL ' T t 0LQLPXOHVWHDWLQVSHQWUX Q Q Q

¦ ¨¨

S

/D DFHODúL UH]XOWDW VH DMXQJH DSOLFkQG PHWRGD YHURVLPLOLW LL PD[LPH 'LQ

w OQ S D T QD wD

D QD S T

VHRE LQH S

D Q

5HSDUWL LDQRUPDO FXGHQVLWDWHDGHSUREDELOLWDWH I [ P D (VWLPDUHDPHGLHL 5 VSXQV$YHP

OQ I [ P

ST

H V S

[ P V

P P [ OQ [ V V V V S

Q ¦ [L HVWHRIXQF LHGHHVWLPD LH QL

'LQWHRUHPDUH]XOW F T [ [Q HILFLHQW DOXL P GHRDUHFH

P P [ OQ [ P V V V V S Q · V § P ' ¨ ¦ [L ¸ 5H]XOW F T HVWH R HVWLPD LH DEVROXW ©Q L ¹ Q

OQ I [ P § Q · ¦ [L ¸ ©Q L ¹

úL 0 ¨

FRUHFW )XQF LDGHYHURVLPLOLWDWHHVWH

3 [ [Q P

Q

¦ [L P

V S Q

Q

LDU GLQ HFXD LD YHURVLPLOLW LL PD[LPH OQ 3

H

L

V

Q

¦ [

UH]XOW

L

P VDX

Q ¦ [L QL

P

E (VWLPDUHDSDUDPHWUXOXL V 5 VSXQV)XQF LDGHYHURVLPLOLWDWHHVWH

3 [ [Q V úL

OQ 3 (FXD LD

Q

¦ [L P

V Q S

Q

H

L

V

Q [L P ¦ V L w OQ 3 FRQGXFH wV

Q OQ V Q OQ S

YHURVLPLOLW LL

PD[LPH

OD

VROX LD

O N O H N N

Q [L P ¦ QL

V

5HSDUWL LD3RLVVRQHVWLPDUHDSDUDPHWUXOXL O GLQ I N O

L

SHED]DXQHLVHOHF LLUHSHWDWHGHYROXP Q

5 VSXQV$YHP

Q

3 [ [Q O H QO

¦ [L OL Q

[ L

'LQHFXD LDYHURVLPLOLW LLPD[LPHRE LQHP O

L

Q ¦ [L QL

Q ¦ [L HVWH R HVWLPD LH HILFLHQW SHQWUX O ÌQWU QL

6 DU W P F T [ [Q

O Q

DGHY U 0 T

O ' T

0LQLPXOGLVSHUVLHLSHQWUXIXQF LLGHHVWLPD LHDEVROXWFRUHFWHHVWH

§ w OQ I N O · Q¦ ¨ ¸ I N O wO ¹ N ©

Q

GDU

N O Q § w OQ I N O · §N · OH Q¦ ¨ ¸ I N O Q¦ ¨ ¸ wO ¹ ¹ N N © N ©O O GHFLPLQLPXOGLVSHUVLHLHVWH Q Q

Q O

(/(0(17('(7(25,$*5$)85,/25 ,QWURGXFHUH'HILQL LL

3ULPD UHIHULUH OD WHRULD JUDIXULORU D IRVW I FXW vQ GH F WUH (XOHU vQ OXFUDUHDQXPLW 3UREOHPDSRGXULORUGLQ.|QLJVEHUJÌQ.LUFKRIIDDERUGDW WHRULDUH HOHORUHOHFWULFHSULQPHWRGDJUDIXULORU ÌQ)RUGúL)XONHUVRQDXDSOLFDWWHRULDJUDIXULORUvQUH HOHOHGHWUDQVSRUW $VWIHO GXS DFHDVW SHULRDG WHRULD JUDIXULORU D IRVW XWLOL]DW SHQWUX UH]ROYDUHD XQRU SUREOHPH FX FDUDFWHU HFRQRPLF SHQWUX SURLHFWDUHD UH HOHORU HOHFWULFH GH FDQDOL]DUHGHJD]HVDXDUH HOHORUGHWHKQLF GHFDOFXORULvQPHGLFLQ 'HILQL LH 8Q JUDI * HVWH R SHUHFKH GH IRUPD * ; * XQGH ; HVWH HVWHRPXO LPHILQLW QXPLW PXO LPHDYkUIXULORUVDXDQRGXULORU RULFHHOHPHQW [ ; VHQXPHúWHYkUI * HVWHRVXEPXO LPHDOXL ; u ; PXO LPHDSHUHFKLORU

RUGRQDWH [L [ M [L [ M ; L

Q M Q L z M QXPLWHDUFH

3HQWUXXQDUF [L [ M * YkUIXO [L VHQXPHúWHH[WUHPLWDWHLQL LDO VXUV LDUYkUIXO [ M H[WUHPLWDWHILQDO GHVWLQD LH *UDIXO * DGPLWHRUHSUH]HQWDUHJHRPHWULF vQSODQRE LQXW DVWIHO YkUIXULOHVHSODVHD] vQSODQvQSR]L LLGLVWLQFWHRDUHFDUH ILHFDUHDUF [L [ M * VHUHSUH]LQW SULQWUROLQLHFHXQHúWHFHOHH[WUHPLW LúL

SHFDUHVHDIO VHQVXOGHOD [L OD [ M

; * GDWGH ; ^[ [ [ [ [ `LDU ^[ [ [ [ [ [ [ [ [ [ [ [ [ [ `

([HPSOX)LHJUDIXO *

*

&XUHSUH]HQWDUHDJHRPHWULF

)LJXUD

6HREVHUY F * SRDWHILGHILQLW FDRDSOLFD LHPXOWLYRF * ; o 3 ;

DGLF * [ HVWHPXO LPHDWXWXURUQRGXULORUILQDOHDOHDUFHORUFHDXFDQRGLQL LDO SH [

$VWIHO JUDIXO GLQ H[HPSOXO GH PDL VXV SRDWH IL VFULV FD ^[ [ [ [ [ ` *[ ^[ [ ` *[ ^[ ` *[ ^[ [ `

; * [

^[ [ ` *[ 'DF [L * [L DUFXO [L [L * VHQXPHúWHEXFO

'DF JUDIXO * FRQ LQHDUFXO [L [ M YRPVSXQHF YkUIXULOH [L úL [ M VXQW

DGLDFHQWHvQ * úLDPkQGRX VXQWLQFLGHQWHFXDUFXO [L [ M 'HILQL LH2VXFFHVLXQHGHDUFHvQFDUHYkUIXOWHUPLQDODOXQXLDHVWHRULJLQH SHQWUXXUP WRUXOVHQXPHúWHGUXP 'HILQL LH8QGUXPHVWHVLPSOXGDF IRORVHúWHXQDUFRVLQJXU GDW 'HILQL LH 8Q GUXP HVWH HOHPHQWDU GDF QX WUHFH GH GRX RUL SULQ DFHODúL YkUI 'HILQL LH 8Q GUXP HOHPHQWDU FDUH FXSULQGH WRDWH YkUIXULOH JUDIXOXL VH QXPHúWHKDPLOWRQLDQ 'HILQL LH 1XP UXO DUFHORU FDUH FRPSXQ XQ GUXP VH QXPHúWH OXQJLPHD DFHOXLGUXP 3HQWUX H[HPSOXO JUDIXOXL GLQ ILJXUD XQ GUXP HOHPHQWDU SRDWH IL G ^[ [ [ [ `OXQJLPHDGUXPXOXL G HVWH

>

@

ÌQWUXQJUDI * VHQXPHúWHPXFKLHRSHUHFKHGHYkUIXUL [L [ M GHYkUIXUL

SHQWUXFDUHDYHPSURSULHWDWHDF [L [ M * VDX [ M [L * PXFKLLOHXQXLJUDI UHSUH]HQWDWJHRPHWULFVHSUH]LQW FDQLúWHVHJPHQWHQHRULHQWDWH [ [ [ [ [ S [ S 'HILQL LH6HQXPHúWHODQ XQúLUGHDUFH O

^

`

FX SURSULHWDWHD F RULFDUH DUFH YHFLQH [L [L [L [L DX R H[WUHPLWDWH

FRPXQ SHQWUXRULFH L S 'HILQL LH 8Q ODQ FDUH QXúL UHSHW YkUIXULOH VH QXPHúWH ODQ HOHPHQWDU LDUXQODQ FDUHQXúLUHSHW PXFKLLOHVHQXPHúWHXQODQ VLPSOX 1XP UXOGHPXFKLLFDUHIRUPHD] XQODQ VHQXPHúWHOXQJLPHDODQ XOXL ([HPSOX ÌQJUDIXOGLQILJXUDXUP WRDUHOHúLUXULGHDUFHVXQWODQ XUL O ^ [ [ [ [ [ [ ` O ^ [ [ [ [ `

O ^ [ [ [ [ [ [ ` O ^ [ [ [ [ [ [ `

'HILQL LH6HVSXQHF XQJUDIHVWHFRQH[GDF vQWUHRULFDUHGRX YkUIXULDOH VDOHH[LVW FHOSX LQXQODQ FDUHV OHOHJHÌQFD]FRQWUDUJUDIXOHVWHQHFRQH[ 8QJUDIVHQXPHúWHWDUHFRQH[GDF vQWUHRULFDUHGRX YkUIXULDOHVDOHH[LVW FHOSX LQXQGUXP

([HPSOX *UDIXO

HVWHFRQH[LDUJUDIXO

)LJXUD

)LJXUDD

)LJXUDE

QXHVWHFRQH[ 'HILQL LH *UDGXO XQXL YkUI [ VH QRWHD] J [ úL UHSUH]LQW QXP UXO GH

DUFHLQFLGHQWHFX [ *UDGXOLQWHULRUDOXQXLYkUI [ VHQRWHD] FX J [ úLHVWH

QXP UXODUFHORUGHIRUPD \ [ * FX \ ; *UDGXOH[WHULRUDOXQXLYkUI [ VHQRWHD] FX J [ úLHVWHQXP UXOGHDUFHGHIRUPD [ \ * FX \ ; ([HPSOX ÌQ JUDIXO GLQ ILJXUD J [

H[LVWkQG GRX DUFH SHQWUX F * [ ^[ ` 'HFL

[ [ [ [ FX GHVWLQD LD [ úL J [ J [ 'HILQL LH6HQXPHúWHVXEJUDI * c ; c * c DOJUDIXOXL * ; * XQJUDI

RE LQXWGLQ * SULQVXSULPDUHDDQXPLWRUYkUIXULúLDUFH 'DF * c VH RE LQH GLQ * SULQ VXSULPDUHD DQXPLWRU YkUIXUL úL D WXWXURU DUFHORULQFLGHQWHFXDFHVWHDYRPVSXQHF VXEJUDIXO * c HVWHLQGXVVDXJHQHUDWGH PXO LPHDGHYkUIXUL ; c 6XEJUDIXO * c VHQXPHúWHJUDISDU LDODOOXL * GDF VHRE LQHGLQJUDIXO * DYkQGDFHOHDúLYkUIXULGDUQXPDLFXRSDUWHGLQDUFHORUDFHVWXLD ([HPSOX )LHJUDIXO

)LJXUDD

ÌQ)LJXUDEHVWHSUH]HQWDWVXEJUDIXO * c JHQHUDWGHQRGXULOH ^[ [ [ [ `

)LGXUDE

LDUvQ)LJXUDFHVWHSUH]HQWDWJUDIXOSDU LDO * cc I U DUFHOH [ [ úL [ [

)LJXUDF

'HILQL LH 8Q JUDI RULHQWDW HVWH FRPSOHW GDF RULFDUH GRX YkUIXUL VXQW DGLDFHQWH 0DWULFLDVRFLDWHXQXLJUDI3URSULHW LDOHJUDIXULORU ÌQSUREOHPHOHFHSRWILUH]ROYDWHFXDMXWRUXOJUDIXULORUDSDUDQXPLWHPDWULFL FHFRQ LQLQIRUPD LLDVXSUDDUFHORUGUXPXULORUVDXDOWRUHOHPHQWHOHJDWHGHJUDIXUL 0DWULFHDFRQH[LXQLORUGLUHFWH )LH XQ JUDI *

; * FX

;

^[ [ [Q ` $VRFLHP DFHVWXL JUDI R

F SHQWUX [ [ * SHQWUX [ [ *

PDWULFHS WUDWLF & DOHF UXLHOHPHQWHVXQW &

FLM

° ® °¯

LM L M Q

L

M

L

M

0DWULFHD & SRDUW QXPHOHGHPDWULFHDDUFHORUPDWULFHDFRQH[LXQLORUGLUHFWH VDXPDWULFHDGHDGLDFHQ SHQWUXJUDIXO *

)LJXUD

([HPSOX3HQWUXJUDIXOGLQILJXUDVFULHPPDWULFHDFRQH[LXQLORUGLUHFWH

&

§ ¨ ¨ ¨ ¨ ¨ ¨ ©

· ¸ ¸ ¸ ¸ ¸ ¸¹

2EVHUYD LL 1XP UXOGHFLIUH GHSHOLQLD [L UHSUH]LQW QXP UXOGHFRQH[LXQLGLUHFWHDOH OXL [L LDU QXP UXO GH FLIUH GH SH FRORDQD [ M UHSUH]LQW QXP UXO FRQH[LXQLORU GLUHFWH FX [ M 'H H[HPSOX GDF QRGXULOH JUDIXOXL GH PDL VXV UHSUH]LQW E QFLLDUDUFHOHFRUHVSXQ] WRDUHUHSUH]LQW UHOD LLOHGHFRODERUDUH LQWHUEDQFDUHDWXQFLFLIUHOHGH GHSHOLQLD [L DUSXWHDUHSUH]HQWDSRVLELOLW LOH OD FDUH EDQFD L IDFH SODVDPHQWH LDU FLIUHOH GH GH SH FRORDQD [ M DU SXWHD UHSUH]HQWDSRVLELOLW LOHGHODFDUHEDQFD M DUSXWHDIDFHvPSUXPXWXUL 'DF GRX JUDIXULDXDFHHDúLPDWULFHDFRQH[LXQLORUGLUHFWHúLDFHHDúLPXO LPH GHYkUIXUL DWXQFLFHOHGRX JUDIXULFRLQFLG *UDGXO H[WHULRU DO YkUIXOXL [L VH RE LQH DGXQkQG HOHPHQWHOH GH SH OLQLD L D PDWULFHL & LDUJUDGXOLQWHULRUDODFHOXLDúLYkUIVHRE LQHDGXQkQGHOHPHQWHOH GHSHFRORDQD L DPDWULFHL &

J [L

Q

¦ FLM J [L M

Q

¦F N

NL

([HPSOX3HQWUXJUDIXOGLQ)LJXUDDYHP J [ úL J [

0DWULFHDGUXPXULORU 'LQ PDWULFHD FRQH[LXQLORU GLUHFWH SULQ DQXPLWH RSHUD LL VH SRDWH R PDWULFH LM L M Q QXPLW PDWULFHD GUXPXULORU VDX PDWULFHD FRQH[LXQLORU WRWDOH vQ

G

' FDUH

G LM

GDF H[LVW GUXPGHOD [L OD [ M ® ¯ GDF QXH[LVW GUXPGHOD [L OD [ M

'HILQL LH 3XWHUHD GH DWLQJHUH S [L D YkUIXOXL [L ; vQ JUDIXO

; * HVWHHJDO

*

FXQXP UXOGHYkUIXULODFDUHVHSRDWHDMXQJHGLQ [L DGLF

HJDO FXQXP UXOGHHOHPHQWHGHÄ ´GHSHOLQLDÄ L ´GLQPDWULFHD '

2EVHUYD LL 0DWULFHD ' D GUXPXULORU JUDIXOXL * SRDWH LQGLFD DEVHQ D VDX SUH]HQ D FLUFXLWHORUvQJUDIXO * DVWIHO

L Q DWXQFLJUDIXO * QXDUHFLUFXLWH

GDF G LL

GDF H[LVW XQLQGLFH L L

Q SHQWUXFDUH G LL

DWXQFLH[LVW vQJUDIXO

* XQFLUFXLWFDUHDUHFDYkUISH [L

'DF S [L DWXQFLGLQYkUIXO [L QXVHDMXQJHQLF LHULúLVHQXPHúWHLHúLUH GLQUH HD 'DF PDWULFHD ' DUH WRDWH HOHPHQWHOH HJDOH FX DWXQFL JUDIXO HVWH WDUH FRQH[ 'DF FHO SX LQ XQ HOHPHQW HVWH HJDO FX vQ ' JUDIXO QX HVWH WDUH FRQH[ 3HQWUX HODERUDUHD XQXL DOJRULWP GH GHWHUPLQDUH D PDWULFLL GUXPXULORU LQWURGXFHPRRSHUD LHDGHFYDW SHPXO LPHDIRUPDW GLQHOHPHQWHOH úL QXPLW RSHUD LHGHDGXQDUHERROHDQ FXUHJXOLOHXUP WRDUH $VWIHODOJRULWPXOGHGHWHUPLQDUHDOPDWULFLLGUXPXULORUXQXLJUDISRUQLQGGH ODPDWULFHDFRQH[LXQLORUGLUHFWHHVWH 3HQWUX FRQVWUXLUHD OLQLHL Ä L ´ GLQ PDWULFHD ' L Q XUP ULP HOHPHQWHOH HJDOHFXÄ ´GHSHOLQLDÄ L ´GLQPDWULFHD & GDF

F LD F LE

# F LJ

DWXQFL

G LD G LE

#

G LJ )RORVLQG DGXQDUHD ERROHDQ VH DGXQ OLQLLOH D E J GLQ PDWULFHD & OD OLQLD Ä L ´QRLOHYDORULÄ ´DS UXWHVHWUHFvQOLQLDÄ L ´DPDWULFHL ' ILH N O P SR]L LLOHRFXSDWHGHDFHVWHQRLYDORULvQFDGUXOOLQLHL $GXQ PERROHDQ OLQLLOH N O P GLQ & ODOLQLDÄ L ´WUHFkQGQRLOHYDORUL GHÄ ´DS UXWHvQOLQLDÄ L ´DPDWULFLL ' FRQWLQXkQGSURFHVXOSkQ ODDSDUL LD XQHLDGLQVLWXD LLOH D VDXWRDWHHOHPHQWHOH G LM M Q GHYLQHJDOHFXÄ ´

E QXPDLDSDUHQLFLXQHOHPHQWHJDOFXÄ ´FD]vQFDUHORFXULOHU PDVHOLEHUH VHFRPSOHWHD] FX]HURXULúLVHWUHFHODOLQLDÄ L ´SHQWUXFDUHVHUHSHW SURFHGHXO

([HPSOX3HQWUXJUDIXOGLQ)LJXUDFXPDWULFHDFRQH[LXQLORUGLUHFWH & DVRFLDW GHWHUPLQ PPDWULFHDGUXPXULORU ' &RQVWUXLPOLQLD DPDWULFLL ' SRUQLQGGHODOLQLD DPDWULFLL & 2EVHUY PF F úL F UHVWXOHOHPHQWHORUILLQGHJDOHFX]HUR $WXQFLDGXQ PERROHDQOLQLD GLQ & FXOLQLLOH úL DOHPDWULFLL &

O O O BBBBBBBBBBBBBBBBBBBBBBBBBB

O

2EVHUY PF OLQLD O GLIHU GHOSULQHOHPHQWXOJHQHUDWSHSR]L LLOH F

úL F 7UHFHPODSDVXOGLQDOJRULWPúLDGXQ PERROHDQOLQLD O FXOLQLLOH úL GLQ &

O O

O

BBBBBBBBBBBBBBBBBBBBBBBBBB

O

2EVHUY PF VDRE LQXWROLQLHFXWRDWHHOHPHQWHOHHJDOHFX GHFLOLQLD D PDWULFLL ' YDIL O '

UHVWXOHOHPHQWHORU ILLQGHJDOHFX]HUR$GXQ PERROHDQOLQLD GLQ & FXOLQLLOH úL O O O 3HQWUX OLQLD DPDWULFLL ' REVHUY PF F

F

BBBBBBBBBBBBBBBBBBBBBBBBBB

O

2EVHUY PF OLQLD O GLIHU GHOLQLD SULQHOHPHQWHOHJHQHUDWHGHSR]L LLOH

F

úL F

$GXQ PERROHDQ O FXOLQLLOH úL

O O

O

BBBBBBBBBBBBBBBBBBBBBBBBBB

O

$PRE LQXWWRDWHHOHPHQWHOHHJDOHFX GHFL O ' 6LPLODUSHQWUXOLQLLOHúLRE LQHPPDWULFHD '

'

§ ¨ ¨ ¨ ¨ ¨ ¨ ©

· ¸ ¸ ¸ ¸ ¸ ¸¹

2EVHUYD LL *UDIXO * DUH FLUFXLWH F FL H[LVW L DVWIHO vQFkW G LL

H[HPSOX G 0DLPXOWWRDWHYDORULOHGLQPDWULFHD ' VXQWHJDOHFX GHFLJUDIXOHVWHWDUH

FRQH[ 3XWHULOHGHDWLQJHUHDOHYkUIXULORU S [L L $OJRULWPXOSUH]HQWDWDQWHULRUGHGHWHUPLQDUHDPDWULFLLGUXPXULORUHVWHGHVWXO GHOHQWvQFHSULYHúWHDSOLFDUHDSHFDOFXODWRUDYkQGFRPSOH[LWDWHD 2 Q GDU HVWHXWLOvQDSOLFD LLHIHFWXDWHPDQXDOSHJUDIXULGHGLPHQVLXQLUHGXVH

'HWHUPLQDUHDGUXPXULORUKDPLOWRQLHQHvQJUDIXULI U FLUFXLWH 'DF JUDIXO * QXDUHFLUFXLWHYRPVFULHPDWULFHD ' DGUXPXULORUJUDIXOXL RUGRQkQG vQ SUHDODELO YkUIXULOH JUDIXOXL vQ RUGLQHD GHVFUHVF WRDUH D SXWHULORU GH DWLQJHUH±DVWIHOWRDWHYDORULOHGHÄ ´GLQPDWULFHYRUDS UHDGHDVXSUDGLDJRQDOHL SULQFLSDOH 'HRDUHFH GDF vQ JUDIXO * H[LVW XQ GUXP GH OD [L OD [ M DWXQFL S [ M S [L

GHRDUHFHRULFHYkUIDWLQVGLQ [ M SRDWHILDWLQVúLGLQ [L SULQWUXQGUXPRE LQXW

vQFDGUXORSHUD LHLGHFRQHFWDUH GDF DU PDL IL SRVLELO FD G LM FX L ! M DWXQFL S [L ! S [ M FHHD FH

FRQIRUPUHDUDQM ULLOLQLLORUúLFRORDQHORUQXPDLHVWHSRVLELO $FHVW SURFHGHX VH QXPHúWH ÄWULDQJXODUL]DUH´ PDWULFHD ' VH YD QXPL ÄIRUP WULXQJXODUL]DW VXSHULRU´

(VWHHYLGHQWF GDF RUGLQHD ^[ [ [ Q `DYvUIXULORUJUDIXOXLFRQGXFHUHOD

RPDWULFHWULDQJXODUL]DW DWXQFL S [ t S [ t t S [ Q

$FHDVW IRUP DUHSURSULHWDWHDF ILHFDUHHOHPHQWHJDOFXÄ ´GHSHILHFDUH OLQLHDPDWULFLLGUXPXOXLFRUHVSXQGHXQXLGUXPIRUPDWGLQWUXQVLQJXUDUF ÌQWUDGHY USUHVXSXQHPF SHOLQLDYkUIXOXL [L FRQVWDW PF

G LN ® ¯G LM

N M M!L

6 SUHVXSXQHPF H[LVW XQGUXPGHOD [L OD [ M IRUPDWGLQPDLPXOWHDUFH

^

`

GHH[HPSOXGUXPXO [L [ N [ N [ M $WXQFLDYHP

G LN

G NM

S [ N ! S [ M

GHFL [ N HVWH vQDLQWHD OXL [ M úL GHFL YDORDUHD G LN

DU IL DQWHULRDU OXL G LM SH

OLQLDYkUIXOXL [L FHHDFHDPSUHVXSXVF QXVHvQWkPSO ([HPSOX )LHPDWULFHD ' DGUXPXULORUXQXLJUDI

[

[

[

[

S [

[ § [ ¨¨ [ ¨ ¨ [ ©

· ¸ ¸ ¸ ¸ ¹

3HQWUXDWULDQJXODUL]DPDWULFHD ' QHIRORVLPGHUHOD LLOH S [ ! S [ ! S [ ! S[ YRP VFULH YkUIXULOH vQ RUGLQHD ^[ [ [ [ ` vQ ORF GH RUGLQHD ^[ [ [ [ ` '

$YHP

'

[ [ [ [ [ § · ¨ ¸ [ ¨ ¸ [ ¨ ¸ ¨ ¸ [ © ¹

FDUHHVWHPDWULFHDWULDQJXODUL]DW DGUXPXULORU $FHVWH FRQVLGHUD LL SHUPLW HODERUDUHD DOJRULWPXOXL GH GHWHUPLQDUH D GUXPXULORUKDPLOWRQLHQHvQJUDIXULOHI U FLUFXLWHDVWIHO

7HRUHPD < &+(1 8Q JUDI I U FLUFXLWH FDUH DUH Ä Q ´ YkUIXUL FRQ LQHXQGUXPKDPLOWRQLDQGDF úLQXPDLGDF DYHP

QQ

Q

¦ S[ L

L

'HPRQVWUD LH )LH G ^[ [ [ Q `GUXPXOKDPLOWRQLDQvQ * DWXQFL

GDF L ! M GLQ [ M QXVHSRDWHDWLQJHYkUIXO [L GHRDUHFHvQFD]FRQWUDUvQ *

DUH[LVWDFLUFXLWH GLQ YkUIXO [L L

Q VH SRW DWLQJH YkUIXULOH [L [L [ Q GHFL

S [L Q L GLQYkUIXO [ Q QXVHSRDWHDWLQJHQLFLXQYkUI ÌQWRWDODYHP

Q

Q

QQ QQ DWXQFL vQ PDWULFHD ' VH

¦ S[ ¦ Q L L

L

5HFLSURF SUHVXSXQHP F J VHVF

L

Q

¦ S[

QQ HOHPHQWHGHÄ ´

L

L

7ULDQJXODUL]kQG VXSHULRU DFHDVW PDWULFH DFHVWH HOHPHQWH YRU RFXSD WRDWH ORFXULOHGLVSRQLELOHGHGHDVXSUDGLDJRQDOHLvQILQDOGUXPXOKDPLOWRQLDQvQVXúLHVWH GDWGHVXFFHVLXQHDYkUIXULORUFRUHVSXQ] WRDUHPDWULFLLWULDQJXODUL]DW VXSHULRU 2EVHUYD LHÌQWUXQJUDII U FLUFXLWHH[LVW FHOPXOWXQGUXPKDPLOWRQLDQ 'DF DU H[LVWD GRX GUXPXUL KDPLOWRQLHQH G + úL G + DWXQFL vQ FHOH GRX GUXPXULDUH[LVWDFHOSX LQGRX YkUIXUL [L [ M DúH]DWHvQRUGLQHLQYHUV FHHDFHDU IDFHV DSDU XQFLUFXLWvQWUH [L úL [ M $OJRULWPXOGHGHWHUPLQDUHDGUXPXOXLKDPLOWRQLDQ (WDSD 6H VFULH PDWULFHD ' G LM L M Q D GUXPXULORU 'DF H[LVW XQ LQGLFH Ä L ´

SHQWUX FDUH G LL DSOLFD (WDSD

DWXQFL JUDIXO DUH FLUFXLWH úL DOJRULWPXO <&KHQ QX VH SRDWH

QQ HOHPHQWHGHÄ ´JUDIXODGPLWH GUXPKDPLOWRQLDQúLVHWUHFHOD(WDSDLDUGDF QXP UXOGHHOHPHQWHÄ ´HVWHPDL QQ JUDIXOQXDUHGUXPKDPLOWRQLDQ PLFGHFkW ÌQFD]FRQWUDUGDF vQPDWULFHH[LVW

(WDSD 2UGLQHD YkUIXULORU vQ FDGUXO GUXPXOXL KDPLOWRQLDQ HVWH GDW GH RUGLQHD GHVFUHVF WRDUHDSXWHULORUGHDWLQJHUH ([HPSOX 6 GHWHUPLQ PGUXPXOKDPLOWRQLDQSHQWUXPDWULFHDGUXPXULORUGLQH[HPSOXO SUHFHGHQW 0DWULFHD QX FRQ LQH QLFL R YDORDUH SH GLDJRQDO GHFL JUDIXO OD FDUH PDWULFHDHVWHDVRFLDW QXFRQ LQHFLUFXLWH $YHP S [ LDUSHQWUX Q

S [ S [ S [ úLDVWIHO ¦ S [L

UH]XOW

QQ

L

'HFLVHSRDWHDSOLFDWHRUHPDOXL&KHQvQ * H[LVW XQGUXPKDPLOWRQLDQLDU DFHVWDHVWH G + ^[ [ [ [ ` 'HWHUPLQDUHDGUXPXOXLKDPLOWRQLDQvQJUDIFXFLUFXLWH $OJRULWPXOGHGHWHUPLQDUHDPDWULFLLGUXPXULORUDUHXQFDUDFWHUSUHDVLQWHWLF vQ VHQVXO F SUH]HQ D XQHL YDORUL GH Ä ´ vQ PDWULFHD GUXPXULORU QX G LQIRUPD LL DVXSUDYkUIXULORUGLQFDUHVHFRPSXQGUXPXULOHFRUHVSXQ] WRDUHELQHvQ HOHVF QLFL DVXSUDQXP UXOXLGHGUXPXULvQWUHYkUIXULOHFDUHFRUHVSXQGDFHORUYDORULGHÄ ´ &DXQH[HPSOXGHDOJRULWPFDSDELOV U VSXQG DFHVWRUGH]LGHUDWHSUH]HQW P DOJRULWPXOIXQGDPHQWDOGDWRUDWOXL$.DXIPDQQ QXPLWDOÄvQPXO LULLODWLQH´ ,QWURGXFHP FD SXQFW GH SOHFDUH R PDWULFH 0 FDUH vQ ORFXO YDORULORU GH Ä ´ XWLOL]DWH vQ PDWULFHD RELúQXLW D DUFHORU XWLOL]HD] vQVXúL DUFXO UHVSHFWLY UHSUH]HQWDWSULQYkUIXULOHFDUHvOFRPSXQ 0 PLM L M Q XQGH

[L [ M GDF H[LVW DUFGHOD [L OD [ M ® vQUHVW ¯ a 3ULQ VXSULPDUHD SULPHL OLWHUH vQ PDWULFHD 0 VH RE LQH R PDWULFH 0 a QXPLW ÄDGHVWLQD LLORUSRVLELOH´6HFRPSXQPDWULFHOH 0 úL 0 SULQRSHUD LD GHÄvQPXO LUHODWLQ ´ 0 / 0 PLM

I U

ÌQPXO LUHDODWLQ DPDWULFLORUVHIDFHIRUPDOFDúLvQPXO LUHDDGRX PDWULFL vQVXPDUHúLI U vQPXO LUHHIHFWLY LQkQGFRQWF SURGXVXOODWLQDGRX FRPSRQHQWHSDUWLFLSDQWHODFDOFXOHVWHQXOGDF FHOSX LQ XQDGLQHOHHVWHQXO SURGXVXOODWLQDGRX FRPSRQHQWHSDUWLFLSDQWHHVWHQXOGDF DXYkUIFRPXQ UH]XOWDWXOFRPSXQHULLFRQVW vQVFULHUHDvQFRQWLQXDUHDYkUIXULORUFRPSRQHQWH DOHVLPEROXULORUSDUWLFLSDQWH

3ULQ

GHILQL LD

SURGXVXOXL

ODWLQ

0

DYHP

0 / 0

0 / 0 « $OJRULWPXO FRQWLQX SkQ OD RE LQHUHD PDWULFLL 0 Q GHRDUHFHvQWUXQJUDIFX Q YkUIXULXQGUXPKDPLOWRQLDQDUH Q DUFH ÌQ PDWULFHD 0 Q FLWLP FRQIRUP PRGXOXL GH VFULHUH GH PDL VXV WRDWH 0

GUXPXULOHKDPLOWRQLHQHDOHJUDIXOXL 'DF WRDWHHOHPHQWHOHOXL 0 Q VXQW]HURXUL 0 Q JUDIXOQXDGPLWH GUXPKDPLOWRQLDQ 2EVHUYD LH3URFHGHXOHVWHDSOLFDELOSHQWUXRULFHWLSGHJUDIRULHQWDWFXVDX I U FLUFXLW GDU SHQWUX JUDIXULOH I U FLUFXLWH VH UHFRPDQG DOJRULWPXO OXL &KHQ vQWUXFkW SHQWUX JUDIXUL GH GLPHQVLXQL PDUL DOJRULWPXO vQPXO LULL ODWLQH HVWH JUHRL GDUVLJXU ([HPSOX 6 VH GHWHUPLQH GUXPXULOH KDPLOWRQLHQH SHQWUX JUDIXO GLQ ILJXUD 5H]ROYDUH &XP úWLP F JUDIXO DUH FLUFXLWH YRP IRORVL PHWRGD vQPXO LULL ODWLQH 0DWULFHOH 0 úL 0 YRUIL

0

§ ¨ ¨ ¨ ¨ ¨ [ [ ¨ ©

a 0

0

§ ¨ ¨ ¨ [ [ [ ¨ ¨ [ [ [ ¨ ¨ ¨ ©

[ [

[ [ [ [

[ [ [ [

§ ¨ ¨ ¨ ¨ ¨ [ ¨ © [ [ [

[

[ [

[ [

[ [ · ¸ ¸ ¸ ¸ [ [ ¸ ¸¹

[ · ¸ ¸ ¸ ¸ [ ¸ ¸¹

[ [ [ ½ ® ¾ [ [ [ ¯ [ [ [ ¿ [ [ [ [ [ [ [ [ [

· ¸ ¸ [ [ [ ¸ ¸ [ [ [ ¸ [ [ [ ¸ ¸ ¸¹

0

§ ¨ ¨ ¨ ¨ [ [ [ [ ¨ ¨ ¨ ¨ ¨ ¨[ [ [ [ ©

0

[ [ [ [ ½ ® ¾ ¯ [ [ [ [ ¿

[ [ [ [

[ [ [ [

[ [ [ [ ½ ® ¾ ¯ [ [ [ [ ¿

§ ¨ ¨ ¨ ¨ ¨ ¨ [ [ [ [ [ ©

· [ [ [ [ ¸ ¸ [ [ [ [ ½ ¸ ® ¾¸ ¯ [ [ [ [ ¿ ¸ [ [ [ [ ¸ ¸ ¸ ¸ ¸ ¹

[ [ [ [ [

[ [ [ [ [ · ¸ [ [ [ [ [ [ [ [ [ [ ¸ ¸ ¸ ¸ ¸ ¹

ÌQJUDIXOGDWH[LVW GUXPXULKDPLOWRQLHQH ÌQ FD]XO vQ FDUH H[LVW PDL PXOWH GUXPXUL KDPLOWRQLHQH SUH]LQW LQWHUHV úL QR LXQHDGHÄFHOPDLEXQ´GUXPKDPLOWRQLDQFHHDFHFRQGXFHODLGHHDGHGUXPXUL RSWLPHvQWUXQJUDI 'UXPXULGHYDORDUHvQWUXQJUDIDOJRULWPXO%HOOPDQ.DODED )LH * ; * XQ JUDI YRP LQWURGXFH R IXQF LH Y * o \ FH DVRFLD] ILHF UXLDUFGLQ * RYDORDUHUHDO 1RW P YLM Y [L [ M úL *Y ; * Y JUDIXO YDOXDW ÌQ FD]XULOH UHDOH

YDOXDUHDSRDWHUHSUH]HQWDGLVWDQ DGLQWUHGRX SXQFWHORFDOLW L WLPSLVDXFRVWXUL vQWURUH HDGHWUDQVSRUWHWF 3HQWUX XQ GUXP G [L [L [L vQ JUDIXO * YRP QXPL ÄYDORDUH D

N

GUXPXOXL´VXPDYDORULORUDUFHORUFRPSRQHQWHDGLF

YG

N

¦Y K

LK LK

9UHP V GHWHUPLQ P GUXPXO Ä G ´ GH OD XQ YkUI RDUHFDUH [L OD YkUIXO [ Q

SHQWUXFDUHYDORDUHDOXL YG V ILHPLQLP 3HQWUX DFHDVWD LQWURGXFHP ÄPDWULFHD H[WLQV D YDORULORU DUFHORU´ 9 YLM L M Q GDW GH

YLM

° ®YLM ° ¯f

SHQWUX L

M

SHQWUX [L [ M *

SHQWUX L z M [L [ M *

úL QRW P FX PLN YDORDUHD PLQLP D GUXPXOXL G GH OD [L OD [ Q vQ JUDIXO GDW FRQVLGHUDWvQPXO LPHDGUXPXULORUGHFHOPXOW N DUFHFX PL YDORDUHDPLQLP D GUXPXOXLGHOD [L OD [ Q FRQVLGHUDW vQPXO LPHDWXWXURUGUXPXULORULQGLIHUHQWGH QXP UXOGHDUFHFRPSRQHQWH $OJRULWPXO GH FRQVWUXLUH D YHFWRULORU PL L P VH ED]HD] SH XUP WRDUHOH SURSR]L LL 3URSR]L LD3HQWUXRULFH N ` DYHP

PLN

^

`

PLQ YLM P MN M Q

'HPRQVWUD LH (VWH HYLGHQW F XQ GUXP GH FHO PXOW N DUFH FX GHVWLQD LD [ Q VH SRDWH RE LQHGLQWUXQGUXPGHFHOPXOW N DUFHFXGHVWLQD LD [ Q SULQDG XJDUHDXQXLDUF ODvQFHSXWXOV X'HFL

^

`

PLQ ®YLM PLQ YG N ½¾ PLQ YLM P MN GN M Q ¯ ¿ M Q 3URSR]L LD'DF H[LVW N ` SHQWUXFDUH PLN PLN SHQWUXRULFH PLN

L Q DWXQFL D PLN

PL V L Q V t N

E PLN PL L Q 'HPRQVWUD LH D GHPRQVWU PSULQLQGXF LHGXS V 3HQWUX V N SURSULHWDWHDHVWHDGHY UDW FRQIRUPHQXQ XOXL 3UHVXSXQkQGSURSULHWDWHDDGHY UDW SHQWUXRYDORDUH V d K DYHP

PL K

PLQ YLM PL K M Q

PLQ YLM PL N M Q

PL N

E UH]XOW vQ PRG HYLGHQW SHQWUX F SULQ DG XJDUHD GH DUFH QRL QX RE LQHP GUXPXULGHYDORDUHPDLPLF $OJRULWPXOGHGHWHUPLQDUHDGUXPXOXLPLQLPHVWH (WDSD 6H FRQVLGHU JUDIXO YDOXDW *Y ; * Y ; ^[ [ [ Q ` VH FRQVWUXLHúWHPDWULFHDHVWLQV DYDORULORUDUFHORU 9

Y

LM L M Q

(WDSD 6HDGDXJ PDWULFLL 9 OLQLLOHVXSOLPHQWDUH PL PL «DVWIHO

D OLQLD PL FRLQFLGHFXWUDQVSXVDFRORDQHL Q DPDWULFLL 9 Y MQ

E SUHVXSXQkQG FRPSOHWDW OLQLD PLN

L Q

W M Q

VH FRPSOHWHD] OLQLD PLN

L Q

FRQIRUPSURSR]L LHL F VHFRQWLQX DSOLFDUHDID]HLE SkQ ODRE LQHUHDDGRX OLQLL PLN úL PLN LGHQWLFH (WDSD 6HGHWHUPLQ UHJUHVLYGUXPXOPLQLPGHOD [L OD [ Q DVWIHO

VHDGXQ OLQLDÄ L ´GLQ 9 FXOLQLD PLN XUP ULQGXVHUH]XOWDWXOPLQLPFHVH N

SRDWH RE LQH 6 SUHVXSXQHP F PL

YLM PLN DWXQFL SULPXO DUF GLQ

GUXPXOPLQLPGHOD [L OD [ Q HVWHDUFXO [L [ M

VH DGDXJ OLQLD Ä M ´ GLQ 9 FX PLN UH LQkQG YDORDUH PLQLP DIODW GH

H[HPSOX SH FRORDQD Ä N ´ DWXQFL DO GRLOHD DUF YD IL [ M [ N úDPG8OWLPXO VXFFHVRUGHWHUPLQDWYDIL [ Q $OJRULWPXOGHGHWHUPLQDUHDGUXPXOXLPD[LPHVWH (WDSD 6HFRQVWUXLHúWHPDWULFHD 9 DYDORULORUDUFHORUDVWIHO

YLM

SHQWUX L M ° SHQWUX [L [ M * ®YLM ° ¯ f SHQWUX L z M [L [ M *

(WDSD 6LPLODUFXHWDSDGLQDOJRULWPXODQWHULRUGDUODSDVXOE OLQLD PLN N

VHFRPSOHWHD] SULQ PL

^

N

PD[ YLM P M M Q

`

L Q

(WDSD 'HWHUPLQDUHDGUXPXOXLPD[LPVHGHWHUPLQ ODIHOFDODHWDSDDQWHULRDU 9RP SUH]HQWD GRX H[HPSOH GH GHWHUPLQDUH D GUXPXOXL PLQLP UHVSHFWLY PD[LPFXDMXWRUXODOJRULWPXOXL%HOOPDQ.DODED ([HPSOX 9kUIXULOH [ [ [ UHSUH]LQW vQWUHSULQGHUL LDU SH DUFH HVWH PDUFDW GXUDWDH[HFXW ULLFRQWUROXOXLvQSXQFWXO [ M GXS HIHFWXDUHDOXLvQSXQFWXO

[L vQXQLWDWHDGHWLPSFRUHVSXQ] WRDUH6 VHGHWHUPLQHWLPSXOPLQLPGHFRQWURO GLQWUH [ úL [

)LJXUD

5H]ROYDUH (WDSD &RQVWUXLPPDWULFHD 9 DYDORULORUDUFHORU [ [ [ [

[

[

[

f

f f

f f

f

f

f

[ [ [

f

f

f

[ [

f

f

f

f

f

f

f

[

f

f

f

f

[

f

f

f

f

f

f

L

f

f

f

P P P P L

L

L

(WDSD D DG XJ P PL ODPDWULFHD 9 FDUHHVWHWUDQVSXV FRORDQHL Y M

E FRPSOHW PPDWULFHD 9 FXOLQLLOH PL PL PL úWLLQGF

PLN

^

`

PLQ YLM P MN M

M Q

$úDGDU SHQWUX OLQLD PL SULPXO HOHPHQW P VH GHWHUPLQ DGXQkQG

HOHPHQWHOH OLQLHL D PDWULFLL 9 FX FHOH DOH OLQLHL PL FHD PDL PLF ILLQG HOHPHQWXOF XWDW

P

^

PLQ Y M P MN M

`

P

PLQ^ f f f f f f` PLQ Y M P MN

P

PLQ^f f f f f f ` PLQ Y M P MN

P

PLQ^f f f f f f f` PLQ Y M P MN

P

PLQ^f f f f f f f f ` PLQ Y M P MN

P

PLQ^f f f f f f ` PLQ Y M P MN

P

PLQ^f f f f f f f ` PLQ Y M P MN

M

^

M

^

M

^

M

^

M

^

M

^

`

`

`

`

`

`

PLQ^f f f f f f f f f ` 3HQWUXOLQLD PL YRPDYHD PL PLQ^YLM P M `

M

P P P

PLQ^ f f f` PLQ^ f f f ` PLQ^ f f f f`

P

PLQ^ f f f f `

P PLQ^ f f f f f ` P PLQ^ f f f `

P

PLQ^ f f f f f f `

3HQWUXOLQLD PL YRPDYHD PL

P P

^

`

PLQ YLM P M M

PLQ^ f f f` PLQ^ f f f `

P

PLQ^ f f f f `

P

PLQ^ f f f `

P

PLQ^ f f f f f f `

P

P

PLQ^ f f f f f `

PLQ^ f f f f `

2EVHUY PF OLQLLOH PL úL PL FRLQFLGLWHUD LLOHVHRSUHVF

(OHPHQWHOHOXL PL UHSUH]LQW YDORDUHDPLQLP DILHF UHLGUXPFDUHDMXQJH

vQ [ (WDSD 6HDGXQ OLQLD GLQ 9 FX PL XUP ULQGXVHUH]XOWDWXOPLQLPFDUHHVWH SULPXODUFYDIL [ [

6H DGXQ OLQLD GLQ 9 FX PL UH]XOWDWXO ILLQG DO GRLOHD DUF YD IL

[ [

6H DGXQ OLQLD GLQ 9 FX PL UH]XOWDWXO PLQLP ILLQG DUFXO

FRUHVSXQ] WRUYDIL [ [

'HFLGUXPXOPLQLPGHOD [ OD [ YDIL G ^ [ [ [ [ ` FX YG

([HPSOX 6H FRQVLGHU JUDIXO GLQ ILJXUD 6 VH GHWHUPLQH YDORDUHD PD[LP DGUXPXOXLGHOD [ OD [

)LJXUD

5H]ROYDUH $SOLF P DOJRULWPXO %HOOPDQ.DODED &DOFXOHOH YRU IL VLVWHPDWL]DWHvQWDEHOXOXUP WRU

9 [ [ [

[

[

[

[

[

f

f

f

f

f

f

f

f

f

f

f

f

f

f

f

f f

[ [ [

[

PL

f

PL

PL

PL

PL

PL

P PD[^ f f f ` P PD[^ f f ` P PD[^ f f f `

P PD[^ f f f ` P PD[^ f f f f f `

P

PD[^ f f f f f f `

P PD[^ f f ` P PD[^ f ` P PD[^ f f `

P P

P

PD[^ f f f ` PD[^ f f f f `

PD[^ f f f f f `

P PD[^ f f ` P PD[^ f ` P PD[^ f f `

P

PD[^ f f f `

P

PD[^ f f f f `

P

PD[^ f f f f `

P P

PD[^ f f f ` PD[^ f f f f `

P PD[^ f f ` P PD[^ f ` P PD[^ f f `

P

PD[^ f f f f f `

P PD[^ f f ` P PD[^ f ` P PD[^ f f `

P P

P

PD[^ f f f ` PD[^ f f f f `

PD[^ f f f f f `

,WHUD LLOH VH RSUHVF DLFL F FL DP RE LQXW OLQLLOH

PL

PL /XQJLPHD PD[LP D

GUXPXOXLGHOD [ OD [ HVWH

(WDSD 'HWHUPLQ PVXFFHVLXQHDDUFHORUvQGUXPXOPD[LPDVWIHORE LQXW $GXQ P OLQLD PL FX OLQLD GLQ 9 YDORDUHD PD[LP RE LQXW HVWH FRUHVSXQ] WRUHLDUFXO [ [

$GXQ POLQLD PL FXOLQLD GLQ 9 YDORDUHDPD[LP RE LQXW HVWH DUFXO YDIL [ [

$GXQ POLQLD PL FXOLQD GLQ 9 YDORDUHDPD[LP RE LQXW YDIL DUFXO YDIL [ [

$GXQ P OLQLD PL FX OLQLD GLQ 9 YDORDUHD PD[LP DUFXO FRUHVSXQ] WRU [ [

$GXQ P OLQLD PL FX OLQLD GLQ 9 YDORDUHD PD[LP YD IL LDU DUFXO

[ [

'UXPXOFRUHVSXQ] WRUYDILGHFL G ^[ [ [ [ [ [ ` FX YG

'DF GRUHDPV GHWHUPLQ PGUXPXOPLQLPGHOD [ OD [ SURFHG PDQDORJ (WDSHOHúLVXQWVLVWHPDWL]DWHvQWDEHOXOGHPDLMRV

[

[

[

[

[

[

f

f

f

f

f

[ [

f

f

f

f

f

f

f

[

f

f

f

9 [ [ [

f

f

PL

f

PL

PL

,WHUD LLOHVHRSUHVFF FLDPRE LQXW PL PL (WDSD 'HWHUPLQ PVXFFHVLXQHDGUXPXOXLPLQLPGHOD[OD[ $GXQ POLQLD PL FXOLQLD YDORDUHDPLQLP HVWH DUFXOYDIL [ [ úL VHRE LQ SHFRORDQDOXL [ $GXQ POLQLD PL FXOLQLD YDORDUHDPLQLP HVWH DUFXOFRUHVSXQ] WRUYD IL [ [ úLVHRE LQHSHFRORDQDOXL [

'HFLGUXPXOPLQLPYDIL G ^[ [ [ ` )OX[PD[LPvQWURUH HDGHWUDQVSRUW

'HILQL LH 8Q JUDI RULHQWDW YDOXDW * ; * S I U FLUFXLWH VH QXPHúWH UH HDGHWUDQVSRUWGDF vQGHSOLQHúWHXUP WRDUHOHFRQGL LL 'DF ; ^[ [ [ Q `DWXQFL L Q DYHP [L [L * ([LVW XQYkUIXQLF [ ; vQFDUHQXLQWU QLFLXQDUFQXPLWVXUVDUH HOHL ([LVW XQXQLFYkUI [ Q GLQFDUHQXLHVHQLFLXQDUFQXPLWGHVWLQD LDUH HOHL * HVWHFRQH[úLH[LVW GUXPXULGHOD [ OD [ Q

6DGHILQLWRIXQF LH F * o \ DVWIHOvQFkW FX t SHQWUXRULFHDUF X * QXP UXO FX VHQXPHúWHFDSDFLWDWHDUH HOHL

'HILQL LH)LLQGGDW RVXEPXO LPH < ; VHQXPHúWHW LHWXU GHVXSRUW < PXO LPHDGHDUFH Z < [L [ M * [L < [ M < *

Z < [ [ * [ < [ < * &DQWLWDWHD F Z < ¦ S HVWHFDSDFLWDWHDW LHWXULL Z <

L

M

L

M

LM [L [ M Z <

'HILQL LH 2 IXQF LH M * o \ VH QXPHúWH IOX[ SH UH HDXD GH WUDQVSRUW

* ; * S GDF vQGHSOLQHúWHXUP WRDUHOHFRQGL LL &RQGL LDGHP UJLQLUHDIOX[XOXL [L [ M * DYHP d M [L [ M d S LM

&RQGL LDGHFRQVHUYDUH

Q

Q

[L ; DYHP

¦ M[N [ M N

[N [ M *

¦ M[ K

M

[K

§¨ [ [ ·¸* © M K¹

2EVHUYD LD &RQGL LD DILUP F SHQWUX RULFH YkUI [ FX [ z [ úL

[ z [ Q VXPDIOX[XULORUGHSHDUFHOHFDUHLQWU vQ [ HVWHHJDO FXVXPDIOX[XULORU SHDUFHOHFDUHLHVGLQ [ 2EVHUYD LD)XQF LD M QXHVWHXQLF 'HILQL LH8QDUF [L [ M * VHQXPHúWHDUFVDWXUDWGDF vQUDSRUWFX M

DUHORFUHOD LD M [L [ M

SLM

6H SXQH SUREOHPD GHWHUPLQ ULL IXQF LHL M DVWIHO vQFkW VXPD IOX[XULORU SH DUFHOHFHLQWU vQ [ Q V ILHPD[LP DúDQXPLWDSUREOHP DIOX[XOXLPD[LP $GLF GLQWUH WRDWH IOX[XULOH M * o \ SRVLELOH vQ UH HDXD *

Ö SHQWUXFDUH VHXUP UHúWHV VHGHWHUPLQHIOX[XO M Q

¦ MÖ [K [Q t

K [K [Q *

Q

¦ M[

K [K [Q *

K

; * S

[ Q

3URSR]L LD )LH * ; * S R UH HD GH WUDQVSRUW DYkQG VXUVD [ GHVWLQD LD [ Q úL M * o \ XQIOX[RDUHFDUHvQUH HDXD * DWXQFL Q

¦ M[ [

L [ [L *

L

Q

¦ M[ M

§¨ [ [ ·¸* © M Q¹

M

[Q

'HPRQVWUD LH 5HOD LD H[SULP IDSWXO F IOX[XO FDUH LHVH GLQ [

DMXQJHvQ [ Q $YHP Z [

Z [ Q úLVHGHGXFHF

ª º « » M [ [ M [ [ ¦ ¦ ¦ L M M Q »¼ [ M ; « [L [ M Z [ M [ M [Q Z [Q ¬ ¦ M[ M [Q ¦ M[ [L [ M [Q FR [Q [ [L Z [L FHHDFHGHPRQVWUHD] DILUPD LD 9DORDUHD

)

¦

[ M [Q Z [Q

M [ M [Q

¦

[ [L Z [L

M [ [L

VHQXPHúWHYDORDUHDWRWDO DIOX[XOXL M * o \

3URSR]L LD )LH * ; * S R UH HD GH WUDQVSRUW úL ILH < ; R VXEPXO LPHFXSURSULHW LOH SHQWUXVXUVD [ DOXL * DYHP [ <

SHQWUXGHVWLQD LD [ Q DOXL * DYHP [ Q < $WXQFLSHQWUXRULFHIOX[ M * o \ DYHP

¦

)

[L [ M Z <

M[L [ M

¦

[L [ M Z <

'HPRQVWUD LH$YHP

¦

[L [ M Z <

M [L [ M

¦

[L [ M Z <

M[L [ M d F Z <

M [L [ M

ª ¦ « ¦ M [L [N ¦ M [N [ M [N < « [L [ Z [ [N [ M Z [N N ¬ N ª ¦ « ¦ M [L [N ¦ M [N [ M [N < « [L [ Z [ [N [ M Z [N N ¬ N

º » » ¼ º » » ¼

ª ¦ « ¦ M [L [N ¦ M [N [ M [N ; ?< « [L [ Z [ [N [ M Z [N N ¬ N

¦

[ [ M Z [

M [ [ M

º » » ¼

)

FHHDFHGHPRQVWUHD] HJDOLWDWHDF FL

) d d

¦

M [L [ M

¦

M [L [ M d

¦

S [L [ M

[L [ M Z <

[L [ M Z <

[L [ M Z <

¦

[L [ M Z <

M [L [ M d

F Z <

ÌQ FRQWLQXDUH YRP FRQVLGHUD F WRDWH FDSDFLW LOH VXQW QXPHUH UD LRQDOH VDX vQWUXFkWQXP UXOWRWDOGHDUFHHVWHILQLWFKLDUQXPHUHQDWXUDOH 3H ED]H FRQVLGHUD LLORU SUHFHGHQWH VH GHGXFH XUP WRUXO DOJRULWP )25')8/.(5621 SHQWUX GHWHUPLQDUHD IOX[XOXL PD[LP vQWUR UH HD GH WUDQVSRUW 3DVXO, 6H FRQVWUXLHúWH XQ IOX[ LQL LDO M FDUH YHULILF FRQGL LLOH GH FRQVHUYDUHvQILHFDUHYkUIúLGHP UJLQLUHSHILHFDUHDUFGHH[HPSOX FKLDU IOX[XO DYkQG FRPSRQHQWH QXOH SH ILHFDUH DUF DO UH HOHL M [L [ M [L [ M * 3DVXO,,

)RORVLQG RSHUD LLOH GH PDUFDUH FH YRU IL SUH]HQWDWH PDL MRV VH FHUFHWHD] GDF IOX[XOLQL LDO M HVWHPD[LPRSHUD LXQLOHGHPDUFDUH FRQVWDXvQXUP WRDUHOH D VHPDUFKHD] VXUVDUH HOHL [ FXVHPQXOÄ ´

E YkUIXULOH [ M Z [ YRU IL PDUFDWH FX Ä [ ´ GDF DUFXO

[ [ HVWHQHVDWXUDW

M

F GDF YkUIXO [ M HVWHGHMDPDUFDWúLGDF SHQWUXXQYkUI [ N Z [ M

DUFXO [ M [ N HVWHQHVDWXUDWDWXQFLPDUF PYkUIXO [ N SULQÄ [ M ´ G GDF YkUIXO [ M HVWH GHMD PDUFDW úL GDF SHQWUX XQ YkUI

[ N Z [ M DUFXO [ N [ M DUH IOX[XO QHQXO PDUF P YkUIXO [ N

SULQÄ [ M ´ ÌQXUPDWHUPLQ ULLRSHUD LHLGHPDUFDUHSXWHPvQWkOQLXUP WRDUHOHVLWXD LL 'DF GHVWLQD LD [ Q D UH HOHL QX VD PDUFDW DWXQFL IOX[XO HVWH PD[LP úL DOJRULWPXOVHWHUPLQ 'DF GHVWLQD LD [ Q VD SXWXW PDUFD DWXQFL IOX[XO QX HVWH PD[LP úL SRDWH IL P VXUDWDVWIHO D VHDOHJHXQGUXPGHOD [ OD [ Q E SHDUFHOHGUXPXOXLPDUFDWFXÄ ´IOX[XOVHPDMRUHD] FXRFDQWLWDWH T GH IOX[GHH[HPSOX T

F SH DUFHOH GUXPXOXL PDUFDW FX Ä³ IOX[XO VH PLFúRUHD] FX DFHHDúL FDQWLWDWH T G IOX[XODUFHORUQHPDUFDWHQXVHVFKLPE H VHUHYLQHOD3DVXO,, $OJRULWPXODUHXQQXP UILQLWGHSDúLLDUIOX[XOPD[LPVHDWLQJHFkQGQXPDL SRDWHILPDUFDW GHVWLQD LD [ Q DUH HOHL 2EVHUYD LH 0 ULPHD IOX[XOXL VH SRDWH IDFH FX PDL PXOW GHFkW R XQLWDWH HYLWkQGXVHDVWIHOSUHDPXOWHRSHUD LLGHPDUFDUHDVWIHOVHFRQVLGHU XQGUXP 9 IRUPDW GLQ GUXPXUL PDUFDWH FX Ä´ VDX Ä³ FH XQHúWH [ FX [ Q XúRU GH J VLW XUP ULQG YkUIXULOH PDUFDWH vQ VHQVXO GH OD [ Q F WUH [ 1RW P 9 PXO LPHD

DUFHORU [ \ XQGH \ HVWHPDUFDWFXÄ´úL 9 PXO LPHDDUFHORU [ \ XQGH \ HVWHPDUFDWFXÄ³&DOFXO P T PLQ ^FX MX ` X9

T

PLQ MX X9

PLQ^T T `2EVHUY PF T ! úLHVWHQXP UvQWUHJ 0 ULPFX T SHILHFDUHDUF X 9 úLPLFúRU PFX T SHILHFDUHDUF X 9 RE LQkQGODLHúLUHXQIOX[P ULWFX T

úL T

6HUHSHW HWDSDDGRXDFXIOX[XORE LQXW9DORDUHDIOX[XOXLPD[LPVHJ VHúWH UHDOL]kQGRW LHWXU SULQVHSDUDUHDFXROLQLHDYkUIXULORUPDUFDWHGHFHOHQHPDUFDWH úL FDSDFLWDWHD DFHVWHL W LHWXUL UHSUH]LQW IOX[XO PD[LP VDX DGXQkQG IOX[XULOH DUFHORULQFLGHQWHLQWHULRUOXL [ Q ([HPSOX)LHUH HDXD

)LJXUD

9kUIXO [ HVWH VXUVD UH HOHL YkUIXO [ HVWH GHVWLQD LD úL VH YHULILF XUP WRDUHOH Z [ Z [ ^ [ [ [ [ [ [ `

Z [

^[ [ [ [ ` Z [

3HQWUX UH HDXD GLQ ILJXU YUHP V GHWHUPLQ P IOX[XO PD[LP &RQVLGHU P IOX[XOLQL LDO M [L [ M [L [ M *

3DVXO 2EVHUY PSULQSURFHGHXOGHPDUFDMDPSXWXWPDUFDGHVWLQD LD [ DUH HOHL $WXQFLIOX[XOQXHVWHPD[LPúLSRDWHILP ULW $OHJHPXQGUXPGHOD [ OD [

G [ [ [

)OX[XOVHPDMRUHD] FXFDQWLWDWHD

T

PLQ ^FX MX ` PLQ^ ` X9

DUFXO [ [ VHYDVDWXUD

)OX[XOYDDYHDYDORDUHD M

M

)LJXUD

$P SXWXW PDUFD GHVWLQD LD [ D UH HOHL IOX[XO QX HVWH PD[LP úL SRDWH IL

P ULW )LH GUXPXO G ^[ [ [ ` P ULP IOX[XO FX T VHYDVDWXUD 1RXOIOX[YDDYHDYDORDUHD M M

DUFXO [ [ [ [

)LJXUD

3ULQUHSHWDUHDSURFHGHXOXLGHPDUFDMDPSXWXWPDUFDGLQQRXGHVWLQD LDGHFL IOX[XOQXHVWHPD[LP)LHGUXPXO G ^[ [ [ [ `

T

PLQ ^FX MX ` PLQ^ ` X9

&XFDQWLWDWHD T

YRPP ULIOX[XOúL M

M

)LGXUD

'HVWLQD LD

D

IRVW

T PLQ^ ` M M

G ^[ [ [ [ ` )OX[XOYDILP ULWFXFDQWLWDWHD T úLRE LQHP PDUFDW

DOHJHP

GUXPXO

([HPSOX 3HQWUX D WUDQVSRUWD vQ ORFDOLW L SURGXVHOH VDOH R ILUP SRDWH RSWD SHQWUX YDULDQWHOH GLQ UH HDXD GH PDL MRV úWLLQG F QXPHUHOH GLQ DIDUD SDUDQWH]HORU UHSUH]LQW FDSDFLW LOHDUFHORULDUQXPHUHOHGLQLQWHULRUYDORULOHXQXLIOX[LQL LDOFH QXVDWXUHD] QLFLXQDUFVHGRUHúWHJ VLUHDIOX[XOXLPD[LPGHWUDQVSRUW

)LJXUD

5H]ROYDUH YHULILF P GDF IOX[ LQL LDO FRQVWLWXLH XQ IOX[ UHDOL]DELO DGLF M * o \ vQGHSOLQHúWH FRQGL LD GH P UJLQLUH D IOX[XOXL GHFL RULFH [L [ M *

DYHP d M [L [ M d SLM L M ^` 2E LQHP

M [ [ M [ [ M [ [ M [ [ M [ [

S M [ [ S M [ [ S M [ [ S M [ [ S M [ [ 3HQWUXFRQGL LDGHFRQVHUYDUH [L ;

DYHP

¦

N [N [ M *

M[ N [ M

¦ M[

K [ M [K *

M

S S S S S

[K

9kUIXUL )OX[FDUHLQWU vQYkUIXO [L )OX[FDUHLHVHvQYkUIXO [L

[ [

[ [

6HREVHUY F úL3URSR]L LDHVWHYHULILFDW DGLF

¦ M[ [L L

¦ M[ M

M

[

GHFLIOX[XOLQL LDOHVWH M 7UHFHPOD3DVXO,,GLQDOJRULWPXO)RUG)XONHUVRQ 'HVWLQD LD [ D SXWXW IL PDUFDW $OHJHP GUXPXO G ^[ [ [ [ ` SHQWUX FDUH T PLQ^ ` VDWXUDW

úL M

)LJXUD

$UFXO [ [ VD

'HVWLQD LD [ D SXWXW IL PDUFDW $OHJHP GUXPXO G ^[ [ [ `

T

PLQ^ ` M

$UFHOH [ [ [ [ VD

VDWXUDW

)LJXUD

'HVWLQD LD [ D SXWXW IL PDUFDW $OHJHP GUXPXO G ^[ [ [ `

T

PLQ^ ` M

$UFXO [ [ VDVDWXUDW

)LJXUD

'HVWLQD LD [ D SXWXW IL PDUFDW $OHJHP GUXPXO G ^[ [ [ [ `

T

PLQ^ ` M

$UFXO [ [ VDVDWXUDW

)LJXUD

M

2EVHUY P F GHVWLQD LD QX VD PDL SXWXW PDUFD 'HFL IOX[XO HVWH PD[LP

(/(0(17('(0$7(0$7,&,),1$1&,$5( 'REkQGDVLPSO

1R LXQHDGHED] DPDWHPDWLFLORUILQDQFLDUHHVWHGREkQGD 'REkQGD HVWH VXPD GH EDQL FDUH VH SO WHúWH GH F WUH GHELWRU FUHGLWRUXOXL SHQWUXXQvPSUXPXWE QHVF 'REkQGD XQLWDU HVWH VXPD GDW GH R XQLWDWH PRQHWDU SH WLPS GH XQ DQ úL HVWH QRWDW L 'REkQGD GDW GH GH XQLW L PRQHWDUH SH WLPS GH XQ DQ VH QXPHúWHSURFHQWQRWDW S 'HFL S { L 3HQWUX 6 XQLW LPRQHWDUHXP SHWLPSGHXQDQVHRE LQH GREkQGD '

6L

6S

3HQWUX 6 XPSHWLPSGH W DQLGREkQGDQXPLW GREkQGDVLPSO HVWH

'

6LW

6SW

6HREVHUY F GREkQGDHVWHGLUHFWSURSRU LRQDO FXVXPDGHSXV FXSURFHQWXO VDXGREkQGDXQLWDU úLFXGXUDWD 'DF DQXOHVWHvPS U LWvQ N S U LHJDOHúL W N HVWHXQQXP UGHDVWIHOGHS U L

6SW N 6LW N N N 'H H[HPSOX GDF N DWXQFL GREkQGD SHQWUX W VHPHVWUH HVWH 6SW 6SW GDF N DWXQFLGREkQGDSHQWUX W WULPHVWUHHVWH ' úL GDF ' 6SW N DWXQFL '

SHQWUXFDUHVHFDOFXOHD] GREkQGDDWXQFL GHYLQH '

]LOH

2EVHUYD LHÌQILQDQ HDQXOFRPHUFLDODUH ]LOHúLILHFDUHOXQ DUH GH

'DF 6 HVWHVXPDGHSXV LQL LDOSHSHULRDGD W FXGREkQG XQLWDU L DWXQFL VXPDILQDO VDXYDORDUHDILQDO HVWH 6 W 6 ' 6 6 LW 6 LW

6FDGHQ FRPXQ VDXVFDGHQ PHGLH )LH VXPHOH 6 6 6 Q SODVDWH FX DFHODúL SURFHQW S SH GXUDWHOH

W W W Q 6XPD GREkQ]LORU DGXVH GH FHOH Q VXPH SH FHOH Q GXUDWH R YRP vQORFXLFXGREkQGDDGXV GHRVXP 6 SHRSHULRDG W $WXQFL 6 SW 6 SW 6 SW 6SW Q Q 'DF VHFXQRDúWH 6 DWXQFLGXUDWD W YDIL 6W 6 W 6 Q W Q W 6 VHYDQXPLVFDGHQ FRPXQ 'DF 6 6 6 6 Q DWXQFLGXUDWD W YDIL

W

6W 6 W 6 Q W Q 6 6 6 Q

VHYDQXPLVFDGHQ PHGLH $SOLFD LH6 VHGHWHUPLQHVFDGHQ DXQHLVXPHGH XPFDUHSURGXFH RGREkQG HJDO FXVXPDGREkQ]LORUSURGXVHGH XPSHWLPSGH ]LOH XPSHWLPSGH ]LOH XPSHWLPSGH ]LOHúL OHLSH WLPSGH ]LOH 2EVHUY PF z DWXQFLVFDGHQ DFRPXQ HVWH

]LOH 3URFHQWXO PHGLX GH GHSXQHUH S SHQWUX FDUH VXPHOH 6 6 6 Q VXQW W

SODVDWH SH SHULRDGHOH W W W Q FX SURFHQWH S S S Q DVWIHO vQFkW V DYHP DFHHDúLGREkQG WRWDO YDILRE LQXWGLQHJDOLWDWHD

GHXQGH

6 SW 6 SW 6 S W Q Q Q

S

6 SW 6 SW 6 SW Q Q

6 SW 6 S W 6 Q S Q W Q 6W 6 W 6 Q W Q

'REkQGDFRPSXV 2 VXP GH EDQL HVWH SODVDW FX GREkQG FRPSXV GDF OD VIkUúLWXO SULPHL SHULRDGH GREkQGD VLPSO D DFHVWHL SHULRDGH HVWH DG XJDW OD VXP SHQWUX D SURGXFH OD UkQGXO HL GREkQG vQ SHULRDGD XUP WRDUH )LH 6 VXP LQL LDO S

S GREkQGD XQLWDU W GXUDWD GH SODVDPHQW D VXPHL 6 QXP U vQWUHJúL 6 W VXPDILQDO GXS W SHULRDGHDWXQFL SURFHQWXO L

$QLL 6XPDSODVDW OD 'REkQGDSURGXV vQ 6XPDRE LQXW OD vQFHSXWXODQXOXL WLPSXODQXOXL VIkUúLWXODQXOXL 6 6 L 6 6 6 L 6 L

6

# W 6W W

6 L

6 L L

6 L

# W 6 L 6 W L

6

# W 6 L L 6 W

6 6 L #

6 W 6 W L

6 L

6 L W

'DF L X YDILXQIDFWRUGHIUXFWLILFDUHJ VLWvQWDEHOHILQDQFLDUHSHQWUX SHQWUXGLIHULWHSURFHQWHDWXQFLVXPDILQDO YDIL

6 L 6 X W 'REkQGDFRPSXV YDILSHQWUX W vQWUHJ ' 6 W 6 6 X W 6 6 X W W

6W

6XPDLQL LDO GHSXV YDIL

6 XQGH

L

6W

6W YW

L

W

Y HVWHIDFWRUGHDFWXDOL]DUH

)RUPXODGHDFWXDOL]DUHHVWH

6 )RUPXODGHIUXFWLILFDUHHVWH

6W

6W

L

6 L

W

W

6 W Y W 6X W

HVWH IDFWRU GH DFWXDOL]DUH X L HVWH IDFWRU GH IUXFWLILFDUH L )DFWRULL X úL Y VHJ VHVFvQWDEHOHILQDQFLDUHSHQWUXGLIHULWHSURFHQWHúLGLIHULWHOH Y

SHULRDGHvQWUHJL

3URFHQWXO S

L VHSRDWHRE LQHGLQ L W 6 W 6

7LPSXOVHSRDWHRE LQHGLQ SULQLQWHUSRODUH $SOLFD LL &H VXP WUHEXLH V GHSXQHP D]L FD V vQFDV P SHVWH DQL VXPD GH OHLúWLLQGF GREkQGDXQLWDU HVWHGH " 'LQ

6

6W

L

W

OHL

&XFHSURFHQWVXPDGH OHLGHSXV WLPSGH DQLGHYLQH OHL" 'LQ

L W ÌQWDEHODYHP

6W 6

GHFLFXSURFHQW 'DF GXUDWDGHSODVDPHQWDVXPHL 6 W QXHVWHXQQXP UvQWUHJFLHVWHGH IRUPD W

Q

K DYHPGRX VROX LL N

D 6ROX LDUD LRQDO SRUQHúWHGHODIRUPD SHQWUXSDUWHDvQWUHDJ GH Q DQL 9DORDUHD ILQDO RE LQXW SHQWUX SODVDUHD VXPHL LQL LDO 6 YD IL

K Q 6 L $FHDVW VXP 6 Q vQWLPSXOIUDF LXQLL DDQXOXLFXGREkQG N K Q K 6 L L $WXQFL XQLWDU L YD DGXFH R GREkQG VLPSO 6 Q L N N Q Q K 6 K 6 L 6 L L GHFL Q N N

6Q

6W

6

K Q N

K· Q§ 6 L ¨ L ¸ N¹ ©

UHSUH]LQW VROX LDUD LRQDO GHFDOFXODVXPHLILQDOHFkQGVHSODVHD] R VXP 6 SHRGXUDW W

Q

K vQUHJLPGHGREkQG FRPSXV N

E 3HQWUXVROX LDFRPHUFLDO SHQWUXVXPD 6 SODVDW SHRSHULRDG W

Q

K N

6HREVHUY F OHXSODVDWFXSURFHQWDQXDO L GHYLQHODVIkUúLWXODQXOXL L úL OHX SODVDW FX SURFHQWXO GH VXESHULRDG LN GHYLQH OD VIkUúLWXO DQXOXL

LN N 3URFHQWHOH L úL LN GHYLQHFKLYDOHQWHGDF

YDORULOHILQDOHODVIkUúLWXO

LN N VDX L N LN 'H H[HPSOX

DQXOXL VXQW HJDOH DGLF L

L 'HFL SH GXUDWD W

SHQWUX VXESHULRDG WULPHVWULDO L

Q

VXPDLQL LDO SODVDW 6 vQUHJLPGHGREkQG FRPSXV YDGHYHQL

6 L LN Q

6W

K

K N

K

6 L L N Q

GHFL

6W

6

6 L

K Q N

Q

K N

6 L W

UHSUH]LQW VROX LDFRPHUFLDO GHFDOFXODVXPHLILQDOHFkQGVHSODVHD] R VXP 6 SHRGXUDW W

Q

K vQUHJLPGHGREkQG FRPSXV N

([HPSOX 6 VH FDOFXOH]H YDORDUHD ILQDO D VXPHL GH XQLW L PRQHWDUH SODVDWH WLPS GH DQL úL OXQL FX SURFHQW DQXDO 'HFL S L 6ROX LDUD LRQDO

6

· § ¨ ¸ ¹ © XP

6ROX LDFRPHUFLDO

6

XP

2EVHUYD LL &HOHGRX VROX LLQXVXQWLGHQWLFH 6ROX LD FRPHUFLDO HVWH PDL GHV XWLOL]DW GHRDUHFH IDFWRUXO IUXFWLILFDUH L X HVWHvQWDEHOHILQDQFLDUHDWkWSHQWUXSXWHULvQWUHJLFkWúLIUDF LRQDUH 9DORULOH ILQDOH DOH XQHL VXPH 6 GHSXVH vQ UHJLP GH GREkQG VLPSO VDX vQ UHJLPGHGREkQG FRPSXV GLIHU vQIXQF LHGHGXUDWD W 6 SODVDW SHRGXUDW GH W DQLvQUHJLPGHGREkQG VLPSO GHYLQH

6W

6 LW

IXQF LHOLQLDU vQUHJLPGHGREkQG FRPSXV GHYLQH W 6 W 6 L IXQF LHH[SRQHQ LDO FXED]DVXSUDXQLWDU 'DF W HVWH DQ DWXQFL 6 6 L vQ UHJLP GH GREkQG VLPSO FX úL 6

6 L vQUHJLPGHGREkQG FRPSXV

'DF W GHH[HPSOX W

DWXQFLFX 6

6 L 6HYHGH

6 L VDXSULQULGLFDUHODS WUDW 6

SULQ 6

§ · 6 ¨ L ¸ úL © ¹

§ L · 6 ¨¨ L ¸¸ GHXQGH 6 ! 6 ¹ © 'DF W ! DWXQFL 6 W 6 L LW úL

F ULGLFkQGODS WUDW 6

6W

6 L

W

W W § · 6 ¨ LW L ¸ ! 6 W © ¹

*UDILFFHOHGRX GREkQ]LHYROXHD] DVWIHO

)LJXUD

2SHUD LXQLGHVFRQW1RWD LLúLGHQXPLUL 2SHUD LXQHD GH VFRQW HVWH FDUDFWHULVWLF vQ JHQHUDO % QFLORU &RPHUFLDOH FDUHFXPS U vQDLQWHGHVFDGHQ DQXPLWHSROL HFXVFRSXOGHDRE LQHRGREkQG 2SROL VHFXPS U ODXQPRPHQWGDWFXSUH XOVDXVXPD6$FHDVWDHVWH HYDOXDW FX SURFHQWXO GH HPLVLXQH S L úL HVWH VFDGHQW GXS PRPHQWXO VDX GXUDWD T 9DORDUHDILQDO ODVFDGHQ DSROL HL.YDIL .

6 LT T d XQ DQ VDX .

T

6 L T t XQ DQ

XQGH .YDORDUHDQRPLQDO DSROL HL 6SUH GHFXPS UDUH LGREkQGDXQLWDU DQXDO 'DF ODXQPRPHQWGDW T T DGLF OD W T T SkQ ODVFDGHQ SROL D SRDWHILYkQGXW XQHLE QFLFRPHUFLDOHDWXQFLSROL DYDDYHDRYDORDUHILQDO VDX FXUV .

6 LT T d XQ DQ VDX .

T

6 L T t XQ DQ

XQGH.YDORDUHDOXL6ODPRPHQWXO T 9DORDUHDVFRQWDW DSROL HLYDORDUHDDFWXDO ODPRPHQWXOYkQ] ULLDFHVWHLD ODPRPHQWXO T T W VHQRWHD] FX.D 9RPQXPLVFRQWGLIHUHQ DGLQWUHYDORDUHDQRPLQDO .úLYDORDUHDVFRQWDW .DQRWDW6 6 . .D 7HRUHWLF VFRQWXO WUHEXLH V UHSUH]LQWH GREkQGD SH SHULRDGD SkQ OD VFDGHQ FRUHVSXQ] WRDUH YDORULL VFRQWDWH VDX D VXPHL SH FDUH R SULPHúWH GH LQ WRUXOSROL HLHYDOXDW FXSURFHQWXOGHHPLVLXQHDOSROL HLVDXFXDOWSURFHQW 'LQ RE LQHP . .D 6 úL .D . 6 $VWIHOSXWHPIDFHXUP WRDUHOHREVHUYD LL VFRQWXOHVWHGHDFFHDúLQDWXU FDúLGREkQGD GHRVHELUHDGLQWUHVFRQWúLGREkQG HVWHF GREkQGDVHDGDXJ ODFDSLWDOLDU VFRQWXOVHVFDGHGLQFDSLWDO 6FRQWXOVLPSOXUD LRQDOQRWDW665YDILGREkQGDGDW GH.DSHSHULRDGDW FXGREkQGDXQLWDU M 665 . D MW $VWIHORE LQHPFXXúXULQ XUP WRDUHOHUHOD LL . úL . . D MW .D MW LDU T . W .MW VDX 665 665 MW T W

XQGH T M SURFHQWGHVFRQWSURFHQWXOGHVFRQWSRDWHILHJDOVDXGLIHULWGH SURFHQWXOGHHPLVLXQHDOSROL HLS L MGREkQGDXQLWDU GHVFRQW WGXUDWDVFRQW ULLP VXUDW vQDQL

ÌQSUDFWLF MWHVWHPLFúLVHQHJOLMHD] DVWIHO MW LDUUHOD LD GHYLQH 66 .MW 2ULFHVFRQWFHDSUR[LPHD] VFRQWXOUD LRQDOVHQXPHúWHVFRQWFRPHUFLDO 6FRQWXO VLPSOX FRPHUFLDO QRWDW 66& YD IL GREkQGD GDW GH YDORDUHD QRPLQDO .SHSHULRDGDWFXGREkQGDXQLWDU M 66& .MW úL . D . MW LDU .D . MW 2EVHUYD LL 665 66& DGLF XWLOL]DUHD VFRQWXOXL VLPSOX UD LRQDO FRQYLQH GH LQ WRUXOXL SROL HL LDU XWLOL]DUHD VFRQWXOXL VLPSOX FRPHUFLDO FRQYLQH E QFL 6FRQWXOVLPSOXFRPHUFLDOQXVHDSOLF SHSHULRDGHGHWLPSPDUL 'LQ úL RE LQHP 66& 665 MW VDX 665 66& MW 6FRQWXO FRPSXV HVWH FHO vQ FDUH FDOFXOHOHOH VH IDF vQ UHJLP GH GREkQG FRPSXV 'DF GREkQGD VH DSOLF DVXSUD YDORULL .D FX GREkQGD XQLWDU M SH SHULRDGD W vQ UHJLP GH GREkQG FRPSXV VH RE LQH VFRQWXO FRPSXV UD LRQDO 6&5 2ULFH VFRQW FH DSUR[LPHD] VFRQWXO FRPSXV UD LRQDO VH QXPHúWH VFRQW FRPSXVFRPHUFLDO6&& 'DF . XPúLW DQDWXQFLGLQ DYHP M 665 M 'HILQL LH1XPLPVFRQWXQLWDUVDXXQLWDWHGHVFRQW M G M VDX G Y ¶ XQGH Y IDFWRUGHDFWXDOL]DUHVDXIDFWRUGHVFRQW M

ÌQUHJLPGHGREkQG FRPSXV YRPDYHD W

. . D M úLDSOLFkQGGHILQL LDVFRQWXOXLFRPSXVUD LRQDORE LQHPVFRQWXOFRPSXVUD LRQDO W 6&5 . D ª« M º» ¬ ¼ VDX W 6&5 . ª« M º» . YW ¬ ¼ 'LQ J VLP . .D M W ùWLLQGF W W M W MW M úL YRPQHJOLMDWHUPHQLLGHJUDGPDLPDUHVDXHJDOFXGRLvQLSRWH]DF GREkQGD XQLWDU MHVWHvQJHQHUDOPLF SHSLD DILQDQFLDU YRPDYHDvQ .MW ª º 6&5 . « » ¬ MW ¼ MW úL FXP RULFH VFRQW FH DSUR[LPHD] VFRQWXO FRPSXV UD LRQDO VH QXPHúWH VFRQW FRPSXVFRPHUFLDO6&&DWXQFLGLQ J VLPF VFRQWXOFRPSXVFRPHUFLDO HVWH 6&& . D MW XQGH . .D MW úL . . D MW 2EVHUYD LL 6&& 665 66&

W

'DF WDQDWXQFL M MW 6&5 6&& W

'DF W DQDWXQFL M

MW 6&5

6&&

W

'DF W!DQDWXQFL M ! MW 6&5 ! 6&&

([HPSOX /D GDWD GH D IRVW FXPS UDW R SROL vQ YDORDUH GH XPDYkQGVFDGHQ DOXQLPDLWkU]LXFXSURFHQWXODQXDOGH'LQ GLYHUVH PRWLYH SRVHVRUXO SROL HL R SUH]LQW OD VFRQWDUH FX OXQL vQDLQWH GH VFDGHQ 6HFHUH

D YDORDUHDQRPLQDO DSROL HLODVFDGHQ E YDORDUHDILQDO DSROL HLODPRPHQWXOVFRQW ULL F YDORDUHD VFRQWDW D SROL HL DSOLFkQG DWkW VFRQWXO VLPSOX UD LRQDO FkW úL VFRQWXOVLPSOXFRPHUFLDOFXSURFHQWHOHT T 6ROX LH 6 XP S L T OXQL DQL T OXQL DQL W DQL D . 6R LT . E . 6 LT

XP

. XP F ÌQFD]XOVFRQWXOXLVLPSOXUD LRQDO . T M .D MW . D XP T M . D XP ÌQFD]XOVFRQWXOXLVLPSOXFRPHUFLDO . D . MW T M XP T M

. D

. D

XP

&RPHQWDULX 3HQWUX T DYHPUHOD LD..DFHHDFHHVWHLQDGPLVLELOF FLDUvQVHPQD F SRVHVRUXO SROL HL YD SULPL SULQ YkQ]DUHD DFHVWHLD R VXP PDL PDUH GHFkW YDORDUHDSROL HLODGDWDYkQ] ULL ([HPSOX /D GDWD GH VH DGXFH SHQWUX VFRQWDUH R SROL GH YDORDUH QRPLQDO . XP D F UHL VFDGHQ HVWH SH 6H DX vQ YHGHUH XUP WRDUHOHFRQGL LLDOHE QFLLFRPHUFLDOH x SURFHQWGHVFRQW x FRPLVLRQGHDFFHSWDUHDHPLVLXQLL x FRPLVLRQSHHIHFWXP x WD[ SHFRPLVLRQIL[ x VHDGDXJ GRX ]LOHGHF WUHEDQF 6HFHUHYDORDUHDVFRQWDW DSOLFkQGXQVFRQWVLPSOXFRPHUFLDO 6ROX LH W ]LOH WPRGLILFDW ]LOH S MM 66& .MW 66& XP XP &RPLVLRQGHDFFHSWDUH &RPLVLRQSHHIHFW XP 7D[ SHFRPLVLRQIL[ XP $*,27$; '(6&217727$/ 66&&RPLVLRQGHDFFHSWDUH &RPLVLRQGHDFFHSWDUHWD[ SHFRPLVLRQIL[ XP 3URFHQWXOGHVFRQWVLPSOXFRPHUFLDOPRGLILFDWHVWHGDWSULQ T $*,2 T 9DORDUHDVFRQWDW . D . $*,2 . D XP )LH T SURFHQW UHDO GH VFRQW T M LDU T SURFHQW HIHFWLY VDX GH UHYHQLUH GHVFRQWT M $YHPUHOD LLOH $*,27D[ SHFRPLVLRQIL[ .MW $*,27D[ SHFRPLVLRQIL[ .DMW

$WXQFL x SURFHQWXOUHDOGHVFRQW $*,27D[ SHFRPLVLRQIL[ XP .MW T x SURFHQWHIHFWLYVDXGHUHYHQLUH GHVFRQW $*,27D[ SHFRPLVLRQIL[ XP .DMW T ([HPSOX 2 SROL DUH YDORDUHD GH HPLVLH GH XP úL HVWH VFDGHQW SHVWH DQLFXSURFHQWXOGH'DF VFRQWDUHDVHIDFHFXSURFHQWXOT VDXT vQUHJLPGHVFRQWFRPSXVVHFHUH D YDORDUHDQRPLQDO E FkWYDSULPLEHQHILFLDUXOFXGRLDQLvQDLQWHGHVFDGHQ " 6ROX LH 6 XP S L T DQL M M T

6 L . XP

.

. 6 L . . XP 6FRQWFRPSXVUD LRQDO . D XP ° ° . D . ® M W ° . D XP ° ¯ 6FRQWFRPSXVFRPHUFLDO . D XP . °° .D ® MW ° . D XP °¯

T

3O LHúDORQDWHUHQWH 3ULQ SO L HúDORQDWH vQ HOHJHP VXPHOH GH EDQL SO WLWH OD LQWHUYDOH GH WLPS HJDOH,QWHUYDOXOGHWLPSFHVHSDU SODWDDGRX VXPHVHQXPHúWHSHULRDG úLSRDWH ILDQXOVHPHVWUXOWULPHVWUXOOXQD 'HFL SO LOH HúDORQDWH VH YRU QXPL DQXLW L GDF VH SO WHVF DQXDO VHPHVWULDOLW L GDF VH SO WHVF VHPHVWULDO WULPHVWULDOLW L GDF VH SO WHVF WULPHVWULDOúLPHQVXDOLW LGDF VHSO WHVFOXQDU ÌQIXQF LHGHVFRSXOXUP ULWSO LOHHúDORQDWHSRWIL GHSODVDPHQWVDXGHIUXFWLILFDUHGDF VHXUP UHúWHFRQVWLWXLUHDXQHLVXPH GH DPRUWL]DUH VDX GH UDPEXUVDUH GDF VFRSXO HVWH GH D UDPEXUVD UHWXUQD R GDWRULH ÌQIXQF LHPRPHQWXOFkQGVHIDFDFHVWHSO LDYHP SO LHúDORQDWHODvQFHSXWXOSHULRDGHLFDUHVHYRUQXPLSO LHúDORQDWHDQWLFLSDWH SO LHúDORQDWHODVIkUúLWXOSHULRDGHLúLFDUHVHYRUQXPLSO LHúDORQDWHSRVWLFLSDWH 3O LOHHúDORQDWHPDLSRWIL WHPSRUDUHGDF QXP UXOGHSO LHVWHILQLW SHUSHWXHGDF QXP UXOSO LORUHVWHQHOLPLWDW YLDJHUHGDF SODWDVHYDIDFHDWkWWLPSFkWSHUVRDQDHVWHvQYLD 3O LOH HúDORQDWH SRW IL FRQVWDQWH VDX YDULDELOH GXS FXP VXPHOH GHSXVH SHULRGLFVXQWFRQVWDQWHVDXQX 3O LOHHúDORQDWHSRWILLPHGLDWHVDXDPkQDWHGXS FXPSULPDSODW HVWHLPHGLDW VDXDPkQDW GXS XQQXP UGHDQLFRQYHQLWFRQWUDFWXDO $QXLW LFRQVWDQWHSRVWLFLSDWH 3ODWD HúDORQDW UHQWD OD VIkUúLWXO ILHF UXL DQ vQ VXP FRQVWDQW VH QXPHúWH DQXLWDWHSRVWLFLSDWHFRQVWDQWH)LH 7 YDORDUHDDQXLW LLFRQVWDQWH Q QXP UXOGH DQL L GREkQGDXQLWDU DQXDO 6 Q VXPDILQDO DXQXLúLUGHDQXLW LODPRPHQWXO Q PRPHQWXOSO LLXOWLPHLDQXLW L

6 Q VHFRPSXQHGLQVXPDYDORULORUILQDOHDILHF UXLDQXLW LODPRPHQWXO Q

6XPD 7 GHSXV ODVIkUúLWXOSULPXOXLDQGHYLQHGXS Q DQLVXPD 7 L

VXPD 7 GHSXV OD VIkUúLWXO FHOXL GH DO GRLOHD DQ GHYLQH 7 L GHSDUWH$WXQFL

Q

Q

úL DúD PDL

7 L

6Q

7 L 7

GHFL

7 L

Q Q

L

Q

L Q L

7

7 L 7

Q

L

L Q

7

L

XQ L

Q L 7

6Q

L

'DF 7 úL YDORDUHD DQXLW LL SRVWLFLSDWH HVWH GH OHX DWXQFL YDORDUHD ILQDO DúLUXOXLGHDQXLW LSRVWLFLSDWHHVWH

VQ

L L

FDOFXODW vQWDEHOHILQDQFLDUHúL

6Q

XQ L

Q

7V Q

([HPSOX &DUH HVWH YDORDUHD ILQDO D XQXL úLU GH DQXLW L SRVWLFLSDWH D XPODPRPHQWXOSO LLXOWLPHLDQXLW L3URFHQWXOHVWH

6Q

XQ 7 L

XP

&H VXP $N WUHEXLH GHSXV vQ PRPHQWXO GH ID SHQWUX FD GXS N DQL V GHYLQ 7 $YHP $N L

N

7 GH XQGH $N

7

L N

GHFL GDF SHVWH N DQL VH

7

SO WHúWHVXPD 7 DFHDVWDHFKLYDOHD] FXSODWDVXPHL $N

L N

vQPRPHQWXOGH

ID 'HDFHHDVXPD $N VHQXPHúWHYDORDUHDDFWXDO DSO LL 7 HIHFWXDW SHVWHXQ QXP U N GHDQL )LH $Q VXPDDFWXDO DúLUXOXLGHDQXLW LODPRPHQWXOVHPQ ULLFRQWUDFWXOXL DGLF FXRSHULRDG vQDLQWHDSULPHLSO L

$Q

7 7 7 Q L L L 7 L L L L Q L Q

GHFL

$Q

7

7 L L L Q

L 7 L

Q

L

Q

YQ L

'DF 7 úLYDORDUHDDQXLW LORUSRVWLFLSDWHHVWHGH OHXDWXQFLYDORDUHD DFWXDO DúLUXOXLGHDQXLW LSDUWLFLSDQWHHVWH

DQ

YQ L

7D Q

FDUHHVWHFDOFXODW vQWDEHOXOILQDQFLDUúL

$Q

ÌQWUHYDORDUHDDFWXDO $Q DúLUXOXLGHDQXLW LSRVWLFLSDQWHúLYDORDUHDILQDO

6 Q DúLUXOXLGHDQXLW LSDUWLFLSDQWHH[LVW UHOD LD $Q 6 Q L Q

$SOLFD LH &H VXP XQLF GHSXV LPHGLDW SRDWH V vQORFXLDVF SODWD D DQXLW LSRVWLFLSDWHD XPILHFDUHFXSURFHQWXO "

$

YQ 7 L

XP

9DORDUHD DFWXDO D XQXL úLU GH DQXLW L FRQVWDQWH SRVWLFLSDWH SHUSHWXH

L L

LPHGLDWH HVWH QRWDW D f HVWH D f

$f

7D f

f

LDU GDF UDWD HVWH 7 DYHP L

3HQWUXYDORDUHDDFWXDO DXQXLúLUGHDQXLW LFRQVWDQWHSRVWLFLSDWHWHPSRUDUH DPkQDWH SUHVXSXQHP F SULPD SODW VH IDFH GXS U DQL SRVWLFLSDW DGLF OD PRPHQWXO U WLPSGH Q U DQL$YHP ª º 7 7 7 7 « » U U Q U Q U U $Q L L L L ¬« L L ¼»

7

L

U

L

Q U

L

7

L

U

L

Q U

L

GHFL U $Q

VDX

U$Q

7Y U

Y QU L

7Y U D Q U

9DORDUHD ILQDO D XQXL úLU GH DQXLW L FRQVWDQWH SRVWLFLSDWH WHPSRUDUH DPkQDWHDGLF SULPDSODW VHIDFHGXS U DQLSRVWLFLSDWDGLF ODPRPHQWXO U LDUXOWLPDSODW ODPRPHQWXO Q WLPSGH Q U DQLHVWH

U

6Q

7 L

Q N

7 L

QN

GHFL U

7 L 7

6Q

L 7

QU

L

7VQ U

ÌQWUH YDORDUHD DFWXDO U $Q D úLUXOXL GH DQXLW L FRQVWDQWH SRVWLFLSDWH WHPSRUDUHDPkQDWHGXS U DQLúLYDORDUHDILQDO FRUHVSXQ] WRDUHH[LVW UHOD LD

7Y U

U $Q

Y QU L

7Y Q

X QU L

U

6Q Y Q

$QXLW LFRQVWDQWHDQWLFLSDWH $QXLW LOH DQWLFLSDWH VH IDF OD vQFHSXWXO DQXOXL DGLF OD PRPHQWHOH Q 6XPD ILQDO HVWH HYDOXDW OD XQ DQ GXS XOWLPD SODW R YRP QRWD

6 QD

6

7 L 7 L 7 L

D Q

7 L 3HQWUX 7

$WXQFL

L

Q

Q

Q 7 L ª L L º ¬ ¼

XQ 7X L L YDORDUHDILQDO DXQXLúLUGHDQXLW LDQWLFLSDWHGH XPHVWH L Q L V QD L

6 QD

7V QD

9DORDUHD DFWXDO D XQXL úLU GH DQXLW L FRQVWDQWH DQWLFLSDWH LPHGLDWH WHPSRUDUH HVWH VXPD QHFHVDU vQ PRPHQWXO LQL LDO SHQWUX D SXWHD SO WL OD ILHFDUH VFDGHQ VXPDIL[ 7

º 7 ª « » Q L « L L »¼ ¬

7 7 7 Q L L L

$QD

7 L 1RWkQG D QD

L

Q

L Q L L DYHP L $QD 7D QD

9DORDUHD DFWXDO D XQXL úLU GH DQXLW L FRQVWDQWH DQWLFLSDWH SHUSHWXH LPHGLDWHHVWH D f

L FX $f L

7D f

9DORDUHD DFWXDO D XQXL úLU GH DQXLW L DQWLFLSDWH FRQVWDQWH WHPSRUDUH DPkQDWHHVWH U

D Q

$

7

L

U

7

L

U

7

7

L

L

Q

U

L

Q U

L

7Y U DQD U

3O LHúDORQDWHIUDF LRQDWH 6H QXPHúWH SODW HúDORQDW IUDF LRQDW FRQVWDQW SODWD HúDORQDW vQ FDUH UDWDDQXDO 7 HVWHvPS U LW vQ N S U LHJDOHILHFDUHFX UN

7 FDUHVHSO WHVFILH N

ODVIkUúLWXOSHULRDGHLILHODvQFHSXWXOSHULRDGHL 'DF SODWDHúDORQDW HVWHOLPLWDW OD Q DQLDWXQFLSODWDIUDF LRQDW GH N UDWH SHDQYDILvQQXP UGH NQ 9DORDUHD ILQDO D XQXL úLU GH SO L HúDORQDWH WHPSRUDUH LPHGLDWH IUDF LRQDWH GH N RULSHDQLHVWH Q

6QN

M · 7 7§ 7 ¨ N ¸ N N© N ¹ N

MN · § ¨ N ¸ © ¹

MN · N § 7 ¨© N ¸¹ 7 MN N N

QN

N

'DUúWLPF L

M · § ¨ N ¸ úLGHFL N ¹ © 6

N Q

Q L 7

L

L MN

Q

MN · N § ¨ N ¸¹ © MN

VDX

6 QN

7V Q

L MN

$SOLFD LH 'H FH VXP GH EDQL YD GLVSXQH R SHUVRDQ FDUH GHSXQH WLPS GH

DQLFkWH XPODVIkUúLWXOILHF UHLOXQLFXSURFHQW " 7 XPODVIkUúLWXOXQXLDQúL 6 XP

9DORDUHD DFWXDO D SO LORU HúDORQDWH SRVWLFLSDWH WHPSRUDUH LPHGLDWH IUDF LRQDWHGH N RULSHDQHVWH

$QN

7

L M N L Q

7D Q

L MN

3O LOH HúDORQDWH SHUSHWXH SRVWLFLSDWH LPHGLDWH IUDF LRQDWH GH N DQL SH DQ VXQWGDWHGH

$fN

7

L Df MN

7

L MN L

7 MN

3O LOHHúDORQDWHWHPSRUDUHSDUWLFLSDWHDPkQDWHIUDF LRQDWHGH N RULSHDQVH FDOFXOHD] SULQ U

6

N Q

L 7

QU

L

L MN

7

L VQ U MN

ÌPSUXPXWXUL 6H QXPHúWH vPSUXPXW R RSHUD LH ILQDQFLDU SULQ FDUH XQ SDUWHQHU 3 LQGLYLGXDOVDXJUXSDW SODVHD] RVXP GHEDQLSHRSHULRDG GHWLPSvQDQXPLWH FRQGL LL XQXL DOW SDUWHQHU 3 LQGLYLGXDO VDX JUXSDW 3DUWHQHUXO 3 VH QXPHúWH FUHGLWRULDU 3 VHQXPHúWHGHELWRU 2SHUD LXQHD SULQ FDUH 3 UHVWLWXLH OXL 3 VXPD GH FDUH D EHQHILFLDW VH QXPHúWHUDPEXUVDUHVDXDPRUWL]DUHDvPSUXPXWXOXL 8Q vPSUXPXW FDUH QX VH PDL vQDSRLD] VH QXPHúWH vPSUXPXWXO QHUDPEXUVDELO 6XPHOH UDPEXUVDWH DQXDO FDUH DX UROXO GH D DPRUWL]D WUHSWDW VXPD vPSUXPXWDW VHQXPHVFDPRUWLVPHQWH

$PRUWL]DUHDXQXLvPSUXPXWSULQDQXLW L FRQVWDQWHSRVWLFLSDWH )LH 9 VXPD vPSUXPXWDW OD PRPHQWXO LQL LDO 7 7Q DQXLW LOH UDWH VXFFHVLYH 3ULPD DQXLWDWH ILLQG SO WLW OD VIkUúLWXO SULPXOXL DQ Q GXUDWD vQ DQL D UDPEXUV ULL 4 4Q DPRUWLVPHQWHOH VXFFHVLYH FRQ LQXWH vQ SULPD D GRXD úL D Q DDQXLWDWH L GREkQGDXQLWDU DvPSUXPXWXOXL &XDFHVWHGDWHVHSRDWHvQWRFPLWDEHOXO $QXLW L 6XPDU PDV GHSODW 0RPHQWH$PRUWL] UL 'REkQGD 9

# S

4 4 # 4S

# Q

# 4Q

G

9 L 7

4 G

9

9 4

G

9L 7

4 G

9

9 4 # 9 S 4 S

# GS

9 S L 7 S

# GQ

9 Q L 7Q

# 4S G S

9S

#

4Q G Q 9Q

# 9Q 4Q

2EVHUYD LL 7DEHOXOHVWHYDODELOSHQWUXRULFHOHJHDDQXLW LORUSHQWUXFDUHQXVDIRUPXODW vQF QLFLRLSRWH] 'LQFRQGL LDFDGXS QDQLV VHUDPEXUVH]HVXPDvPSUXPXWDW UHLHVH 9Q FHHDFHLPSOLF 9Q

7Q

4Q $WXQFLFDOFXO PXOWLPDDQXLWDWH 4Q G Q 4Q 9Q L 4Q 4Q L

GHXQGH

7Q

4Q L

'HFL XOWLPD DQXLWDWH HVWH HJDO FX XOWLPXO DPRUWLVPHQW OD FDUH VH DGDXJ GREkQGDFRUHVSXQ] WRDUH 5HOD LD vQWUH VXPD vPSUXPXWDW 9 úL DPRUWLVPHQWH VH RE LQH VXPkQG PHPEUXFXPHPEUXXOWLPDFRORDQ 9 9 9Q 9 9 9Q 4 4 4Q

9Q ùLGLQ 9Q

UH]XOW 9

9 4 4 4Q

4 4 4Q

6XPDvPSUXPXWDW HVWHHJDO FXVXPDDPRUWLVPHQWHORU

5HOD LDvQWUHDQXLW LúLDPRUWLVPHQWH 6HFDOFXOHD]

7S 7S

4 S 9 S L 4 S 9 S L

'HRDUHFHGLQWDEHO 9 S 9 S

4 S 4 S L 9 S 9 S 4 S 4S L4S

L4 S GHFL

4 S 4 S L

7 S 7 S

5HOD LH DGHFYDW SHQWUX RULFH OHJH D DQXLW LORU 6H GLVWLQJ XUP WRDUHOH VLWXD LL ÌPSUXPXWXULFXDQXLW LUDWH FRQVWDQWHSO WLELOH ODVIkUúLWXODQXOXLSRVWLFLSDW &XP 7

7

UH]XOW

4R

7Q

7 LPSOLF 7 S 7 S

4 S L VDX 4 S

úL IRORVLQG

4 L S

'DF DQXLW LOHVXQWFRQVWDQWHDPRUWLVPHQWHOHVXFFHVLYHIRUPHD] RSURJUHVLH JHRPHWULF FUHVF WRDUHFXUD LD L &XP Q 9 4 4 4Q 4 4 L 4 L LPSOLF Q L 4 L

9 GHFL

9

4

4

9

L Q L

VDX

L

L Q

3HQWUX FDOFXOXO DQXLW LL SOHF P GH OD 7Q

7 GHXQGH 4 Q L

4Q

7

L

4Q L DVWIHO F

«GHFL

9

7

4 4 4Q

L

Q

7

L

Q

$VWIHO

7 L

Q · 7 L 7 § ¨ ¸ L ¨ L Q L ¸ L © ¹ L

9 VDX

7

L 7 L 9

Q

L

L

Q

4 G

7

4 G

7 o G

7 o G

7 4 7 4

7Q 4Q G Q 7 o G Q 7 4Q &DOFXOkQG

Q

&DOFXOXOGREkQ]LLvQDFHDVW VLWXD LHGHYLQH

7

7 L L L L

G G

4 4

4 L 4

G G

4 4

4 L 4 L 4L L

4L

GLIHUHQ HOHVXFFHVLYHDOHGREkQ]LORUXUPHD] RSURJUHVLHJHRPHWULF FUHVF WRDUHFX SULPXOWHUPHQ 4L úLUD LD L 7DEHOXOGHDPRUWL]DUHDXQHLVXPHSULQDQXLW LFRQVWDQWHSRVWLFLSDWHYDIL 6XPD $PRU GDWRUDW 6XPDGDWRUDW OD WLV OD 'REkQGD $QXLWDWHD $QLL VIkUúLWXOSHULRDGHL PHQXO vQFHSXWXO SHULRDGHL 9 G 9 L 9 9 4 4 7 G 4

9 # # 9 Q Q Q 9Q

G G Q GQ

9L

4 7 G 4 9 9 4 # # # # 9Q L 4Q 7 G Q 4Q 9Q 9Q 4Q 9Q L

4Q

7

G Q 4Q

9Q

$SOLFD LH8QvPSUXPXWGH XUPHD] DILUDPEXUVDWvQ DQLSULQ UDWHDQXLW L FRQVWDQWHSRVWLFLSDWHFX &DUHHVWHWDEORXOGHDPRUWL]DUH" 6ROX LH G 9 L $QXLWDWHDFRQVWDQW 7 GLQ YDIL

7

9

L

L

Q

3ULPXODPRUWLVPHQWGLQ HVWH

4

9

VDX

L

L

4

Q

7 G

$PRUWLVPHQWH

4

4 L

4 L

4

4 L

4

6XPHOHU PDVHGHSODW ODVIkUúLWXODQXOXLVXQW

9

9 4

9

9 4

9 9 4 9

'REkQ]LOHYRUIL

G

9 L

G

9L

G

9 L

G

9 L

7DEHOXOGHDPRUWL]DUHHVWH

6XPDU PDV GHSODW ODVIkUúLWXODQXOXL

$QL $PRUWLVPHQWH 'REkQ]L $QXLW L

2EVHUY PF

4 4 4 4 a G G G G

L

L

¦ 4L ¦ G L

¦7

L

L

6XPDUDPEXUVDW GXS SODWDD S DDQXLW LHVWH 5 S

5S GHFL 5 S

4

4 4 4 S

4 4 L 4 L

L S 'LQ SXWHPVFRDWH4 úLUH]XOW

L

L

5S

9

5S

9

L Q

GHXQGH

S

S L

L

L S L Q

6XPDU PDV GHSODW GXS SODWDDSDQXLW LLHVWH

9S

9 5 S

9 9

GHXQGH

9S

L S L Q

9

Q S L L 9 L Q

L Q L S L Q

ÌPSUXPXWXULFXDQXLW LUDWH FRQVWDQWHFXGREkQG SO WLW OD vQFHSXWXODQXOXLDQWLFLSDW /DVHPQDUHDFRQWUDFWXOXLVHSO WHúWHGREkQGDSHQWUXSULPXODQúLGHFLVXPD UHDO SO WLW QXHVWH 9 FL 9 9 L 3HQWUXILHFDUHGLQDQLLXUP WRULGREkQGDVHFDOFXOHD] DVXSUDVXPHLU PDVH GHSO WLWúLVHSO WHúWHRGDW FXDPRUWLVPHQWXO 7DEHOXOSHQWUXvPSUXPXWXULFXDQXLW LSO WLWHODvQFHSXWXODQXOXLHVWH

$PRUWLV $QLL 'REkQ]L PHQWHOH G 9 L

6XPDU PDV GHSODW OD VIkUúLWXODQXOXL 9 9 L

$QXLW L

4

G

9L 7

4 L9

9

9 4

# S

4 # 4S

G

9 L 7

9

GS

# 9 SL 7S

4 L9 # 4 S L9 S

9 4 # 9 S 4 S

# Q

# 4Q

# G Q 9Q L 7Q

# 4Q L9Q

9S

# 9Q 4Q

9Q

'DF 9Q

DWXQFL 7Q 4Q &DOFXOkQGGLIHUHQ DDGRX DQXLW LVXFFHVLYH 4 S 9 S L 4 S 9 S L 7S 7S 4 S 9 S 4 S L 4 S 9 S L

GDF

DQXLW LOH

4 S L 4 S

VXQW

FRQVWDQWH

7

DGLF

4 S L 4 S

7

7Q

7

UH]XOW

úLDWXQFL

4 S

4S

4

L

L S

6XPDHIHFWLYvPSUXPXWDW HVWHHJDO HVWHFXVXPDDPRUWLVPHQWHORUDWXQFL

4 4 4 L L L Q U Q XQGH U HVWHUD LDVHULHL U VDX 4 U L Q L L 9 4 L L Q

9 GHFL 9

VDX

4 4 4Q

4

9

4

L L

Q

L L Q

$SOLFD LH8QvPSUXPXWGH XPHVWHUDPEXUVDELOFXFLQFLDQLSULQ DQXLW LFRQVWDQWHFXGREkQG SO WLELO ODvQFHSXWXODQXOXLFXSURFHQWGH &DUH HVWHWDEORXOGHDPRUWL]DUH"

6ROX LH 6HFDOFXOHD]

4 4 4 4 4

4 L 4 L 4 L 4 L

6XPHOHU PDVHGHSODW VXQW

9

9 4

9

9 4

9

9 4

9

9 4

9

9 4

'REkQ]LOHVXQW

4

9L

G

9 L

G

9 L

G

9 L

4 G

4 G

4 G

4 G

7DEORXOGHDPRUWL]DUHHVWH $QLL $PRUWLVPHQW 'REkQ]L $QXLW L

G

6HSRDWHYHULILFDF DQXLWDWHDHVWHFRQVWDQW

7

6XPDU PDV GHSODW ODVIkUúLWXODQXOXL

ÌPSUXPXWXULUDPEXUVDELOHRVLQJXU GDW D 2SHUVRDQ FDUHDI FXWvPSUXPXWXO 9 SO WHúWHDQXDOGREkQ]LOHDVXSUDVXPHL vPSUXPXWDWH 9 XUPkQGFDVXPDvPSUXPXWDW V ILHSO WLW GXS Q DQLRGDW FXGREkQGDXOWLPXOXLDQ'REkQ]LOHVXQWFDOFXODWHFXGREkQG XQLWDU L 7 9 L G

7

# Q

9 L # 9 L 9

7Q

G G Q 9

$FHVWPRGGHUDPEXUVDUHDXQXLvPSUXPXWHVWHXWLOL]DWGDF VXPD 9 QXHVWH IRDUWHPDUH E 'DF SHUVRDQD VDX vQWUHSULQGHUHD FDUH DSULPLWvPSUXPXWXOFDXW V úLFUHH]H VXPD 9 SULQGHSXQHULSHULRGLFHODREDQF SHED]DGREkQ]LORUXQLWDUH L OD VIkUúLWXOFHORU Q DQLDWXQFLSUHVXSXQHPF DQXLW LOH 7 c VXQWFRQVWDQWHSULPD ILLQGGHSXV ODVIkUúLWXOSULPXOXLDQ$QXLWDWHD 7 c VHYDRE LQHGLQ 7 7 c 9 L

7

# Q

7Q

7 c 9 L # 7 c 9 L

$FHVWPRGGHUDPEXUVDUHHVWHFXQRVFXWVXEGHQXPLUHDGHVLVWHPDPHULFDQ 'HFLSHUVRDQDVDXvQWUHSULQGHUHDFDUHDI FXWvPSUXPXWXOSO WHúWHDWkWVXPD vPSUXPXWDW FkWúLGREkQ]LOHGXS Q DQL6XPDFHXUPHD] V ILHUDPEXUVDW GXS

Q DQLHVWH 4Q

9 L Q

3HQWUXSUHJ WLUHDDFHVWHLVXPHSHUVRDQDYDSODVDODVIkUúLWXOILHF UXLDQODR EDQF RDQXLWDWHFRQVWDQWDFRQIRUPIRUPXOHL

7 c 9

Lc

Lc

9 Lc

Q

Lc

4Q

Lc

Lc $SOLFD LH 2 SHUVRDQ vPSUXPXW VXPD GH SH FDUH XUPHD] V R UDPEXUVH]HSHVWH DQLvPSUHXQ FXGREkQGDFDOFXODW FXSURFHQWGH 3HQWUX Q

Lc

Q

Q

DFRQVWLWXLDFHDVW VXP SHUVRDQDGHSXQHODVIkUúLWXOILHF UXLDQRVXP GHEDQLFX SURFHQWGH &DUHHVWHVXPDSHFDUHRGHSXQH" 6ROX LH

7c

9 Lc

Q

Lc

Lc

Q

/DVIkUúLWXOD DQLDGHSXVVXPDGH

ÌPSUXPXWXULFXDPRUWLVPHQWHHJDOH 'DF 4

4

4Q

4 GLQHJDOLWDWHD9 4 4Q UH]XOW 9 4 Q $QXLW LOHFDUHYHULILF 7 S 7 S 4 S 4 S L FRQGXFOD 9 9 9 L L Q Q Q

7 S 7 S úLGHFL

7 S

7

9 L Q

7S 4

7DEORXOGHDPRUWL]DUHDXQXLvPSUXPXWFXDPRUWLVPHQWHHJDOHHVWH 6XPDU PDV GH $QLL $PRUWLVPHQWHOH 'REkQ]L $QXLW L SODW ODVIkUúLWXO DQXOXL 4 G 9 L 9 9 4 7 4 G 4 G 9L 7 4 G 9 9 4

# S

# 4

# Q

# 4

GS

# 9 S L 7 S

# 4 G S 9S

GQ

# 9Q L 7Q

# 4 GQ

# 9 S 4 9Q

#

$SOLFD LH2SHUVRDQ DvPSUXPXWDWVXPDGH SHFDUHXUPHD] V R UDPEXUVH]HvQ DQLFXSURFHQWXOGH SULQDQXLW LSDUWLFLSDWHFXDPRUWLVPHQWH HJDOH&DUHHVWHWDEORXOGHDPRUWL]DUH" 6ROX LH 9 úL Q GHXQGH

9 Q

4 úLRE LQHP

9

9 4

9

9 4

9

9 4

9

G

9 L

G

9L

G

9 L

G 7

9 L 4 G

7

4 G

7

4 G

7

4 G

7DEORXOGHDPRUWL]DUHYDIL

$QLL $PRUWL]DUH 'REkQGD $QXLWDWHD

'HFL 4

6XPDU PDV GHSODW ODVIkUúLWXODQXOXL

9

(/(0(17('(0$7(0$7,&,$&78$5,$/(

7RWDOLWDWHDRSHUD LLORUILQDQFLDUHúLDQRUPHORUSHED]DF URUDVHIDFFDOFXOH GH DVLJXU UL FX DMXWRUXO WHRULHL SUREDELOLW LORU úL DOH VWDWLVWLFLL PDWHPDWLFH VXQW VHPQLILFDWH SULQ WHUPHQXO GH DFWXDULDW 'HFL WRDWH SUREOHPHOH SXVH GH SUDFWLFD RSHUD LLORUGHDVLJXU ULGHSHUVRDQHVHVWXGLD] SULQÄPDWHPDWLFLDFWXDULDOH´ 5ROXO DVLJXU ULORU vPSRWULYD SHULFROHORU FDUH DPHQLQ YLD D VDX FDSDFLWDWHD GHPXQF DRDPHQLORUHVWHELQHFXQRVFXWÌQXUPDFDODPLW LORUXQHOHSLHUGHULSRW ILDFRSHULWHFRPSHQVDWH GLQWUXQIRQGQXPLWIRQGGHDVLJXUDUH )RQGXO GH DVLJXUDUH VH FUHHD] SULQ Y UV PLQWHOH SHUVRDQHORU IL]LFH VDX MXULGLFHILLQGFRQFHQWUDWvQRUJDQL]D LLVSHFLDOHGHDVLJXU UL $VLJXU ULOHLQGLIHUHQWGDF VXQWREOLJDWRULLVDXIDFXOWDWLYHVHvPSDUWvQ DVLJXU ULGHSHUVRDQH DVLJXU ULGHEXQXUL $VLJXU ULOH VXQW REOLJDWRULL GDF VH IDF SH ED]D XQRU OHJL úL VXQW IDFXOWDWLYH GDF DSDUSHED]DXQRUvQ HOHJHULvQWUHS U L &RQWUDFWXOVDXOHJHDGHDVLJXUDUHSUHYHGHFRQGL LLGHDVLJXUDUHVDXREOLJD LL SUHFLVHSHQWUXFHOHGRX S U L 'HFL DVLJXUDUHD SRDWH IL GHILQLW FD R PHWRG GH FUHDUH D IRQGXOXL GH DVLJXUDUHSULQSULPDGHDVLJXUDUHvQYHGHUHDFRPSHQV ULLSLHUGHULORUSURYRFDWHGH FDODPLW LúLDFFLGHQWH ÌQRSHUD LLOHGHDVLJXUDUHVHGHRVHEHVFROHJ WXU MXULGLF XQDHFRQRPLF úL XQDWHKQLF /HJ WXUDMXULGLF SULYHúWHIRUPHvQFDUHLDXQDúWHUHDVLJXU ULOHDYkQGODED] OHJLOHúLFRQWUDFWHOHGHDVLJXUDUHH[LVWHQWH /HJ WXUD HFRQRPLF D DFHVWRU RSHUD LL SULYHúWH DFRSHULUHD QHYRLORU HFRQRPLFHFDUHVHIDFHSULQSULPHGHDVLJXUDUH 7HKQLFD DVLJXU ULORU XUP UHúWH FD RSHUD LD GH DVLJXUDUH V ILH R RSHUD LH HFKLWDELO DGLF V H[LVWHXQHFKLOLEUXILQDQFLDUvQWUHREOLJD LLOHFHORUGRX S U L $VLJXU ULGHSHUVRDQH 6FRSXO DVLJXU ULORU GH SHUVRDQH HVWH V RIHUH RDPHQLORU JDUDQ LL PDWHULDOH FDUH V L SXQ OD DG SRVW GH FRQVHFLQ HOH DQXPLWRU HYHQLPHQWH FD VF GHUHD FDSDFLW LLGHPXQF SLHUGHUHDSDU LDO VDXWRWDO DFDSDFLW LLGHPXQF GHFHVXO (YHQLPHQWHFHVHGDWRUHD] DFFLGHQWHORUVDXDOWRUFDX]HúLvPEUDF GLIHULWHIRUPH GHDVLJXUDUHSRWULYLWRELHFWLYXOXLDVLJXU ULLúLFRQGL LLORUGHDVLJXUDUH $VLJXUDWXOSO WHúWHWD[HOHGHDVLJXUDUHDWkWWLPSFkWHVWHvQYLD VDXSkQ OD H[SLUDUHD WHUPHQXOXL GH DVLJXUDUH $VLJXUDWRUXO SO WHúWH VXPD DVLJXUDW OD LYLUHD DFFLGHQWXOXL 7D[HOH SO WLWH GH DVLJXUDW LQVWLWX LHL GH DVLJXUDUH SHQWUX VXPHOH DVLJXUDWH VH QXPHVFSULPHGHDVLJXUDUH3ULPHOHGHDVLJXUDUHVXQWXQLFHGDF VXQWSO WLWHRGDW SHQWUX WRW WLPSXO DVLJXU ULL VDX SHULRGLFH GDF VH SO WHVF DQXDO WULPHVWULDO OXQDU HWF

3ULPHOH GH FDOFXOHD] FX DMXWRUXO XQHL HFXD LL VWDELOLW HFKLWDELO SHQWUX FHOH GRX S U L 3ULPD GH DVLJXUDUH VH GHWHUPLQ LQkQG VHDPD DWkW GH SRVLELOLW LOH GH SODW DORUGHF WUHDVLJXUDWFkWúLGHIDSWXOF IRQGXULOHFRQVWLWXLWHGHDVLJXUDWRU ILLQGWHPSRUDUGLVSRQLELOHHOHVHDIO vQFLUFXLWXOHFRQRPLFúLvLDGXFXQYHQLWSH FDUH DVLJXUDWRUXO vO IRORVHúWH vQ IDYRDUHD DVLJXUD LORU PLFúRUkQG FRUHVSXQ] WRU SULPDGHSODW 3HQWUXFDRSHUD LDV ILHHFKLWDELO vQPRPHQWXOvQFHSHULLDVLJXU ULLYDORDUHD PHGLH D VXPHORU SO WLWH GH DVLJXUDWRU WUHEXLH V ILH HJDO FX YDORDUHD PHGLH D VXPHORUSO WLWHGHDVLJXUDW 7HRUHPD FRPSXQHULL FRQWUDFWHORU 'DF $ HVWH R DVLJXUDUH GH YLD FRPSXV GLQ DVLJXU ULOH SDU LDOH $ $ $Q LDU 3 3 3Q VXQW SULPHOH FRUHVSXQ] WRDUH DVLJXU ULORU SDU LDOH DWXQFL YDORDUHD SULPHL WRWDOH SHQWUX DVLJXUDUHDGHYLD $ HVWH 3 3 3 3Q 'HPRQVWUD LH )LH ; YDORDUHD DFWXDO D VXPHORU SH FDUH LQVWLWX LD GH DVLJXUDUH OH YD vQFDVD SHQWUX DVLJXUDUHD $ úL ; , YDORDUHD DFWXDO D VXPHORU SDU LDOH FH XUPHD] V ILH vQFDVDWH SHQWUX DVLJXU ULOH SDU LDOH $L L Q 6XPHOHVHYRUSO WLGDF DVLJXUDWXOHVWHvQYLD 3ULPHOH GH DVLJXUDUH VXQW YDORULOH PHGLL DOH YDULDELOHORU DOHDWRDUH ; UHVSHFWLY ; L úL 3 0 ; 3L 0 ; L &XP ;

; ; ; Q DWXQFLPHGLDHVWH

0 ; 0 ; 0 ; 0 ; Q 3 3 3Q

VDX 3 $VLJXU ULOH GH SHUVRDQH VH vPSDUW vQ DVLJXU UL GH YLD úL DVLJXU UL GH DFFLGHQW $VLJXU ULOH GH YLD VXQW GHWHUPLQDWH GLQ REVHUYD LL VWDWLVWLFH DVXSUD XQRU IDFWRULFHLQIOXHQ HD] YLD D 3ULQWUH IDFWRULL FHL PDL LPSRUWDQ L vQ FDOFXOXO DVLJXU ULORU GH YLD HVWH PRUWDOLWDWHD LQGLYL]LORU FDUH HVWH VWXGLDW vQ IXQF LH GH YkUVW SURIHVLH VH[ UHJLXQHJUDGGHFLYLOL]D LHHWF$FHVWVWXGLXDOPRUWDOLW LLDF S WDWXQIXQGDPHQW úWLLQ LILFRGDW FXGH]YROWDUHDWHRULHLSUREDELOLW LL ,QWHQVLWDWHD PRUWDOLW LL XQXL JUXS GH LQGLYL]L GH DFHHDúL YkUVW F FL YkUVWD HVWHIDFWRUXOFXRLQIOXHQ SUHGRPLQDQW vQIXQF LHGHVH[úLHYHQWXDOSHFDWHJRULL GHSURIHVLLVHVWXGLDW FXDMXWRUXOXQRUFRHILFLHQ LQXPHULFLFDUHSRDUW QXPHOHGH IXQF LL ELRPHWULFH $FHVWHD VXQW SUREDELOLWDWHD GH YLD úL GH PRDUWH IXQF LD GH VXSUDYLH XLUHúLYLD DPHGLH

3UREDELOLWDWHDGHYLD úLGHPRDUWH

)LH R SRSXOD LH GLQ LQGLYL]L GH DFHHDúL YkUVW [ DQL QRWDW 0 [ )LH $

HYHQLPHQWXOFDRSHUVRDQ GLQ 0 [ V ILHvQYLD DODvPSOLQLUHDYkUVWHLGH [ DQL $WXQFL SUREDELOLWDWHD GH YLD HVWH SUREDELOLWDWHD HYHQLPHQWXOXL $ GHFL S[ 3 $ S [ [ 'DF $ HVWH HYHQLPHQWXO RSXV HYHQLPHQWXOXL $ DGLF HYHQLPHQWXO FD R SHUVRDQ GH YkUVWD [ DQL GLQ 0 [ V QX PDL ILH vQ YLD OD vPSOLQLUHD YkUVWHL GH

3 $ T[ [

[ DQLDWXQFLSUREDELOLWDWHDGHGHFHVYDIL T[

ÌQ JHQHUDO S [ \ HVWH SUREDELOLWDWHD FD R SHUVRDQ GH YkUVWD [ V ILH vQ

YLD ODvPSOLQLUHDYkUVWHL \ $WXQFL S [ \ T [ \ 'DF ] HVWH R YkUVW FXSULQV vQWUH [ DQL úL

S [ \

DVWIHOF

\ DQL DWXQFL

S [ ] S ] \ VDX S [ \ S [ [ S [ [ S \ \

'DF \

S [ \

S[ S [ S \

[ Q YRPQRWD S [ [ Q Q S[ úL T [ [ Q Q T[ 'HVLJXU

S[

S[ S[ S[ Q

)XQF LDGHVXSUDYLH XLUHYDILYDORDUHDPHGLHDQXP UXOXLGHSHUVRDQHFDUH DMXQJV vPSOLQHDVF YkUVWDGH [ DQLQRWDW V[ 1XP UXOGHSHUVRDQHFDUHDMXQJ V vPSOLQHDVF YkUVWDGH [ DQLHVWHRYDULDELO DOHDWRDUHGLVFUHW GHIRUPD Q

§ ; ¨¨ © S

" S "

QD · ¸ SQD ¸¹

XQGH QD HVWHQXP UXOGHSHUVRDQHGHYkUVWD D DQL'HVLJXU SL t L QD

¦S L

Q úL

L

'HRDUHFHWR LLQGLYL]LLGHYkUVWDGH D DQLDXDFHHDúLSUREDELOLWDWHGHDILvQ YLD ODvPSOLQLUHDYkUVWHLGH [ DQLDWXQFLYDULDELODDOHDWRDUH ; XUPHD] ROHJH ELQRPLQDO FX L Q L SL &QL D > S D [ @ >TD [ @ D SHQWUXFDUH 0 ;

QS GHFL 0 ; QD SD [ V[

3UREDELOLWDWHD GH YLD VH SRDWH GHWHUPLQD vQ IXQF LH GH IXQF LD GH VXSUDYLH XLUHDVWIHO

V[ QD DWXQFL SD \

S D [ D[ SD \ V \ SD [ QD

'DF

S [ \

\ Q D GHFL V[

V\

S [ \ ÌQSDUWLFXODUGDF \

V[

SD [ S [ \

V[

T [ [ P

F

UH]XOW

V[ V[ P V[

6LPLODU

S[

DVWIHO

[ P DWXQFL V S [ [ P [ P V[ V[ V \

úLGLQ T [ \ S [ \

S [ [

T [ T [ [ XQGH V[ V[ DQL

V [ V[ V [ V [ [[

G [ UHSUH]LQW QXP UXOSHUVRDQHORUFDUHGHFHGDWvQWUH [ úL [

&XP S [ ! S[ UH]XOW

V [ VDX V[ V V[

ÌQFRQFOX]LHIXQF LDGHVXSUDYLH XLUHHVWHGHVFUHVF WRDUHvQUDSRUWFXYkUVWD 'DF [ FUHúWHQHFRQWHQLWDWXQFL V[ WLQGHOD]HUR 9LD D PHGLH HVWH YDORDUHD PHGLH D QXP UXOXL GH DQL SH FDUH DUH V L PDL WU LDVF R SHUVRDQ vQ YkUVWD GH [ QRWDW 9[ 1XP UXO GH DQL SH FDUH vL PDL WU LHúWH R SHUVRDQ vQ YkUVW GH [ DQL HVWH R YDULDELO DOHDWRDUH GLVFUHW ; 'HRDUHFH GHFHVHOH VXQW GLVWULEXLWH XQLIRUP vQ WLPSXO DQXOXL YRP OXD PLMORFXO DQXOXLDWXQFL

§ " ; ¨ ¨ © T[ T[ "

· "¸ ¸ "¹ Q Q T [ Q

T[ HVWHSUREDELOLWDWHDFDRSHUVRDQ vQYkUVW GH [ DQLV GHFHGH]HODRYkUVW FXSULQV vQWUH [ Q úL [ Q DQL$VWIHO Q 0 ; T[ T[ 9[ Q Q T [ Q Q

GHFL

9[

[

¦ Q

Q V[ Q V[ Q V[

XQGH VD FRQVLGHUDW YLD D OLPLWDW QLPHQL QX HVWH QHPXULWRU 9kUVWD OLPLW VD FRQVLGHUDW GHDQL 'H]YROWkQGVHULD RE LQHP

V[ Q V[ V[ § · VV V[ ·V § ¨ ¸ ¨ Q ¸ [ Q V[ V[ V[ ¹ © ¹ © V[ V[ V[ V[ Q V[ Q V[ V[ Q V[ V[

9[

[

V[ V[ 1HJOLMkQG

¦ Q

V[ Q

V[

[

¦V Q

[Q

V[

VHRE LQHYLD DPHGLH [

9[

¦V Q

V[

[Q

7RDWH DFHVWH IXQF LL FDUH DP Y ]XW F VHUYHVF OD P VXUDUHD GXUDWHL YLH LL úL QXPLWH GLQ DFHVW PRWLY IXQF LL ELRPHWULFH QH YRU DMXWD OD vQWRFPLUHD GH WDEHOH GH PRUWDOLWDWHvQIXQF LHGHYkUVWDúLGXS VH[FRQGL LLVRFLDOHPDWHULDOHHWFWDEHOH FDUHYRUILYHULILFDWHFRQWLQXXSHQWUXDRE LQHSULPHGHDVLJXUDUHFkWPDLFRUHFW 7DEHOHOHGHPRUWDOLWDWHFXSULQGXUP WRDUHOHFRORDQHFRORDQDYkUVWHLFRORDQD YDORULORU IXQF LHL GH VXSUDYLH XLUH V[ DGLF QXP UXO LQGLYL]LORU GLQ JUXSXO LQL LDO FDUH VXSUDYLH XLHVF SkQ OD YkUVWD GH [ DQL FRORDQD GLIHUHQ HORU G [

V [ V [ DGLF QXP UXO LQGLYL]LORU FDUH DX GHFHGDW vQWUH [ úL [ DQL GLQWUH FHL V[ FDUH G[ HWF HUDXvQYLD ODYkUVWDGH [ DQLFRORDQD T [ V[

$VLJXUDUHDXQHLVXPHvQFD]GHVXSUDYLH XLUHOD vPSOLQLUHDWHUPHQXOXLGHDVLJXUDUH

'DF R SHUVRDQ GH [ DQL FRQWUDFWHD] R DVLJXUDUH vQ YDORDUH GH XP XUPkQGFDDFHDVW VXP V LVHSO WHDVF GDF HVWHvQYLD SHVWH Q DQLDVLJXUDWXO YDWUHEXLV SO WHDVF RVXP SHQWUXDFHDVW DVLJXUDUHFDUHHVWHYDORDUHDPHGLHD YDULDELOHL

§ DQ ; ¨¨ © Q S[

GHFL

· ¸ ¸ Q T[ ¹

0 ; D Q Q S[

3

DQ

V[ Q V[

$FHDVW YDORDUH PHGLH QRWDWH Q ( [ QXPLW VXP XQLWDU DPkQDW VDX IDFWRUGHDFWXDOL]DUHYLDJHUVHPDLSRDWHVFULH Q

V[ Q D [ D V[ D [ Q

([

D [ Q V[ Q D [ V[

1XP UXO D [ V [ '[ HVWH QXP U GH FRPXWD LH SHQWUX WRDWH YkUVWHOH úL SURFHQWHOHX]XDOHH[LVWkQGvQWRFPLWHWDEHOHDFWXDULDOHúL Q

([

'[ Q '[

3ULPDXQLF SHQWUXRVXP vQYDORDUHGH 6 XQLW LPRQHWDUHYDIL

3

6 Q ([

6

'[ Q '[

'DF $[ Q HVWHVXPDSO WLW XQHLSHUVRDQHGHYkUVWD [ GDF HVWHvQYLD OD vPSOLQLUHDYkUVWHLGH [ Q DQLDWXQFLYDORDUHDDFWXDO DVXPHLODYkUVWDGH [ DQL HVWH $[Q Q ( [ $[ Q $SOLFD LH 2 SHUVRDQ GH GH DQL FRQWUDFWHD] R DVLJXUDUH vQ YDORDUH GH XQLW L PRQHWDUH SO WLELO vQ FD] GH VXSUDYLH XLUH OD vPSOLQLUHD YkUVWHL GH DQL &DUH HVWH SULPD XQLF SH FDUH WUHEXLH V R SO WHDVF SHQWUX DFHDVW DVLJXUDUHSURFHQWXOILLQG " 6ROX LH3ULPDHVWH

3

6

'[ Q '[

' '

$QXLW LYLDJHUHSRVWLFLSDWHLPHGLDWH

3ULPD XQLF SH FDUH WUHEXLH V R SO WHDVF XQ DVLJXUDW GH [ DQL SHQWUX D SULPLFkWHXPODVIkUúLWXOILHF UXLDQSHWRDW GXUDWDYLH LLRYRPQRWD D[ 'LQWHRUHPDFRPSXQHULLFRQWUDFWHORUDFHDVWDYDIL

D[

'[ '[ ' '[ '[ ' '[ '[ '[ '[ 9RPQRWDXQDOWQXP UGHFRPXWD LH 1 [ '[ '[ ' $WXQFL 1 [ D[ '[ 'DF VXPD DVLJXUDW DQXDO HVWH vQ YDORDUH GH 6 XQLW L PRQHWDUH DWXQFL

([ [ ([

SULPDXQLF YDIL

3

6 D[

6

1 [ '[

$SOLFD LH&DUHYDILSULPDXQLF SHFDUHWUHEXLHV RSO WHDVF XQDVLJXUDWvQ YkUVW GH DQL vQ PRPHQWXO FRQWUDFW ULL DVLJXU ULL SHQWUX D SULPL WRW UHVWXO YLH LLODVIkUúLWXOILHF UXLDQFkWH XPSURFHQWXOILLQG " 6ROX LH3ULPDFRQIRUPIRUPXOHL HVWH

3

1 '

$QXLW LYLDJHUHDQWLFLSDWHLPHGLDWH 3ULPDXQLF SHFDUHWUHEXLHV RSO WHDVF RSHUVRDQ vQYkUVW GH [ DQLDVWIHO FDODvQFHSXWXOILHF UXLDQV SULPHDVF FRWDGHXPSHWRDW GXUDWDYLH LLVDOH QRWDW D [ YDIL

D[

( [ ( [ [ ( [

6HREVHUY F D [

'[ '[ ' '[ '[ '[

1[ '[

D[

'DF VXPDDVLJXUDW HVWH 6 XPDWXQFLSULPDXQLF YDIL

3

6 D[

6

1[ '[

$SOLFD LH&DUHHVWHSULPDXQLF SHFDUHWUHEXLHV RSO WHDVF RSHUVRDQ vQ YkUVW GH DQLFDUHSULPHúWHRSHQVLHYLDJHU DQXDO GH XPDQWLFLSDWFX SURFHQWGH "

6ROX LH3ULPDXQLF HVWH

3

D[

1 '

$QXLW LOLPLWDWHOD Q DQL

$QXLW LOHOLPLWDWHOD Q DQLSRWILSRVWLFLSDWH Q D [ VDXDQWLFLSDWH Q D[ 3ULPD XQLF SHFDUHWUHEXLHV RSO WHDVF RSHUVRDQ vQYkUVW GH [ DQLSHQWUXDvQFDVD WLPSGH Q DQLODVIkUúLWXOILHF UXLDQXPHVWH Q

D[

'[ ' [ Q '[ '[

([ Q ([

1 [ 1 [ Q '[

'DF VXPDDVLJXUDW HVWHGH 6 XPSULPDXQLF YDIL

3

6 Q D[

6

1 [ 1 [ Q '[

6LPLODUSULPDXQLF SHFDUHWUHEXLHV RSO WHDVF XQDVLJXUDWvQYkUVW GH [ DQLSHQWUXDSULPLFkWHXPODvQFHSXWXOILHF UXLDQWLPSGH Q DQLGDF HVWHvQ YLD HVWH Q D[

1 [ 1 [Q 'DF VXPDvQFDVDW ODvQFHSXWXOILHF UXLDQHVWH 6 '[

DWXQFLSULPDXQLF YDIL

3

6 Q D[

6

1 [ 1 [Q '[

2EVHUY PF Q D[ Q D[ $SOLFD LH 6 VH GHWHUPLQH SULPD XQLF SH FDUH WUHEXLH V R SO WHDVF R SHUVRDQ vQYkUVW GH DQLvQPRPHQWXOFRQWUDFW ULLDVLJXU ULLSHQWUXDvQFDVDOD VIkUúLWXO ILHF UXL DQ SkQ OD vPSOLQLUHD YkUVWHL GH DQL VXPD GH XP SURFHQWXOILLQGGH 'DUFXvQFDVDUHDODvQFHSXWXOILHF UXLDQ" 6ROX LH'LQ

3

'LQ 3 3

1 1 '

1 1 '

XP

XP

$QXLW LYLDJHUHDPkQDWH

3ULPD XQLF SH FDUH WUHEXLH V R SO WHDVF XQ DVLJXUDW vQ YkUVW GH [ DQL SHQWUX D SULPL XP OD VIkUúLWXO ILHF UXL DQ GXS WUHFHUHD D Q DQL GDF HVWH vQ YLD 'LQWHRUHPDFRPSXQHULLFRQWUDFWHORUDYHP Q

D[

Q

'[ Q ' '[ '[

( [ [ ( [

'DF VXPDDVLJXUDW HVWHGH 6 XPSULPDXQLF YDIL

3

6 Q D[

6

1 [ Q '[

1 [ Q '[

3HQWUXDQXLW LYLDJHUHDPkQDWHDQWLFLSDWFX Q DQLSULPDXQLF YDIL Q

D[

Q

'[ Q ' '[ '[

( [ [ ( [

'DF VXPDDVLJXUDW HVWHGH 6 XPSULPDXQLF YDIL

3

6 Q D[

6

1 [Q '[

1 [Q '[

$SOLFD LH&DUHHVWHSULPDXQLF SHFDUHXUPHD] V RSO WHDVF XQLQGLYLGvQ YkUVW GH DQL vQ PRPHQWXO FRQWUDFW ULL DVLJXU ULL SHQWUX D vQFDVD GXS vPSOLQLUHDYkUVWHLGH DQLWRWUHVWXOYLH LLFkWH XPODVIkUúLWXOILHF UXL DQSURFHQWXOILLQGGH "'DUODvQFHSXWXOILHF UXLDQ" 6ROX LH'LQ

3

1 '

XP

1 '

XP

'LQ

3

$VLJXUDUHDGHSHQVLH 9DORULOH DFWXDOH DOH DQXLW LORU YLDJHUH VWXGLDWH SkQ DFXP SHUPLW V VH VWDELOHDVF SULPHOHXQLFHSHQWUXDVLJXUDUHDGHSHQVLH /DDVLJXU ULOHGHSHQVLHWUHEXLHV VHGHWHUPLQHSULPDXQLF SHFDUHWUHEXLHV R SO WHDVF XQ DVLJXUDW R GDW SHQWUX WRWGHDXQD SHQWUX D SULPL OD PRPHQWXO FRQWUDFW ULL DVLJXU ULL R SHQVLH YLDJHU DQXDO GH 6 XQLW L PRQHWDUH 3HQVLD YLDJHU DQXDO SRVWLFLSDW RQRW P 3[ úLFHDDQWLFLSDW 3[ $YHP

1[ '[ 1 3[ 6 D[ 6 [ '[ 'DF DVLJXUDWXOGRUHúWHRSHQVLHOXQDU GH 6 XPSULPDXQLF YDIL 3[

6 D[

3[

6 D[

3[

6 D[

6

§ 1 · 6 ¨ [ ¸ © '[ ¹ §1 · 6 ¨ [ ¸ © '[ ¹

1RWkQG FX Q 3[ SULPHOH SO WLWH GH DVLJXUDW WLPS GH Q DQL OD VIkUúLWXO

ILHF UHLOXQLúLFX 6 SHQVLLOHOXQDUHYLDJHUHSHFDUHXUPHD] V OHSULPHDVF GXS

Q DQLRE LQHPUHOD LD Q 3[ Q D[ GHXQGH Q

3[

6

6

Q

D[

Q D[

1 [ Q '[ Q 1 [ 1 [ Q '[ '[ Q

$SOLFD LH &DUH HVWH SULPD SH FDUH XUPHD] V R SO WHDVF R SHUVRDQ vQ YkUVW GH DQL OD VIkUúLWXO ILHF UHL OXQL SkQ OD vPSOLQLUHD YkUVWHL GH DQL SHQWUX D SXWHD vQFDVD OD VIkUúLWXO ILHF UHL OXQL R SHQVLH YLDJHU GH XP SURFHQWXOILLQGGH " 6ROX LH$YHP 6 [ Q 'LQ

3

1 ' 1 1 ' '

$VLJXUDUHDGHGHFHV /D DVLJXU ULOH GH GHFHV WUHEXLH V VH GHWHUPLQH VXPD SH FDUH XUPHD] V R SO WHDVF XQLQGLYLGvQYkUVW GH [ DQLSHQWUXFDODGDWDPRU LLVDOHvQWUHSULQGHUHD GHDVLJXUDUHV SO WHDVF XUPDúLORURDQXPLW VXP GHEDQLIL[DW SULQFRQWUDFWXO GHDVLJXUDUH

3ULPDXQLF SHQWUXDVLJXUDUHDGHGHFHVHVWHGHFLVXPDSHFDUHXUPHD] V R SO WHDVF DVLJXUDWXOvQWUHSULQGHULLGHDVLJXUDUHODPRPHQWXOFRQWUDFW ULLDVLJXU ULL R GDW SHQWUX WRWGHDXQD 6XPD SH FDUH R YD SO WL vQWUHSULQGHUHD XUPDúLORU OD PRPHQWXOGHFHVXOXLVHQXPHúWHVXP DVLJXUDW )LH 0 [ YDORDUHD PHGLH DFWXDO D XQXL OHX SO WLW OD GDWD GHFHVXOXL XQHL SHUVRDQHvQYkUVW GH [ DQLDGLF YDORDUHDPHGLHDFWXDO DDVLJXU ULLGHGHFHVFDUH HVWHYDORDUHDPHGLHDYDULDELOHL § ¨ Y ; ¨ V[ V[ ¨ © V[

FX

0[

0 ;

[

¦ Q

[

¦

Y

Q · "¸ Y ¸ V V " [ Q [ Q "¸ V[ ¹

"

V [ V [ V[

V[ Q V[ Q Q Y V[

V[ Q V[ Q Y

[

¦ Q

V[ Q V[ Q Q Y [ Y [ V[ Y

[Q

V[ Y [

Q

6H YRU LQWURGXFH QXPHUH GH FRPXWD LH & [

5[

V[ V[ Y

[

$WXQFL

& [ & [ & úL 0[

5[ '[

'DF VRFLHWDWHD GH DVLJXUDUH XUPHD] V SO WHDVF vQ PRPHQWXO GHFHVXOXL VXPDGH 6 XQLW LPRQHWDUHDWXQFLSULPDXQLF YDIL

3

6 0[

6

5[ '[

$SOLFD LH &DUH H SULPD XQLF SH FDUH WUHEXLH V R SO WHDVF R SHUVRDQ vQ YkUVW GH DQLSHQWUXFDvQPRPHQWXOGHFHVXOXLXUPDúLLV SULPHDVF XPFXSURFHQWGH " 6ROX LH

3

0 '

$VLJXU ULGHGHFHVOLPLWDWHúLDPkQDWH

'DF DVLJXUDUHDGHGHFHVVHIDFHSHXQWHUPHQOLPLWDWGHDQL Q vQFHSkQGGH ODGDWDvQFKHLHULLFRQWUDFWXOXLGHDVLJXUDUHDWXQFLYDORDUHDDFWXDO DXQHLXPFDUH VHSO WHúWHDVLJXUDWXOXLvQYkUVW GH [ DQLODvQFKHLHUHDDVLJXU ULLFkQGGHFHVXOD VXUYHQLWvQGHFXUVXODFHVWRUDQLHVWH

Q

& [ & [ & [ Q '[

0[

5[ 5[ Q '[

'DF DVLJXUDUHD QX vQFHSH LPHGLDW V IXQF LRQH]H FL GXS Q DQL DGLF R DVLJXUDUHGHGHFHVDPkQDW VXPDVHSO WHúWHQXPDLGDF DVLJXUDWXOGHFHGHD] GXS WUHFHUHDD Q DQLGHODvQFKHLHUHDDVLJXU ULL 9DORDUHDDFWXDO DXQHLXPFDUHVHSO WHúWHGDF DVLJXUDWXOvQYkUVWDGH [ DQLODGDWDFRQWUDFW ULLDVLJXU ULLPRDUHGXS H[SLUDUHDWHUPHQXOXLGHDPkQDUHGH Q DQLHVWH

5[ Q '[ ÌQWUHDVLJXUDUHDGHGHFHVSHWRDW YLD D 0 [ úLDVLJXU ULOHGHGHFHVOLPLWDWHúL Q

& [ Q & '[

0[

DPkQDWHH[LVW UHOD LD

0[

Q

0 [ Q 0 [

$SOLFD LH&DUHHVWHSULPDXQLF SHFDUHWUHEXLHV RSO WHDVF RSHUVRDQ GH DQLSHQWUXFDvQPRPHQWXOGHFHVXOXLXUPDúLLV SULPHDVF XPGDF GHFHVXO DUHORFSkQ ODvPSOLQLUHDYkUVWHLGH DQLFXSURFHQWXO S "'DUGDF GHFHVXO VXUYLQHGXS GHDQL" 6ROX LH'LQ Q

0[

'LQ Q

0[

5 5 '

5 '

XP

$VLJXU ULPL[WH $FHVWHDVLJXU ULXWLOL]DWHFHOPDLDGHVHDSUHVXSXQvQDFHODúLWLPSDVLJXUDUHD XQHLVXPHSHWHUPHQIL[úLRDVLJXUDUHGHGHFHVvQFDGUXODFHOXLDúLWHUPHQ 'DF GXUDWD DVLJXU ULL HVWH GH Q DQL vQWUHSULQGHUHD GH DVLJXUDUH SO WHúWH DVLJXUDWXOXLGDF HVWHvQYLD ODH[SLUDUHDDFHVWXLWHUPHQVXPDDVLJXUDW LDUGDF D GHFHGDW vQDLQWHD DFHVWXL WHUPHQ SO WHúWH OD GDWD GHFHVXOXL XUPDúLORU IL[D L SULQ FRQWUDFWVXPDDVLJXUDW 3HQWUX DFHDVWD YDORDUHD DFWXDO OD FRQWUDFWDUHD DVLJXU ULL VH VWDELOHúWH DGXQkQG VDUFLQLOH vQWUHSULQGHULL SHQWUX DVLJXUDUHD GH GHFHV úL DVLJXUDUHD VXPHL OD WHUPHQDWXQFL

3

Q

0 [ Q 5[

5[ 5[ Q '[ Q '[ '[

'DF VXPDDVLJXUDW HVWH 6 XPDWXQFLSULPDXQLF HVWH

3

6

5[ 5[ Q '[ Q '[

$SOLFD LH&DUHHVWHSULPDXQLF SHFDUHWUHEXLHV RSO WHDVF XQDVLJXUDWvQ YkUVW GH DQLvQPRPHQWXOFRQWUDFW ULLDVLJXU ULLSHQWUXDvQFDVDGDF HVWHvQ YLD ODYkUVWDGH DQLVXPDGH XPLDUGDF DGHFHGDWSkQ OD DQL VXPDGH XPV ILHvQFDVDW GHXUPDúLODPRPHQWXOGHFHVXOXLSURFHQWXO HVWH " 6ROX LH'LQ

3

5 5 ' '

02'(/(0$7(0$7,&(3(1758*(67,81($672&85,/25 1R LXQLJHQHUDOH 'HILQL LH 3ULQ VWRF VH vQ HOHJH R UH]HUY GH EXQXUL PDWHULDOH GHVWLQDWH YkQ] ULLVDXIRORVLULLvQSURFHVXOGHSURGXF LH ([HPSOHVWRFXULGHP UIXULGHPDWHULLSULPHGHSLHVHGHVFKLPEHWF3HQWUX D FRQVWLWXL VWRFXUL DYHP FKHOWXLHOL GH DSURYL]LRQDUH VDX SURGXF LH FKHOWXLHOL GH VWRFDMSLHUGHULSHQWUXGHSUHFLHUHDP UIXULORUúLDOWHOH 2ULFH JHVWLXQH GH VWRF SUHVXSXQH LQWU UL vQ VWRF LQSXWV úL LHúLUL GLQ VWRF RXWSXWV GHWHUPLQDWHGHFHUHUHDGHEXQXULFHSRDWHILGHWHUPLQLVW úLFXQRVFXW VDX DOHDWRDUHFXRUHSDUWL LHVWDWLVWLFFXQRVFXW VDXQHFXQRVFXW ÌQ DFWLYLWDWHD GH PDQDJHPHQW D VWRFXOXL LQWHUYLQ XUP WRDUHOH HOHPHQWH FHUHUHDGHEXQXULQLYHOXOVWRFXOXLYROXPXOFRPHQ]LLGHUHDSURYL]LRQDUHSHULRDGD GHUHDSURYL]LRQDUHFRVWXULGHVWRFDUHGHSHQDOL]DUHGHODQVDUHDFRPHQ]LL 3ROLWLFD HFRQRPLF GHWHUPLQ GHFL]LLOH FH VH LDX vQ RUJDQL]DUHD úWLLQ LILF D VWRFXULORUDYkQGODED] XQFULWHULXGHRSWLPDFHVWDILLQGGHRELFHLFRVWXOJOREDO PLQLP 'HILQL LH6HQXPHúWHSROLWLF RSWLP DFHDDFWLYLWDWHGHPDQDJHPHQWDVWRFXOXL FDUHLPSOLF XQFRVWWRWDOPLQLP (OHPHQWHOHXQHLSROLWLFLRSWLPHVXQWQLYHOXORSWLPDOVWRFXOXLYROXPXORSWLPDO XQHLFRPHQ]LGHUHDSURYL]LRQDUHSHULRDGDRSWLP GHUHDSURYL]LRQDUHQXP UXORSWLP GHUHDSURYL]LRQ ULFRVWXOWRWDOPLQLPJHVWLXQHDRSWLP ÌQ JHVWLXQHD úWLLQ LILF D VWRFXULORU XQ URO LPSRUWDQW vO DX PRGHOHOH HFRQRPLFRPDWHPDWLFH D QLYHOXULORU VWRFXULORU úL D PRPHQWHORU vQ FDUH VH IDFH UHDSURYL]LRQDUHDFXDMXWRUXOF URUDSXWHPVWDELOLSROLWLFLRSWLPH'XS QDWXUDORU PRGHOHOHSRWILGHWHUPLQLVWHVDXDOHDWRDUH 0RGHOHGHWHUPLQLVWH 0RGHOGHVWRFDUHDXQXLSURGXVFXFHUHUHFRQVWDQW SHULRDG FRQVWDQW GHUHDSURYL]LRQDUHúLI U OLSV GHVWRF 6HFRQVLGHU F VHVWRFKHD] XQVLQJXUSURGXVDOF UXLFRQVXPHVWHRIXQF LH OLQLDU GH WLPS FHUHUHD SURGXVXOXL HVWH 4 SH R SHULRDG GH WLPS T UHDSURYL]LRQDUHVWRFXOXLVHIDFHLQVWDQWDQHXODLQWHUYDOHGHWLPSHJDOHFX 7 úLvQ FDQWLW LHJDOH T ùWLLQG FRVWXO XQLWDU GH VWRFDUH vQ XQLWDWHD GH WLPS FV FRVWXO GH ODQVDUH D FRPHQ]LLGHUHDSURYL]LRQDUH F UHSUH]HQWkQGWRWDOXOFKHOWXLHOLORUOHJDWHGHRSHUD LL GH UHDSURYL]LRQDUH FH QX GHSLQGH GH T úL F QX VH DGPLWH OLSV GH VWRF VH FHUH JHVWLXQHDRSWLP FRVWXOWRWDOPLQLP

2DVWIHOGHJHVWLXQHVHSUH]LQW FDvQILJXUD

)LJXUD

9UHP V VFULHP IXQF LD RELHFWLY D PRGHOXOXL FH FXSULQGH WRDWH FKHOWXLHOLOH OHJDWHGHJHVWLXQHDVWRFXOXL 2EVHUY P F SHQWUX ILHFDUH SHULRDG 7 VH IDF FKHOWXLHOLOH F GHRDUHFHvQVWRFVHFRQVLGHU F VHDIO FDQWLWDWHDPHGLH

DYHPQXP UXODSURYL]LRQ ULORU

4 T

Y

T7FV

T 3HULRDGHOHILLQGHJDOH

T 7

$VWIHOIXQF LDRELHFWLYÄFRVWWRWDO´YDILRE LQXW SULQvQPXO LUHDFKHOWXLHOLORU FRUHVSXQ] WRDUHXQHLSHULRDGHFXQXP UXOSHULRDGHORU Y

§ · & T ¨ F T7FV ¸Y © ¹

4F TTFV T

ÌQORFXLQGvQUHOD LD UHOD LD YRPRE LQH

& T

9ROXPXO RSWLP DO XQHL FRPHQ]L GH UHDSURYL]LRQDUH TÖ VH RE LQH SXQkQG

FRQGL LDGHPLQLPSHQWUXIXQF LD & T 'HULYDWHOHDFHVWHLIXQF LLVXQW

4F TFV T & ccT 4F T

& cT

5H]ROY P & cT

úLRE LQHP

4F TFV

TÖ

úLFXP & ccTÖ ! DWXQFLH[WUHPXOHVWHXQPLQLP'LQFRQVLGHUHQWHHFRQRPLFHVH FRQVLGHU QXPDLYDORULOHSR]LWLYHDOHOXL T ÌQORFXLQG vQ RE LQHPQXP UXORSWLPGHUHDSURYL]LRQ ULFkWúL SHULRDGDRSWLP

YÖ

4 TÖ

T4FV F

7Ö

T YÖ

TF 4FV

ÌQORFXLQG vQ RE LQHPJHVWLXQHDRSWLP &Ö T

&Ö

& TÖ

4TFFV

([HPSOX &HUHUHD SHQWUX XQ DQXPLW DSDUDW HOHFWURFDVQLF HVWH GH EXF LSHDQ$SURYL]LRQDUHDXQXLGHSR]LWFXDFHVWSURGXVVHIDFHvQFDQWLW LHJDOH ODLQWHUYDOHGHWLPSHJDOHLDUSURGXVHOHVXQWVFRDVHFXXQULWPFRQVWDQWGLQVWRF ùWLLQG F SHQWUX D VWRFD vQ GHSR]LW XQ VLQJXU DSDUDW WLPS GH XQ DQ VH SO WHVF XP FRVWXO GH ODQVDUH DO FRPHQ]LL HVWH XP úL F QX VH DFFHSW OLSVD SURGXVXOXLGLQVWRFV VHGHWHUPLQHYROXPXORSWLPDOXQHLFRPHQ]LQXP UXORSWLP GHDSURYL]LRQ ULSHULRDGDRSWLP GHUHDSURYL]LRQ ULúLJHVWLXQHDRSWLP 5 VSXQV 4 EXF L T DQ FV XP F XP

| EXF L YÖ | DSURYL]LRQ UL 7Ö | | ]LúL &Ö XP TÖ

0RGHOGHVWRFDUHDXQXLSURGXVFXFHUHUHFRQVWDQW SHULRDG FRQVWDQW GHUHDSURYL]LRQDUHúLFXSRVLELOLWDWHDOLSVHLGHVWRF

9RPDGPLWHLSRWH]HOHGLQPRGHOXOFXGHRVHELUHDF VHDGPLWHOLSV GH VWRF SHQDOL]DW FX XQ FRVW XQLWDU GH SHQDOL]DUH F S SHQDOL]DUHD SHQWUX OLSVD XQXL SURGXVvQXQLWDWHDGHWLPS 3HULRDGDFRQVWDQW GHWLPS 7 DIRVWvPS U LW vQGRX VXESHULRDGHSHULRDGD 7 vQFDUHVWRFXOVDWLVIDFHFHUHUHDSHULRDG vQFDUHVHYDSO WLSHQWUXVWRFXOPHGLX

V FRVWXOXQLWDUGHVWRFDM FV úLSHULRDGD 7 vQFDUHVWRFXOQXPDLVDWLVIDFHFHUHUHD

SHULRDG vQ FDUH VH YD SO WL SHQWUX OLSVD PHGLH SHQDOL]DUH F S

TV FRVWXO XQLWDU GH

0RGHOXOVHSUH]LQW JUDILFvQILJXUD

)LJXUD

9UHP V GHWHUPLQ P FRVWXO JOREDO & T V ÌQWUR SHULRDG 7 VH YRU IDFH FKHOWXLHOLOH

V TV F 7FV 7F S

V TV § · & T V ¨ F 7FV 7F S ¸Y © ¹

&RVWXOJOREDOYDIL

ÌQUHOD LD LQWURGXFHPUHOD LD úLRE LQHP

& T V F

4 V T TV T 7F S 7FV T 7 7

'LQDVHP QDUHDWULXQJKLXULORUGUHSWXQJKLFHIRUPDWHvQILJXUDDDFHVWXL PRGHOUH]XOW

7 7

V 7 T 7

TV T

'LQ úL DYHP

& T V

T T 4 T V F S F V FV T T T

9UHPV GHWHUPLQ PPLQLPXOIXQF LHLRELHFWLY5H]ROY PVLVWHPXO

w& T V °° wT ® ° w& T V °¯ wV

GHXQGHUH]XOW

T T 4F V F T V FS V ° T T T ° ® ° V TF T V TF S °¯ T V T

'LQSULPDUHOD LHDVLVWHPXOXL UH]XOW

4F FV F S V TF S FS

T

'LQDGRXDUHOD LHDVLVWHPXOXL UH]XOW

V

FS

FV F S

T

,QWURGXFkQG vQ RE LQHP YDORDUHD RSWLP SHQWUX YROXPXO FRPHQ]LL TÖ

4F FV F S T FV FS

TÖ 1RW P

U

FS FV F S

QXPLWIDFWRUGHSHQDOL]DUH &XDFHDVW QRWD LHUHOD LD UHVSHFWLY YRUGHYHQL

TÖ VÖ UTÖ

4F TFV U 4F U TFV

& T V DUHPLQLPXO & TÖ VÖ QXPLWJHVWLXQHRSWLP SHQWUXF 'TÖ VÖ ! ° ® w & TÖ VÖ ° wT ! ¯

2E LQHP SHULRDGD RSWLP SUHFXP úL QXP UXO RSWLP GH DSURYL]LRQ UL GLQ UHOD LLOH úL

YÖ

4 TÖ

4TFV U F

7Ö

T YÖ

TF 4FV U

úLUHVSHFWLY

*HVWLXQHD RSWLP VH RE LQH vQORFXLQG vQ SH T úL V FX YDORULOH RSWLPH TÖ úL VÖ GLQ úL DGLF

&Ö

4TFV U

2EVHUYD LH 'DF F S o f GLQ UH]XOW F U o úL DMXQJHP OD PRGHOXO FDUHDSDUHFDXQFD]SDUWLFXODUDOPRGHOXOXL ([HPSOX/DRSDWLVHULHQHFHVDUXOOXQDUHVWHGH NJGH]DK U&RVWXOGH VWRFDMSHQWUX NJGH]DK UHVWHGH XPSH]LFRVWXOGHODQVDUHDOFRPHQ]LLHVWH GH XP LDU vQ FD] GH OLSV GH VWRF VH DSOLF R SHQDOL]DUH FX XP]L SHQWUX NJGH]DK UOLSV 6 VHGHWHUPLQHYROXPXORSWLPDOXQHLFRPHQ]LVWRFXO RSWLP QXP UXO RSWLPGHDSURYL]LRQ ULSHULRDGDRSWLP úWLLQGF DSURYL]LRQDUHD VHIDFHvQFDQWLW LHJDOHODLQWHUYDOHGHWLPSHJDOH 6ROX LH 4

T F F S TÖ

'HDVHPHQHD VÖ

&Ö

4F T FV U

TÖ U # YÖ

4T FV F U

FV

$VWIHO U

$YHP

# 4 T 7Ö 5H]XOW TÖ YÖ

#

0RGHOGHVWRFDUHDXQXLSURGXVFXFHUHUHFRQVWDQW SHULRDG FRQVWDQW GHUHDSURYL]LRQDUHI U OLSV GHVWRF OXkQGvQFRQVLGHUDUHúLFRVWXOGHDFKL]L LHVDXGHSURGXF LH

&RQVLGHU PJHVWLXQHDXQXLVWRFGHFDQWLWDWH 4 DXQXLVLQJXUSURGXVSHXQ LQWHUYDOGHWLPS T 5HDSURYL]LRQDUHDVWRFXOXLVHIDFHLQVWDQWDQHXODLQWHUYDOHHJDOH FX 7 úLvQFDQWLW LHJDOHFX T SUH XOXQLWDUGHFXPS UDUHDOSURGXVXOXLVDXFRVWXO XQLWDU GH SURGXF LH HVWH FD FRVWXO IL[ DO FRPHQ]LL HVWH FE LDU FRVWXO XQLWDU GH VWRFDM FV VHSUHVXSXQHSURSRU LRQDOFXFKHOWXLHOLOHI FXWHSHQWUXDSURYL]LRQDUHDFX RXQLWDWHGHSURGXVFRHILFLHQWXOGHSURSRU LRQDOLWDWHILLQG D 'LQLSRWH]HUH]XOW F DFHVWPRGHOHVWHRYDULDQW DPRGHOXOXL vQFDUH FRVWXOGHODQVDUHHVWH F TFD FE LDUFRVWXOXQLWDUGHVWRFDM

§ F · D¨¨ FD E ¸¸ T¹ ©

FV

)RORVLPDFHODúLFULWHULXGHRSWLPFDúLODPRGHOXOvQFDUHFRVWXOGHODQVDUH IXQF LDRELHFWLY GHYLQHGXS vQORFXLUHDOXL F úL FV FXH[SUHVLLOH úL

& T FHVHUHVFULH

& T

4 TFD FE T TD§¨¨ FD FE ·¸¸ T © T ¹

4 FE DTTFD 4FD DFE T

'LQFRQGL LDGHRSWLPSHQWUXIXQF LDRELHFWLYDYHP

& cT 5H]ROYkQGHFXD LD & cT

TÖ FX & ccTÖ !

4 F DTFD E T

YRPJ VLSHQWUXFRPDQGDRSWLP 4FE DTFD

'LQ úL UH]XOW

YÖ

4 TÖ

D4TFD FE

úLUHVSHFWLY

7Ö

T YÖ

TFE D4FD

'LQ úL RE LQHPJHVWLXQHDRSWLP

&Ö

& TÖ

D4TFD FE 4FD DTFE

([HPSOX 8Q PDJD]LQ GH SURGXVH HOHFWURQLFH DUH R FHUHUH WULPHVWULDO GH

FRPSRQHQWH HOHFWURQLFH GH DFHODúL WLS 3HQWUX ILHFDUH FRPDQG VH FKHOWXLHVF XP LDU FRVWXO GH DFKL]L LH HVWH GH XP SHQWUX ILHFDUH

SURGXV&RHILFLHQWXOGHSURSRU LRQDOLWDWHvQWUHFRVWXOXQLWDUGHVWRFDMúLFRVWXOXQLWDU GHODQVDUHHVWH ùWLLQGF QXVHDGPLWHOLSV GHVWRFV VHGHWHUPLQHSROLWLFD RSWLP GHUHDSURYL]LRQDUH 6ROX LH 6H FXQRVF 4 T FD FE úL IDFWRUXO GH SURSRU LRQDOLWDWHDVRFLDWVWRF ULL D

)RORVLPUHOD LD DYHP

#

TÖ

3HULRDGDRSWLP UHDSURYL]LRQDUHHVWH

# 4 # 6HRE LQHFRVWXOPLQLP LDUQXP UXOGHUHDSURYL]LRQ UL YÖ TÖ &Ö & TÖ 7Ö

0RGHOGHVWRFDUHDPDLPXOWRUSURGXVH

ÌQ FHOH PDL PXOWH FD]XUL vQ SUDFWLF VH IDF VWRFXUL GH PDL PXOWH SURGXVH 9RPFRQVWUXLRYDULDQW DPRGHOXOXLSHQWUXFD]XODPDLPXOWRUSURGXVH 6H VWRFKHD] N SURGXVH 3L L N DO F URU FRQVXP HVWH GDW GH IXQF LL OLQLDUH GH WLPS FHUHUHD SURGXVXOXL 3L HVWH 4L SHQWUX R SHULRDG GH WLPS T UHDSURYL]LRQ ULORUVHIDFLQVWDQWDQHXODLQWHUYDOHGHWLPS 7L vQFDQWLW LHJDOHFX TL

FRVWXULOH XQLWDUH GH VWRFDUH VXQW FVL FRVWXULOH GH ODQVDUH FL L

N úL QX VH

DGPLWHOLSV GHVWRFSHQWUXQLFLXQSURGXV 'LQUHOD LD RE LQHPFRVWXOJOREDOGHVWRFDMSHQWUXSURGXVXO 3L HVWH

4L FL TL TFVL TL

&L TL

LDUIXQF LDRELHFWLYSHQWUXSURGXVHOHVWRFDWHYDIL

& T T TN

N

¦ & T L

L

L

)XQF LLOH &L TL L N VXQW LQGHSHQGHQWH PLQLPXO VXPHL ORU DUH ORF R GDW FXPLQLPXOILHF UXLDGLQWUHHOH9RPDYHDXUP WRDUHOHUHOD LL

w& T T TN ° wTL ° ® ° w&L TL °¯ wTL

L

N

LQkQG FRQW GH UHOD LLOH úL GH UHOD LLOH úL J VLPSHQWUXSURGXVHOH 3L XUP WRDUHOHYDORUL

4L FL

TÖL

TFVL

T4L FVL

YÖL

FL

TFL

7ÖL

4L FVL

LDUSHQWUXJHVWLXQHDRSWLP

&L TÖL

N

&Ö XQGH &Ö L

¦ &Ö L

L

TFL FVL 4

([HPSOX6HRUJDQL]HD] SHRSHULRDG GH ]LOHDQFRPHUFLDO ODR FRIHW ULH VWRFXO SURGXVHORU I LQ ]DK U XOHL vQ FDQWLW LOH 4 WRQH 4

WRQ FRVWXULOH GH ODQVDUH D FRPHQ]LL ILLQG F

WRQH 4

F

OHLUHVSHFWLY F

OHLW]L FV

OHLW]L FV

OHL

OHL&RVWXULOHGHVWRFDMVXQW FV

OHLW]L6HFHUYDORULOHHOHPHQWHORURSWLPHDOH

DFWLYLW LLGHPDQDJHPHQWDOVWRFXOXL

TÖ TÖ TÖ 3HQWUX QXP UXO DSURYL]LRQ ULORU DYHP YÖ # YÖ # úL YÖ # 3HQWUX JHVWLXQLOH RSWLPH SH SURGXV RE LQHP &Ö # &Ö úL &Ö GH XQGH 6ROX LH 6H RE LQH

&Ö

¦ &Ö L

L

0RGHOHSUREDELOLVWH 0RGHOGHVWRFDUHDXQXLSURGXVFXFHUHUHDDOHDWRDUHFX SLHUGHUHvQFD]XOVXUSOXVXOXLGHVWRFFXFKHOWXLHOLVXSOLPHQWDUHvQ FD]XOOLSVHLGHVWRFúLFXFRVWGHVWRFDMQHJOLMDELO

6H VWRFKHD] XQ VLQJXU SURGXV VWRFXO FRQVWLWXLW OD XQ DQXPLW PRPHQW VH

§ [ ·

¸¸ QRWHD] FX V DF UHLFHUHUHHVWHYDULDELODDOHDWRDUH ; FXUHSDUWL LD ; ¨¨ © S [ ¹ [

§ [ · ¸¸ [ > f SHQWUX FHUHUH SHQWUX FHUHUH GLVFUHW úL ; ¨¨ © I [ ¹

FRQWLQX ([FHGHQWXOGHVWRFFkQG [ d V VHSHQDOL]HD] FXRSLHUGHUHXQLWDU F OLSVD GH VWRF FkQG [ ! V VH SHQDOL]HD] FX FKHOWXLHOL VXSOLPHQWDUH GH UHDSURYL]LRQDUH F LDUFKHOWXLHOLOHGHVWRFDMVXQWIRDUWHPLFLvQUDSRUWFX F úL F úLVHSRWQHJOLMD 3UH]HQW PVHSDUDWPRGHOXOSHQWUXFD]XOGLVFUHWúLSHQWUXFD]XOFRQWLQXX &D]XOGLVFUHW 1RW P FX (V YDULDELOD DOHDWRDUH H[FHGHQW GH VWRF FH DUH UHSDUWL LD

§V [· ¸¸ [ V úLQRW PFX /V YDULDELODDOHDWRDUHOLSV GHVWRFFHDUH (V ¨¨ © S[ ¹ § [ V· ¸¸ [ V V UHSDUWL LD /V ¨¨ © S[ ¹ 0HGLLOHFHORUGRX YDULDELOHDOHDWRDUHYRUIL

¦ V [ S [

0 /V

¦ [ V S[

úLUHVSHFWLY

V

0 (V

[ f

[ V

$SOLFkQG SHQDOL] ULOH F úL F FHORU GRX PHGLL 0 (V úL 0 /V GHWHUPLQ P IXQF LD RELHFWLY FH UHSUH]LQW FKHOWXLHOLOH PHGLL WRWDOH OHJDWH GH PDQDJHPHQWXOVWRFXOXL V

& V F ¦ V [ S [ F [

f

¦ [ V S[

[ V

9UHPV GHWHUPLQ PVWRFXORSWLP VÖ SHFDUHOYRPRE LQHSXQkQGFRQGL LD GHPLQLPSHQWUXIXQF LD & V & V ILLQGRIXQF LHGLVFUHW PLQLPXOHLYDIL VÖ SHQWUXFDUH & VÖ ! & VÖ & VÖ GHFLSHQWUXDOGHWHUPLQDSH VÖ YRPUH]ROYDVLVWHPXO

'LQ DYHP

& V

& V & V ! ® ¯& V & V !

V

F ¦ V [ S [ F [

f

¦ [ V S [

[ V

V

F ¦ V [ S [ F [ V

V

[

[

f

¦ [ V S [

F ¦ V [ S [ F ¦ S [ F 1RW P ) V

[ V

f

¦

[ V

[ V S [ F

¦ S [

[ V

V

¦ S[ úLLQWURGXFkQGvQH[SUHVLDOXL & V RE LQHP [

& V & V F F ) V F

6LPLODUGLQ RE LQHP

& V

f

V

f

F ¦ V [ S [ F ¦ [ V S [ [

[ V

V

V

f

f

[

[

[ V

[ V

V

f

[

[ V

F ¦ V [ S [ F ¦ S [ F ¦ [ V S [ F ¦ S [

F ¦ V [ S [ F ¦ [ V S [ F ) V F ) V VDX

& V & V F F ) V F

ÌQORFXLQGvQ UHOD LLOH úL DYHP

& V & V F F ) V F ! ® ¯& V & V F F ) V F !

GHXQGH

) V

F ) V F F

$VWIHOVWRFXORSWLP VÖ HVWHDFHDYDORDUHDOXL V FHVDWLVIDFHUHOD LD úL YRPQRWDFX U

F UDSRUWXOGHSHQDOL]DUH F F

2EVHUYD LL 'LQUHOD LD úLGLQIDSWXOF ) V HVWHQHGHVFUHVF WRDUHUH]XOW F H[LVW VÖ XQLF 'DF ) VÖ U ) VÖ DWXQFL & VÖ & VÖ GHFL PLQLPXO DUH ORF SHQWUXGRX YDORUL VÖ úL VÖ 'DF ) VÖ U ) VÖ DWXQFL & VÖ & VÖ GHFL PLQLPXO DUH ORF SHQWUXYDORUL VÖ úL VÖ ([HPSOX8QDWHOLHUDXWRDUHQHYRLHGHXQQXP UGHSLHVHGHXQDQXPLWWLS 6H FHUH QXP UXO GH SLHVH FH WUHEXLHVF VWRFDWH úWLLQG F GDF H[LVW XQ VXUSOXV GH SLHVH H[LVW SLHUGHUL vQ YDORDUH GH XP úL GDF QX VH DFKL]L LRQHD] VXILFLHQWH SLHVHOH OLSV VH YRU SURFXUD FX XQ SUH GH FRVW PDL ULGLFDW FX XP'LQGDWHOHVWDWLVWLFHRE LQHPXUP WRDUHDFHUHUHGHSLHVH 3LHVHvQORFXLWH [

1XP UXOGHPDúLQLFX [ SLHVHvQORFXLWH

ùWLLQGF FRVWXOGHVWRFDMHVWHQHJOLMDELOvQUDSRUWFXFHOHODOWHFRVWXULVHFHUH VWRFXORSWLPúLJHVWLXQHDRSWLP 6ROX LH F

F

GHFL U

F F F

2UJDQL] PFDOFXOHOHDVWIHO

[ SLHVHvQORFXLWH IUHFYHQ HDEVROXWH 1 L S [ 3 ;

[ ) V

2EVHUY P F ) U ) GHFL VWRFXO RSWLP HVWH V SLHVHGHVFKLPESHPDúLQ vQFRQGL LLOHXQXLFRVWPLQLP

&

[

[

¦ [ S [ ¦ [ S [

&D]XOFRQWLQXX

§V [· ¸¸ © I [ ¹

1RW PFX (V YDULDELODDOHDWRDUHH[FHGHQWGHVWRFFXUHSDUWL LD (V ¨¨ V

[ > V @ FX PHGLD 0 (V

³ V [ I [ G[ úL / YDULDELOD DOHDWRDUH OLSV V

GH

§ [ V· ¸¸ [ >V f FXPHGLD 0 /V © I [ ¹

VWRFFXUHSDUWL LD /V ¨¨

f

³ [ V I [ G[ V

$VWIHOIXQF LDRELHFWLYDYDORULLPHGLLDFKHOWXLHOLORUWRWDOHHVWH V

f

V

& V F ³ V [ I [ G[ F ³ [ V I [ G[

3XQHPFRQGL LDGHPLQLPSHQWUXIXQF LD & V RE LQHP V

f

V

& c [ F ³ I [ G[ F ³ I [ G[

úLQRW P

) V

V

³ I [ G[

5H]ROY PHFXD LD

& cV

'LQUHOD LLOH RE LQHP

F) V F ) V

úLGHFLDYHP

) V

F F F

$VWIHOVROX LDRSWLP VÖ HVWHVROX LDHFXD LHL ) V U XQGH U DUHDFHHDúL VHPQLILFD LHFDvQFD]XOGLVFUHW 2EVHUY PF H[WUHPXOXQLF ) V HVWHQHGHVFUHVF WRDUH HVWHXQPLQLPF FL

& ccVÖ !

([HPSOX 'LQ GDWHOH VWDWLVWLFH VH úWLH F FHUHUHD vQ WRQH SHQWUX XQ DQXPLW SURGXVHVWHRYDULDELO DOHDWRDUHFRQWLQX FXGHQVLWDWHDGHSUREDELOLWDWH

I [

° [ SHQWUX [ >@ ® ° SHQWUX [ >@ ¯

ÌQLSRWH]DvQFDUHSLHUGHUHDSHQWUXRWRQ GHSURGXVHVWHGH XPLDUvQ FD]XOOLSVHLGHSURGXVVHIDFFKHOWXLHOLVXSOLPHQWDUHGH XPV VHRUJDQL]H]H JHVWLXQHDRSWLP 6ROX LH $YHP F HFXD LD ) V

F

U XQGH V

) V

³ I [ G[

V V

'LQ HFXD LD F FL V

DVWIHO F U

³ [ G[

3HQWUX D J VL 6 UH]ROY P

[ [

RE LQHP VÖ

V

V V

VLQJXUD VROX LH FRQYHQDELO

> @ 3HQWUX FDOFXOXO JHVWLXQLL RSWLPH vQORFXLP vQ IRUPXOD

úLRE LQHP

· §· § · § & ¨ ¸ ³ [ ¨ [ ¸ G[ ³ [ ¨ [ ¸ G[ ¹ ©¹ © ¹ ©

0RGHOGHVWRFDUHDXQXLSURGXVFXFHUHUHDOHDWRDUHFX FRVWGHVWRFDUHúLFRVWGHSHQDOL]DUHSHQWUXOLSV GHVWRF

)LH ; R YDULDELO DOHDWRDUH FH UHSUH]LQW FHUHUHD OD XQ PRPHQW GDW

§ [ ·

§ [ · ¸¸ SHQWUX FHUHUH GLVFUHW úL ; ¨¨ © I [ ¹ [ > f SHQWUX FHUHUH FRQWLQX FRVWXO XQLWDU GH VWRFDM HVWH FV FRVWXO XQLWDU

¸¸ [ FX UHSDUWL LD ; ¨¨ © S [ ¹

GH SHQDOL]DUH SHQWUX OLSV GH VWRF HVWH F S LDU QLYHOXO VWRFXOXL OD XQ PRPHQW GDWHVWH V ÌQJHVWLXQHDDFHVWXLVWRFSHRSHULRDG 7 VHSRWLYLGRX VLWXD LLúLDQXPH &HUHUHD QX GHS úHúWH VWRFXO GHFL H VDWLVI FXW vQ WRDW SHULRDGD 7 DGLF [ d V YH]LILJXUD &HUHUHD HVWH PDL PDUH GHFkW VWRFXO [ ! V SH SHULRDGD 7 FHUHUHD HVWH VDWLVI FXW vQSHULRDGD 7 FHUHUHDQXHVWHVDWLVI FXW SHULRDGDGHSHQXULH úL

7 7

7 YH]LILJXUD

)LJXUD

)LJXUD

9RPVWXGLDVHSDUDWFD]XOFHUHULLGLVFUHWHúLFD]XOFHUHULLFRQWLQXH

&D]XOGLVFUHW

3HQWUX VLWXD LD GLQ ILJXUD VH REVHUY F VWRFXO PHGLX SHQWUX FDUH V

[·

§

¦ ¨© V ¸¹ S[ 3HQWUX VLWXD LD GHVFULV vQ

VH SO WHúWH FRVWXO XQLWDU FV HVWH

[ f

V S[ SHQWUX FDUH VH YRU IDFH FKHOWXLHOL [ V XQLWDUH GH VWRFDM FV SH SHULRDGD 7 úL R OLSV PHGLH GH VWRF SHQXULH PHGLH ILJXUD VWRFXO PHGLX YD IL

¦

f

[V S [ SHQDOL]DW FXXQFRVWXQLWDUGHSHQDOL]DUH F S SHSHULRDGD 7 V

¦

[

9RPGHWHUPLQDIXQF LDRELHFWLYFHUHSUH]LQW FKHOWXLHOLOHPHGLLWRWDOHSHQWUX SHULRDGD7

&7 V

7 7

V f [· V § FV7 ¦ ¨ V ¸ S [ FV7 ¦ S [ ¹ [ © [ V f [V S[ F S7 ¦ [ V

ÌQILJXUDVHIRUPHD] WULXQJKLXULGUHSWXQJKLFHDVHPHQHDúLYRPDYHD

V 7 úL [ 7

[V GHXQGH [ V 7 7 úL 7 [

[V 7 [ ÌQORFXLPUHOD LD vQH[SUHVLDOXL &7 V úLRE LQHP &7 V

ª V § [· V 7 «FV ¦ ¨ V ¸ S [ FV ¹ «¬ [ ©

f

¦

[ V

S [ [

f º [ V S [ » FS ¦ [ V [ »¼

1RW PFX & V FKHOWXLHOLOHWRWDOHPHGLLvQXQLWDWHDGHWLPSúLUHOD LD GHYLQH &7 V 7& V

6WRFXORSWLP VÖ VHYDRE LQHGLQFRQGL LDGHPLQLPSHQWUXIXQF LD & V 'LQ FRQGL LDGHPLQLPSHQWUXIXQF LLGLVFUHWH & VÖ ! & VÖ & VÖ UH]XOW F YDORDUHDRSWLP VÖ VHRE LQHFDVROX LHDVLVWHPXOXLGHLQHFXD LL

& V & V ! ® ¯& V & V !

&DOFXO P & V FXDMXWRUXOUHOD LHL úLDYHP

& V

V [· § FV ¦ ¨ V ¸ S [ FV ¹ [ © V

f

¦

S [

[ V

[

[ V S [ FS ¦ [ V [

f

5HVFULHPVXPHOHGLQSDUWHDDGRXDDHJDOLW LL2E LQHP V

[·

§

V

[·

§

V

¦ ¨© V ¸¹ S[ ¦ ¨© V ¸¹ S[ ¦ S[ [

[

[

V [· V § SV ¦ S[ ¨ V ¸ S[ ¦ ¹ [ © [ f f S[ S [ SV ¦ ¦ [ V [ V [ V [ V

[ V S[ f [ V S[ ¦ ¦ [ [ f

[ V

[ V

f S[ [V S[ ¦ [ V [ V [

[ V S[ f ¦ [ ¦ f

[ V

[

[ V S[ f S[ V f S[ ¦ [ ¦ ¦ [ f

[ V

[ V

[ V

ÌQORFXLPUHOD LLOH vQ RE LQHP

ª V · f S[ º § & V & V FV F S «¦ S [ ¨ V ¸ ¦ FS ¹ [ V [ »¼ © ¬[

VDX

& V & V

F

V

F S /V F S

XQGH

· f S[ § S [ V ¨ ¸¦ ¦ ¹ [ V [ © [ V

/V $QDORJYRPJ VL

& V & V FV F S /V F S

ÌQORFXLPUHOD LLOH úL vQ DYHP

°FV F S /V F S ! ® °¯ FV F S /V F S !

GHXQGHRE LQHPF

FS

FX U

FV F S

/V U /V

9DORDUHD RSWLP D VWRFXOXL VÖ VH RE LQH FD VROX LH D LQHFXD LHL 6H SRDWHDU WDXúRUF & ccVÖ ! úLGHFL VÖ VROX LDLQHJDOLW LL HVWHSXQFWGH

PLQLP*HVWLXQHDRSWLP VHRE LQHFDOFXOkQGSH & VÖ ([HPSOX 'LQ GDWHOH VWDWLVWLFH VH FXQRDúWH F FHUHUHD GH SLHVH GH VFKLPE D XQXLDWHOLHUDXWRSHRSHULRDG GH V SW PkQL VHSUH]LQW DVWIHO FHUHUHD [ QXP UGHSLHVHGHVFKLPE

SUREDELOLWDWHD

S[

6HúWLHF VHDGPLWFKHOWXLHOLGHVWRFDMSH]LGH XPúLOLSVDGHSLHVH GLQ VWRF DGXFH R SLHUGHUH GH XP]L SHQWUX R SLHV OLSV V VH GHWHUPLQH VWRFXORSWLP 6ROX LH F S

úL FV

GHFL U

2UJDQL] PGDWHOHDVWIHO

V [ S[ ¦ S[

S[ [

[

2EVHUY PF

¦ [

/ U

S[ § · S [ /V ¨ V ¸¦ [ ¹[ [ ©

/ UH]XOW VÖ

&D]XOFRQWLQXX

5H]ROYkQG FDOFXOHOH VLPLODU FD úL vQ FD]XO GLVFUHW YRP VFULH IXQF LD RELHFWLY±FKHOWXLHOLWRWDOHPHGLLDVWIHO V f f I [ [ V [· § & V FV ³ ¨ V ¸ I [ G[ V FV ³ G[ F S ³ I [ G[ [ [ © ¹ V V 6WRFXORSWLP VÖ VHRE LQHGLQFRQGL LDGHRSWLPSHQWUXIXQF LD & V )XQF LD

FV úL F S FV

& V vúLDWLQJHPLQLPXOvQSXQFWXO VÖ SHQWUXFDUH /V U XQGH U I [ ) V V ³ G[ LDU ) V [ V f

/V

V

V

³ I [ G[ $VWIHO

f

& cV FV ³ I [ G[ VFV ³

5H]ROY PHFXD LD & cV f

) V V ³ V

V

I [ [V G[ F S ³ I [ G[ [ [ V f

úLRE LQHP

I [ G[ [

FS F S FV

VDX /V

U

6ROX LDHFXD LHL /V U RQRW PFX VÖ úLSHQWUXF & ccV ! DFHVWDHVWH SXQFWGHPLQLP ([HPSOX &HUHUHD XQXL SURGXV HVWH R YDULDELO DOHDWRDUH ; FDUH DUH UHSDUWL LD

I [

[ ° ® ° ¯

SHQWUX [ >@

SHQWUX [ >@ &RVWXO VWRF ULL XQXL SURGXV HVWH XP OLSVD DFHVWXL SURGXV VH SHQDOL]HD] FXXQFRVWXQLWDUVXSOLPHQWDUGHUHDSURYL]LRQDUHGH XP&DUH

HVWHVWRFXORSWLPúLJHVWLXQHDRSWLP FRQVLGHUkQGFRVWXOGHVWRFDMQHJOLMDELO 6ROX LH9ROXPXORSWLPVHGHWHUPLQ UH]ROYkQGHFXD LD XQGH

) V

V

[ ³ G[

V I [ G[ GDF V >@ úL ³ [ V f

[

³ [ G[ V

V

FV

&XP F S

U

5H]ROY P HFXD LD

V V V GH XQGH VÖ VLQJXUD U G FLQ FRQYHQDELO FHDODOW V QXDSDU LQHGRPHQLXOXLGHGHILQL LHDIXQF LHLFHUHUH 3HQWUX D GHWHUPLQD FRVWXO PLQLP vQORFXLP V FX vQ IRUPXOD FH

GHYLQH

&

[ [ G[ [·[ [ § ³ ¨ ¸ G[ ³ G[ ³ ¹ [ [ ©

(/(0(17('(7(25,$$ù7(37 5,, ÌQYLD DGH]LFX]LvQSURGXF LDGHEXQXULúLGHVHUYLFLLvQWkOQLPIHQRPHQH GHDúWHSWDUHJHQHUDWHILHGHRDPHQLILHGHPDúLQLDWXQFLFkQGFHUHUHDFXUHQW GH VHUYLFLLGHS úHúWHFDSDFLWDWHDGHDDVLJXUDVHUYLFLLOHFHUXWH$VWIHOGDF QXP UXOGH RDPHQLVDXGHPDúLQLFDUHDúWHDSW HVWHSUHDPDUHODXQPRPHQWGDWDWXQFLYRP DYHDFKHOWXLHOLQHSURGXFWLYHSHQWUXvQWUHSULQGHUHDUHVSHFWLY 'HDFHHDVHLPSXQH HODERUDUHD XQXL SODQ DGHFYDW GH DúWHSWDUH GLQ SXQFW GH YHGHUH HFRQRPLF FDUH V FRQGXF ODVDWLVIDFHUHDFHUHULORUGHVHUYLFLLvQFRQGL LLFkWPDLDYDQWDMRDVH 3ULPHOH OXFU UL OHJDWH GH VLVWHPHOH GH DúWHSWDUH DSDU LQ OXL (UODQJ UHIHULWRDUHODSUREOHPDvQFHUF ULLUD LRQDOHDFHQWUDOHORUWHOHIRQLFH 7HRULD DúWHSW ULL WHRULD ILUHORU GH DúWHSWDUH VDX WHRULD FR]LORU HVWH DFHD UDPXU DPDWHPDWLFLLFHVWXGLD] IHQRPHQHOHGHDúWHSWDUH 0RGHOHOH GH DúWHSWDUH VDX GLYHUVLILFDW FRQWLQXX úL DX S WUXQV vQ FHOH PDL YDULDWHGRPHQLLDWkWGLQVIHUDSURGXF LHLFkWúLGLQFHDDVHUYLFLLORU 9RPHQXPHUDSULQFLSDOHOHHOHPHQWHDOHSUREOHPHLIHQRPHQXOXLGHDúWHSWDUH 6WUXFWXUDGHED] úLFDUDFWHULVWLFLOHXQXLVLVWHPGHDúWHSWDUH ÌQWUXQPRGHOGHDúWHSWDUHSURFHVXOGHED] HVWHXUP WRUXOXQLW LOHFDUHFHUV ILH VHUYLWHVXQWJHQHUDWHvQWLPSGHRVXUV DLQWU ULORU6HUYLUHDHVWHDVLJXUDW GHXQDVDXPDL PXOWHVWD LGHVHUYLUH8QLW LOHFHQXSRWILVHUYLWHLPHGLDWYRUIRUPDFRDGDVDXILUXOGH DúWHSWDUH 'HFL x 6XUVDUHSUH]LQW PXO LPHDXQLW LORUFHVROLFLW XQVHUYLFLXODXQPRPHQW GDW (D SRDWH IL ILQLW VDX LQILQLW 6RVLUHD XQLW LORU vQ VLVWHPXO GH DúWHSWDUH GHWHUPLQ YDULDELOD DOHDWRDUH ; D QXP UXOXL GH XQLW L FH LQWU vQ VLVWHP vQ XQLWDWHDGHWLPS x )LUXO GH DúWHSWDUH HVWH GHWHUPLQDW GH QXP UXO XQLW LORU FDUH DúWHDSW ILQLWVDXLQILQLW OLPLWDWVDXQHOLPLWDW x 6WD LD GH VHUYLFLX UHSUH]LQW ILH XQ OXFU WRU PHFDQLF DXWR FDVLHU YL]LWDWRUHWF ILHRPDúLQ FHHIHFWXHD] XQVHUYLFLXFHDIRVWVROLFLWDW9RPQRWD FX < YDULDELODDOHDWRDUHFHUHSUH]LQW WLPSXOGHVHUYLUHDXQHLXQLW LvQVWD LDGH VHUYLFLX 'LQSUDFWLF VHLDXYDORULOHHPSLULFHSHQWUXYDULDELOHOHDOHDWRDUH ; úL < FX DMXWRUXO F URUD VH GHWHUPLQ OHJLOH GH UHSDUWL LH úL SDUDPHWULL SHQWUX YDULDELOHOH DOHDWRDUH ; úL < SULQDMXVWDUHDXQHLGLVWULEX LLHPSLULFHODRGLVWULEX LHWHRUHWLF IRORVLQG PHWRGHOH GLQ WHRULD SUREDELOLW LORU úL VWDWLVWLFD PDWHPDWLF $QVDPEOXO IRUPDW GLQ ILUXO GH DúWHSWDUH úL VWD LLOH GH VHUYLUH IRUPHD] VLVWHPXO GH DúWHSWDUH 6FKHPDWLFVLWXD LDVHSUH]LQW DVWIHO

)LJXUD6LVWHPGHDúWHSWDUH

/D XQ PRPHQW GDW R XQLWDWH FH DúWHDSW V ILH VHUYLW HVWH DOHDV SHQWUX VHUYLUHSULQWURDQXPLW UHJXO QXPLW GLVFLSOLQ GHVHUYLUH &HDPDLGHVXWLOL]DW GLVFLSOLQ GHVHUYLUHHVWHÄSULPXOVRVLWSULPXOVHUYLW´ VDX),)2 RDOW PHWRG FXDSOLFD LLvQPHWDOXUJLHPHWRGDÄXOWLPXOVRVLWSULPXO VHUYLW´/,)2 'LVFLSOLQDGHVHUYLUHHVWHXQHOHPHQWGHFRUHFWLWXGLQHvQWUHFOLHQ L GDUQXHVWHLPSRUWDQW SHQWUXVWD LDGHVHUYLUHFHIDFHDFHOHDúLVHUYLFLLSHQWUXRULFH FOLHQW 'XS QXP UXO XQLW LORU GH VHUYLUH úL QXP UXO VWD LLORU VHUYLWH SXWHP DYHD XUP WRDUHDFODVLILFDUHDIHQRPHQHORUGHDúWHSWDUH XQILURVWD LH XQILUPDLPXOWHVWD LL PDLPXOWHILUHRVWD LH PDLPXOWHILUHPDLPXOWHVWD LL LDUGXS QDWXUDVRVLULORUVDXDVHUYLFLLORUSXWHPDYHD PDLPXOWHILUHVRVLULFRQVWDQWHVHUYLFLLFRQVWDQWH VRVLULFRQVWDQWHVDXVHUYLFLLDOHDWRDUH VRVLULDOHDWRDUHFXVHUYLFLLFRQVWDQWH VRVLULDOHDWRDUHVHUYLFLLDOHDWRDUH 0 VXUDUHDSHUIRUPDQ HORUVLVWHPXOXLGHDúWHSWDUH 5HOD LLGHED] ÌQWURSUREOHP GHDúWHSWDUHVHvQWkOQHVFXUP WRULLLQGLFDWRULSULQFLSDOL P HVWHQXP UXOGHXQLW LDOHSRSXOD LHLFHVRVHVFvQVLVWHP P SRDWHILILQLW VDXLQILQLW V HVWHQXP UXOGHVWD LLGHVHUYLFLX SQ W HVWHSUREDELOLWDWHDFDvQVLVWHPXOGHDúWHSWDUHV VHJ VHDVF Q XQLW LOD PRPHQWXO W 9RPQRWDVLPSOLILFDW SQ

QW HVWHQXP UXOGHXQLW LFHVHJ VHVFvQVLVWHPXOGHDúWHSWDUHODPRPHQWXO W FDUHHVWHRYDULDELO DOHDWRDUHFXGLVWULEX LD

§ QW ¨¨ © S

S

" Q " P· ¸ S " SQ " SP ¸¹

YDORDUHD VD PHGLH QXP UXO PHGLX GH XQLW L GLQ VLVWHP OD XQ PRPHQW W YD IL

QW

P

¦ QS Q

Q

&kQG P

f

f VHLPSXQHFRQGL LDFD QW

¦ QS Q

V ILHFRQYHUJHQW

Q

Q I W HVWH R YDULDELO DOHDWRDUH FH UHSUH]LQW QXP UXO GH XQLW L GLQ ILUXO GH DúWHSWDUHODPRPHQWXO W FDUHVHUHSUH]LQW SULQ

" K " P V· § V ¸ Q I W ¨ S S " SK V " SP ¸ ¨¦ L V ©L ¹ FXPHGLD Q I W QXP UXOPHGLXGHXQLW LFHVHDIO vQILUGDW GH f

Q I W 3HQWUX P

f VHULD

¦ NS N

f

¦ Q V S

VN

Q V

f

¦ Q V S

Q

Q V

Q

Q I W YDWUHEXLV ILHFRQYHUJHQW

QV W UHSUH]LQW QXP UXOGHXQLW LFHVXQWVHUYLWHODXQPRPHQW W

FXPHGLD

§ QV W ¨ S ¨ © QV W

GHFL YRP DYHD UHOD LD QW

S

"

V · ¸ " ¦ SQ ¸ Q V ¹ f

V

f

N

Q V

¦ NSN V¦ SQ Q I W QV W FH H[LVW úL vQWUH YDORULOH PHGLL

QV W UHSUH]LQW QXP UXOPHGLXGHXQLW LVHUYLWHODPRPHQWXO W 3QW ! N SUREDELOLWDWHDFDQXP UXOXQLW LORUGLQVLVWHPODPRPHQWXO W V ILHPDLPDUHGHFkW N 'DU N

3QW ! W 3QW d N ¦ SL L

W I WLPSXOPHGLXGHDúWHSWDUHvQILUDXQHLXQLW L W V WLPSXOPHGLXGHDúWHSWDUHDXQHLXQLW LvQVLVWHP 2EVHUYD LH W I úL W V GHSLQG GH OHJLOH VHUYLFLXOXL úL VRVLULORU úL YRU IL GHWHUPLQDWHSHQWUXILHFDUHPRGHOvQSDUWH

/HJLSUREDELOLVWLFHDOHVRVLULORUúLDOHVHUYLFLLORU

)LH ; YDULDELODDOHDWRDUHFHUHSUH]LQW QXP UXOGHXQLW LVRVLWHvQXQLWDWHD GHWLPSvQWUXQVLVWHPGHDúWHSWDUH9UHPV VWXGLHPUHSDUWL LDYDULDELOHL ; DYkQG XUP WRDUHOHLSRWH]H 3UREDELOLWDWHDVRVLULLXQHLXQLW LODXQPRPHQWGDWHVWHFRQVWDQW úLQXGHSLQGH GHFHVDvQWkPSODWDQWHULRU 3UREDELOLWDWHDVRVLULLXQHLXQLW LvQWUXQLQWHUYDOIRDUWHPLFGHWLPS W W K GH OXQJLPH K HVWH SURSRU LRQDO FX OXQJLPHD LQWHUYDOXOXL RULFDUH DU IL W DGLF HVWH OK 2K XQGH

2K Ko K

OLP 2K úL OLP Ko

XQGH O HVWHXQFRHILFLHQWGHSURSRU LRQDOLWDWHFRQVWDQWúLSR]LWLY 3UREDELOLWDWHDFDvQLQWHUYDOXOGHWLPS W W K V ILHPDLPXOWGHFkWRVRVLUH HVWHDSUR[LPDWLYHJDO FX]HURFkQG K vQGHSOLQHúWHFRQGL LD 6HDUDW F vQDFHVWHLSRWH]HDYHP 3URSR]L LD 9DULDELOD DOHDWRDUH ; FH UHSUH]LQW QXP UXO GH XQLW L VRVLWHSHXQLWDWHDGHWLPSvQWUXQVLVWHPGHDúWHSWDUHDUHUHSDUWL LD3RLVVRQ $GLF SUREDELOLWDWHD FD vQ LQWHUYDOXO GH WLPS W W ! V DLE ORF Q VRVLUL HVWH HJDO

Q O W OW FX 3Q W H O ! Q ` 3HQWUX W

WLPS HDHVWHHJDO FX 3Q

Q OQ O H Q

XQLWDWHD GH

$VWIHO REVHUY P F O FRHILFLHQWXO GH SURSRU LRQDOLWDWH LQWURGXV vQ LSRWH]D UHSUH]LQW QXP UXOPHGLXGHXQLW LVRVLWHvQXQLWDWHDGHWLPS ÌQLSRWH]HOH DSOLFDWHSHQWUXQXP UXOXQLW LORUVHUYLWHGHRVWD LHFH OXFUHD] QHvQWUHUXSW YRP RE LQH UD LRQkQG VLPLODU QXP UXO GH VHUYLFLL FH SRW IL I FXWH GH R VWD LH vQWUXQ WLPS W HVWH R YDULDELO SRLVVRQLDQ 'DF P HVWH FRHILFLHQWXO GH SURSRU LRQDOLWDWH LQWURGXV vQ HO YD IL QXP UXO PHGLX GH XQLW L VHUYLWHvQXQLWDWHDGHWLPS 3URSR]L LD 9DULDELOD DOHDWRDUH < FH UHSUH]LQW WLPSXO GLQWUH GRX VRVLULFRQVHFXWLYHDUHRUHSDUWL LHH[SRQHQ LDO 'HPRQVWUD LH6HFRQVLGHU FDPRPHQWLQL LDOPRPHQWXOvQFDUHDVRVLWSULPD GLQWUH FHOH GRX XQLW L úL FDOFXO P SUREDELOLWDWHD FD WLPSXO < GLQWUH FHOH GRX VRVLULV ILHPDLPDUHGHFkWXQWLPSRDUHFDUH W ! 1RW PFX 3 W SUREDELOLWDWHDFDvQWLPSXO W V QXDYHPQLFLRVRVLUHGHFL

3< ! W 3 W H OW GHXQGH 3< d W H OW

$VWIHO IXQF LD GH UHSDUWL LH D YDULDELOHL < YD IL ) W H OW VSHFLILF YDULDELOHL < GH UHSDUWL LH H[SRQHQ LDO FX GHQVLWDWHD GH UHSDUWL LH I W ) cW OH OW úLGHFL

0 <

W

f

³ WI W GW ³ WOH

OW

GW

O

ÌQ FRQFOX]LH LQWHUYDOXO PHGLX GLQWUH GRX VRVLUL FRQVHFXWLYH HVWH LQWHUYDOXO QXP UXOXLPHGLXGHVRVLULvQXQLWDWHDGHWLPS 2EVHUYD LH$QDORJSXWHPGHGXFHF WLPSXOGLQWUHGRX VHUYLFLLFRQVHFXWLYH HVWHRUHSDUWL LHH[SRQHQ LDO úLF LQWHUYDOXOPHGLXGLQWUHGRX VHUYLFLLFRQVHFXWLYH HVWHLQYHUVXOQXP UXOXLPHGLXGHVHUYLFLLvQXQLWDWHDGHWLPSSHQWUXQRL

P

([HPSOX 'LQ GDWHOH VWDWLVWLFH QXP UXO FOLHQ LORU FH VRVHVF OD R ILUP VXQW SRLVVRQHQHFXQXP UXOPHGLXGHRSHUVRDQ SHRU LDUWLPSXOPHGLXGHVHUYLUHD XQXL FOLHQW HVWH VHFXQGH 6 VH GHWHUPLQH LQWHUYDOXO PHGLX GLQWUH GRX VRVLUL FRQVHFXWLYHúLSUREDELOLWDWHDFDvQ PLQXWHV QXYLQ QLFLXQFOLHQW 6ROX LH)RORVLQGFDXQLWDWHGHWLPSPLQXWXOQXP UXOPHGLXGHVRVLULSHPLQXWYD IL O

O

,QWHUYDOXO PHGLX vQWUH GRX VRVLUL FRQVHFXWLYH YD IL OW Q UH]XOW &XP 3Q W H OW Q

3 H

H #

'HGXFHUHDHFXD LLORUGHVWDUHSHQWUXXQIHQRPHQ GHúWHSWDUHvQUHJLPVWD LRQDU

)LHVLVWHPXOGHDúWHSWDUHFDXQVLVWHPFXVW ULOH ( ( (Q VWDUHD (Q ILLQG VWDUHDVLVWHPXOXLvQFD]XOvQFDUHvQHOVHJ VHVF Q XQLW L$VRFLHPILHF UHLVW UL (Q R SUREDELOLWDWH 3Q W GH DSDUL LH FH GHSLQGH GH WLPSXO W 3UHVXSXQHP F IXQF LLOH 3Q W DXSURSULHW LGHFRQWLQXLWDWHúLGHULYDELOLWDWHSRWULYLWHúLF f

¦ 3 W Q

Q

/DPRPHQWXO W SUHVXSXQHPF QXH[LVW QLFLRXQLWDWHvQVLVWHPGHFLVH DGDXJ FRQGL LLOHLQL LDOH

SHQWUX Q 3Q ® ¯ SHQWUX Q z

9RPGHGXFHXQVLVWHPGHHFXD LLFHFRQGXFHODGHWHUPLQDUHDSUREDELOLW LORU 3Q W QXPLWVLVWHPXOHFXD LLORUGHVWDUH$VWIHOYRPGHWHUPLQDUHDFRPSRUWDPHQWXO

^

`

úLSDUDPHWULGHSHUIRUPDQ DVLVWHPXOXLFXDMXWRWXOSUREDELOLW LORU 3Q W

Q`

6HSUHVXSXQFXQRVFXWHXUP WRDUHOH 3UREDELOLWDWHD GH WUHFHUH GH OD VWDUHD (Q OD VWDUHD (Q vQ LQWHUYDOXO GH WLPS

IRDUWH VFXUW W W K HVWH O Q K 2K úL FRUHVSXQGH XQHL VRVLUL vQ VLVWHP 3UREDELOLWDWHD GH D QX DYHD QLFL R VRVLUH vQ VLVWHP YD IL >O Q K 2K @

3UREDELOLWDWHD GH WUHFHUH GLQ VWDUHD (Q vQ VWDUHD (Q vQ LQWHUYDOXO GH WLPS

W W K

HVWH P Q K 2K úL YD FRUHVSXQGH XQHL VHUYLUL SOHF UL

3UREDELOLWDWHDGHDQXDYHDQLFLRVHUYLUHHVWH >P Q K 2K @

3UREDELOLWDWHDGHWUHFHUHGLQVWDUHD (Q vQWURVWDUH (Q N VDX (Q N FX N `

N ! HVWH 2K $OWIHOVSXVvQWUXQLQWHUYDOVFXUWGHWLPSSRDWHDYHDFHOPXOW

RVRVLUHúLFHOPXOWRVHUYLUH

&D]XO Q &DOFXO PSUREDELOLWDWHDFHvQVLVWHPXOGHDúWHSWDUHV QXH[LVWHQLFLRXQLWDWH OD PRPHQWXO W K 3 W K LQkQG FRQW GH VLWXD LLOH SRVLELOH OD PRPHQWXO W 6LWXD LLOHDFHVWHDSRWIL D QXH[LVW QLFLRXQLWDWHODPRPHQWXO W úLQXVRVHúWHQLFLRXQLWDWHvQLQWHUYDOXO W W K E ODPRPHQWXO W H[LVW RVLQJXU XQLWDWH 6LWXD LLOHD úLE UHSUH]LQW HYHQLPHQWHLQFRPSDWLELOHFDUHVXQWIRUPDWHGLQ HYHQLPHQWHLQGHSHQGHQWHúLQHJOLMkQGIXQF LD 2K ILLQGIRDUWHPLF GDF K o SUREDELOLWDWHD 3 W K YDIL

3 W K 3 W O K 3 W PK OK 5HVFULLQGúLWUHFkQGvQVWkQJDSH 3 W DYHP

VDX

3 W K 3 W O K3 W PK3 W OPK 3 W ÌPS U LPSULQ K úLWUHFHPODOLPLW 3 W K 3 W OLP O 3 W P3 W Ko K

3cW O 3 W P3 W

&D]XO Q !

&DOFXO P SUREDELOLWDWHD FD vQ VLVWHPXO GH DúWHSWDUH V H[LVWH Q XQLW L OD PRPHQWXO W K 3Q W K LQkQG FRQW GH XUP WRDUHOH VLWXD LL SRVLELOH OD PRPHQWXO W D /DPRPHQWXO W H[LVW Q XQLW LvQVLVWHPQXVRVHúWHQLFLRXQLWDWHúLQXSOHDF QLFLRXQLWDWHvQLQWHUYDOXO W W K E /DPRPHQWXO W H[LVW Q XQLW LvQVLVWHPSOHDF RXQLWDWHúLQXVRVHúWHQLFL RXQLWDWHvQLQWHUYDOXO W W K F /DPRPHQWXO W H[LVW Q XQLW LvQVLVWHPVRVHúWHRXQLWDWHúLQXSOHDF QLFL RXQLWDWHvQLQWHUYDOXO W W K G /DPRPHQWXO W H[LVW Q XQLW LvQVLVWHPVRVHúWHRXQLWDWHúLSOHDF RXQLWDWH vQLQWHUYDOXO W W K (YHQLPHQWXOGHDH[LVWD Q XQLW LvQVLVWHPXOGHDúWHSWDUHODPRPHQWXO W K UHSUH]LQW UHXQLXQHDDSDWUXHYHQLPHQWHLQFRPSDWLELOHúLILHFDUHHVWHRLQWHUVHF LH GHWUHLHYHQLPHQWHLQGHSHQGHQWH3UREDELOLWDWHDF XWDW 3Q W K YDIL

3Q W K 3Q W O Q K P Q K 3Q W O Q K P Q K

3Q W O Q K P Q K 3Q W O QP Q K 7UHFHP 3Q W vQPHPEUXOVWkQJvPS U LPOD K WUHFHPODOLPLW úLRE LQHP 3 W K 3Q W OLP Q O Q P Q 3Q W P Q 3Q W O Q 3Q W Ko K

5HVFULLQGDYHP

3QcW O Q 3Q W O Q P Q 3Q W P Q 3Q W

5HOD LLOH úL IRUPHD] VLVWHPXO HFXD LLORU GH VWDUH FH VH UH]ROY vQFRQGL LLOH úL $FHVW VLVWHP YD IL UH]ROYDW vQ UHJLP VWD LRQDU DWXQFL FkQG SUREDELOLW LOH 3Q W QXGHSLQGGHWLPSDGLF 3QcW UH]XOWkQGF 3Q W SQ FRQVWDQWRULFH

Q

6LVWHPXOGHYLQH

O S O S ® ¯O Q SQ O Q P Q SQ P Q SQ

&RQGL LD GHYLQH

f

¦S Q

Q

Q t

6LVWHPXO HVWHFXQRVFXWVXEQXPHOHGHVLVWHPXOHFXD LLORUGHVWDUHvQ UHJLP VWD LRQDU 9RP FRQYHQL FD vQ DFHVW FD] QLFL FHLODO L LQGLFDWRUL QX VH VFULX IXQF LHGH W

'LQSULPDHFXD LHDVLVWHPXOXL RE LQHP

O S P úLvQORFXLPvQHFXD LD SHQWUX Q RE LQHP O S O P S P S S

GHXQGHUH]XOW

S $U W PSULQLQGXF LHGXS Q F

O O S P P

O OO Q S PP P Q

SQ

'LQHFXD LD DVLVWHPXOXL VFULV SHQWUX Q DYHP O Q SQ O Q P Q SQ P Q SQ GHXQGH

SQ

OQ P O SQ Q SQ Q SQ P Q P Q P Q

LQHPFRQWvQ GHLSRWH]DGHLQGXF LHúLGHIDSWXOF SQ GHXQGHUH]XOW LPHGLDWF

O Q SQ PQ

O OO Q S PP P Q

SQ

'HFLDPGHWHUPLQDWH[SUHVLDWXWXURUSUREDELOLW LORUvQIXQF LHGH S

SQ

Q

O N PN

S N

'DF vQORFXLP vQUHOD LD RE LQHP

S

Q f § O · ¨¨ ¦ N ¸¸ © Q N PN ¹

0RGHOHGHDúWHSWDUH 9RPSUH]HQWDFkWHYDPRGHOHGHDúWHSWDUHFXQRWD LLOHGHULJRDUH2QRWD LH SHQWUXPRGHOXOGHDúWHSWDUHDIRVWLQWURGXV GH'.HQGDOOvQúLDUHLQIRUPD LD DVXSUDPRGHOXOXLRUJDQL]DWDVWIHO D E F G H I 9RPQRWDFX 0 IDSWXOF VRVLULOHVDXVHUYLULOH DXUHSDUWL LD3RLVVRQ

'H H[HPSOX PRGHOXO 0 0 V ),)2 1 f GHVFULH XQ PRGHO FX VRVLUL SRLVVRQLHQH VHUYLUL SRLVVRQLHQH V VWD LL GH VHUYLUL D F UHL GLVFLSOLQ GH VHUYLUHHVWHÄSULPXOVRVLWSULPXOVHUYLW´QXP UXOPD[LPGHFOLHQ LvQVLVWHPILLQG 1 FHSURYLQGLQWURSRSXOD LHLQILQLW 0RGHOFXILUQHOLPLWDW 0 0 ),)2 f f $FHVWPRGHOHVWHGHVFKLVRLQILQLWDWHGHXQLW LvQVXUV FXXQILUúLRVLQJXU VWD LHGHVHUYLUH 6FKHPDWLFPRGHOXOVHSUH]LQW DVWIHO

)LJXUD

8QLW LOHVRVHVFDOHDWRUGXS RUHSDUWL LH3RLVRQGHSDUDPHWUX O LQGLIHUHQW GH VWDUHD VLVWHPXOXL GHFL O Q O 6HUYLUHD QX GHSLQGH GH VWDUHD VLVWHPXOXL GHFL

PQ

P Q ` 7LPSXOSHWUHFXWvQVLVWHPHVWHHJDOFXWLPSXOSHWUHFXWvQILUXOGH

DúWHSWDUHSOXVWLPSXOGHVHUYLUH $VWIHO LQkQG FRQW GH FHOH GH PDL VXV IRUPXOD GH FDOFXO SHQWUX SUREDELOLW LOH SQ vQIXQF LHGH S DYHP Q

§O· ¨¨ ¸¸ S ©P¹

SQ 1RW P FX U

SQ

O IDFWRU GH VHUYLFLX VDX LQWHQVLWDWH GH WUDILF úL RE LQHP P

UQ S 5HOD LD QHFRQGXFHODUHOD LD

S

f § · ¨ ¦ U Q ¸ Q © ¹

3HQWUXFDVXPDVHULHLGHPDLVXVFDUHHVWHRVHULHJHRPHWULF FXUD LD U ! V ILHFRQYHUJHQW VHLPSXQHFRQGL LD U vQDFHVWFD]FDSDFLWDWHDGHVHUYLUHvQ VLVWHPHVWHFRUHVSXQ] WRDUH 'DF U t DWXQFLYRPDYHDDJORPHUDUHDúLVHUYLFLXOQXSRDWHILDVLJXUDWGH RVLQJXU VWD LH ÌQ FD]XO U VXPD VHULHL GLQ SDUDQWH] vQ UHOD LD YD IL XQGH

S

U

GH U

$FXP SXWHP GHWHUPLQD WRDWH FDUDFWHULVWLFLOH PRGHOXOXL 1XP UXO PHGLX GH XQLW LvQVLVWHPILUVWD LH HVWH

Q

f

Q

GDU

f

¦ QU Q

Q

f

f

Q

Q

¦ QUQ U U U ¦ QUQ

¦ QSQ

U U QU Q G U U U Q GU

$VWIHOUHOD LD GHYLQH

Q

G § · ¨ ¸ G U © U ¹

U U

U

1XP UXO GH XQLW L vQ FXUV GH VHUYLUH SRDWH OXD QXPDL YDORULOH úL GHFL

· § ¸¸ úLDWXQFL QV ¨¨ © S S ¹ QV S )RORVLQG IRUPXOD Q

U U

Q I QV RE LQHP F QXP UXO PHGLX GH XQLW L FH

DúWHDSW V ILHVHUYLWHGLQILUXOGHDúWHSWDUH YDIL

QI

Q QV

U U U

GHFL

U VDX Q I U

QI

O PP O

7LPSXOPHGLXGHDúWHSWDUHDXQHLXQLW LvQILU W I HVWHGDWGHUDSRUWXOGLQWUH QXP UXOPHGLXGHXQLW LFHDúWHDSW vQILUúLQXP UXOGHXQLW LHIHFWLYVHUYLWHvQ XQLWDWHDGHWLPS

WI

QI P QV

U P U

LDUWLPSXOGHDúWHSWDUHDXQHLXQLW LvQVLVWHPXOGHDúWHSWDUHHVWH

WV

WI

P

P U

3UREDELOLWDWHDFDQXP UXOXQLW LORUFHVHJ VHVFvQVLVWHPODXQPRPHQWGDW V ILHPDLPDUHGHFkWXQQXP U N YDIL

3Q ! N

f

¦ SQ

Q N

U U GHFL

f

¦ U U U U Q

N

UN

Q N N

U U

U U

N

U

U

N

3Q ! N UN

' PI U DGHPRQVWUDSUREDELOLWDWHDFDRXQLWDWHV DúWHSWHvQILUPDLPXOW GHFkWWLPSXO W 3 W I ! W UH P O W

([HPSOX /D R FDV GH ELOHWH D XQHL VWD LL GH PHWURX VRVHVF vQ PHGLH F O WRULSHRU &DVLHUDVHUYHúWHvQPHGLH F O WRULSHPLQXW D 6 VH VFULH GHQVLWDWHD GH UHSDUWL LH D VRVLULORU úWLLQG F VXQW DOHDWRDUH úL DX UHSDUWL LD3RLVVRQ E 6 VHVFULHUHSDUWL LDWLPSXOXLGHVHUYLUHúWLLQGF HVWHH[SRQHQ LDO F 6 VHVFULHSUREDELOLWDWHDFDvQVLVWHPXOGHDúWHSWDUHV QXH[LVWHQLFLXQF O WRU ODXQPRPHQWGDW G 6 VHVFULHSUREDELOLWDWHDFHvQVLVWHPV H[LVWHGRLF O WRULODXQPRPHQWGDW H 7LPSXOPHGLXGHDúWHSWDUHDXQXLF O WRUSkQ V ILHVHUYLWúLWLPSXOPHGLXGH DúWHSWDUHvQvQWUHJXOVLVWHPGHDúWHSWDUH 6ROX LH3UREOHPDVHvQFDGUHD] vQFRQGL LLOHPRGHOXOXLSUH]HQWDW8QLWDWHDGHWLPS SHFDUHRDOHJHPHVWHPLQXWXO O F O WRULPLQXW P F O WRULPLQXWGHXQGH

O P

U D O F O WRULPLQXW GHFL UHSDUWL LD VRVLULORU vQ VLVWHP DGLF D YDULDELOHL DOHDWRDUH ÄQXP UXO GH XQLW L VRVLWH vQ VLVWHP SH XQLWDWHD GH WLPS´ HVWH

§ Q · ¨ Q ¸ Q ¨ H ¸ © Q ¹

E WLPSXO GH VHUYLUH DUH R UHSDUWL LH H[SRQHQ LDO FX SDUDPHWUXO P F O WRULPLQXW I [

H W ® ¯

PLQXWHDGLF VHFXQGH F S U

SHQWUX W t 0HGLD WLPSXOXL GH VHUYLUH HVWH SHQWUX W

G S

H W I

WV

§· U S ¨ ¸ ©¹ U PLQXWH P U PLQXW P U

0RGHOFXILUOLPLWDW 0 0 ),)2 1 f

$FHVW PRGHO HVWH DVHP Q WRU FX FHO SUHFHGHQW FX SUHVXSXQHUHD F ILUXO GH DúWHSWDUH HVWH OLPLWDW úL DUH R FDSDFLWDWH P UJLQLW OD 1 XQLW L GHFL vQ ILUXO GH DúWHSWDUH VH SRW DIOD FHO PXOW 1 XQLW L 2ULFH XQLWDWH FDUH VRVHúWH FkQG VLVWHPXOHVWHÄSOLQ´UHIX] V LQWUHvQVLVWHPúLvOS U VHúWHSHQWUXWRWGHDXQD )RUPXOHOH GLQ PRGHOXO SUHFHGHQW YRU IL DGDSWDWH LQkQG FRQW V DYHP 1 WHUPHQL úL QX R LQILQLWDWH DGLF VXPHOH VH YD IDFH QXPDL SkQ OD Q 1 $VWIHO DYHP

1

¦ SQ Q

GHXQGH S

S U U 1

S

U 1 U

U U 1

2EVHUY P F SHQWUX DFHVW PRGHO QX HVWH QHFHVDU FRQGL LD U VXPD SUREDELOLW LORUDYkQGVHQVúLSHQWUX U t 3XWHP LQWHUSUHWD LQWXLWLY F QXP UXO GH XQLW L FH SRW DS UHD vQ VLVWHP HVWH FRQWURODWGHQXP UXOPD[LPGHXQLW LvQFRDG 1 úLQXGHUDWHOHVRVLULORUúL VHUYLFLLORU&DRFRQVHFLQ UDWDVRVLULORU O QXDIHFWHD] FRQGL LLOHGHVWD LRQDULWDWH DOHVLVWHPXOXL 'LQUHOD LD UH]XOW

SQ

Q U °U 1 ® U ° ¯

SHQWUX Q d 1

1

¦ QSQ Q

1

¦ QSQ Q

1

¦ QU Q Q

SHQWUX Q ! 1

1XP UXOPHGLXGHXQLW LvQVLVWHPHVWHGDWGH

Q

U U 1

U U U 1

1

¦ QU

Q

Q

3HQWUX D FDOFXOD XOWLPD VXP

1

¦ QU

Q

YRP GHULYD WHUPHQ FX WHUPHQ

Q

LGHQWLWDWHD

1

¦U

U 1 FHYDGHYHQLSULQGHULYDUH U

Q

Q

1

¦ QUQ Q

$VWIHO

1 U 1 1U 1 U

U 1 U 1 1U 1 U U 1

Q

1XP UXOPHGLXGHXQLW LvQILUXOGHDúWHSWDUHYDIL

QI 6XPD

1

1

¦ QSQ Q

¦ QU

Q

1

¦ QUQ Q

U U 1

U U 1 Q ¦ QU U 1 Q

VH FDOFXOHD] FD úL VXPD DQWHULRDU GRDU F vQ ORF GH 1

Q

DYHP 1 úLYRPRE LQH

U 1U 1 1 U 1 U U 1

QI

7LPSXO PHGLX GH DúWHSWDUH D XQHL XQLW L vQ ILU W I FDUHGXS vQORFXLUHGHYLQH

U 1U 1 1 U 1 P U U 1 LDUWLPSXOPHGLXGHDúWHSWDUHvQVLVWHP W V W I YDIL P WI

WV

1 U 1 1U 1 P U U 1

QI P QV

FX QV

S

([HPSOXÌQWURSDUFDUHPDúLQLOHVRVHVFFRQIRUPOHJLL3RLVVRQFXUDWDGH PDúLQL SH RU 3DUFDUHD DUH ORFXUL 7LPSXO GH VWD LRQDUH D XQHL PDúLQL HVWH H[SRQHQ LDOFXPHGLDGH SHRU D &DUHHVWHSUREDELOLWDWHDFDRPDúLQ V QXDúWHSWH"&DUHHVWHSUREDELOLWDWHDV J VHDVF XQORFOLEHUvQSDUFDUH" E &DUHHVWHWLPSXOPHGLXGHDúWHSWDUHSkQ FkQGRPDúLQ S U VHúWHSDUFDUHD"

6ROX LH &D]XOGLQSUREOHP VHvQFDGUHD] vQPRGHOXO 0 0 ),)2 1 f vQ FDUH 1 $OHJHP FD XQLWDWH GH WLPS RUD DWXQFL O PDúLQLRU P

O P

PDúLQLRU UH]XOW U

D 3UREDELOLWDWHDFDRPDúLQ V QXDúWHSWHHVWH

S

U U

#

3UREDELOLWDWHD FD WRDWH ORFXULOH V ILH RFXSDWH HVWH S J VHDVF XQ ORF GHFL SUREDELOLWDWHD V S # E WLPSXOPHGLXGHDúWHSWDUHvQVLVWHPYDIL

WV

U S

OLEHU

YD

IL

#

0RGXOGHDúWHSWDUHFXVRVLULSRLVVRQLHQHWLPSGHVHUYLUH H[SRQHQ LDOFXVVWD LLLGHQWLFHSRSXOD LHLLQILQLW 0 0 V ),)2 f f

9RPSUHVXSXQHF QXP UXOVWD LLORU V HVWHPDLPDUHFDXQXILHFDUHVWD LHDYkQG DFHODúLSDUDPHWUXGHVHUYLUH P VRVLULOHDYkQGRUHSDUWL LH3RLVVRQGHPHGLH O WLPSXOGH VHUYLUH H[SRQHQ LDO LDU WUHFHUHD GLQ ILUXO GH DúWHSWDUH vQ RULFDUH VWD LH OLEHU VH IDFH vQ RUGLQHDVRVLULORU 3RSXOD LDGLQFDUHSURYLQXQLW LOHHVWHLQILQLW DúDF QXP UXOPHGLXDOXQLW LORUFH VRVHVFvQVLVWHPXOGHDúWHSWDUHHVWHFRQVWDQWúLHJDOFX O 3HQWUX FDOFXOXO SUREDELOLW LORU DVRFLDWH VW ULORU VLVWHPXOXL VH XWLOL]HD] VLVWHPXO JHQHUDO GH HFXD LL GH VWDUH vQ FD]XO VWD LRQDU úL IRUPXOHOH úL vQFDUH O Q O Q ` LDUSHQWUX P Q YRPFRQVLGHUDGRX FD]XUL D FkQGQXP UXO Q DOXQLW LORUFHVHDIO vQVLVWHPvQPRPHQWXO W HVWHPDLPLF GHFkW V YRU OXFUD GRDU Q VWD LL GLQ FHOH V LDU P Q YDILGH Q RULPDLPDUH GHFkWSHQWUXRVLQJXU VWD LH E FkQG Q t V WRDWH VWD LLOH YRU OXFUD OD PRPHQWXO UHVSHFWLY úL DWXQFL P Q YD IL VP $VWIHO

PQ

QP ® ¯VP

SHQWUX d Q V SHQWUX Q t V

ÌQORFXLPUHOD LOH vQUHOD LD FX U

O IDFWRUXOGH U

VHUYLFLXDOXQHLVWD LLYRPDYHD 'DF d Q V SQ 'DF Q t V SQ

OQ S P P QP

Q U S Q

OQ S P P V P VP VP

UQ S VV Q V

Q V RUL

5H]XOW

UQ ° S ° Q SQ ® Q ° U S °¯ VV Q V

VDX

SHQWUX d Q V

SHQWUX Q t V

UQ S d Q V Q SV N U N SV N t

SQ XQGH

U

O PV

U V

VHPDLQXPHúWHIDFWRUXOGHXWLOL]DUHDOVLVWHPXOXL3HQWUXDVHHYLWDDJORPHUD LD DFHVWIDFWRUHVWHQHFHVDUV ILHVXEXQLWDUDGLF U HFKLYDOHQWFX

O VP

U GH V

XQGH U V DVWIHOYRPSXWHDFRQFOX]LRQDF IDFWRUXOGHVHUYLFLXDOXQHLVWD LLSRDWH ILVXSUDXQLWDUGDUPDLPLFFDQXP UXOVWD LLORU V &XP

f

¦S Q

Q

úL LQkQG FRQW GH IRUPD SUREDELOLW LORU SQ YRP DYHD

f UQ UV U Q V S S ¦ ¦ Q Q Q V V V

VDX

§ V UQ U V f QV · S ¨¨ ¦ ¦ U ¸¸ © Q Q V Q V ¹

úL LQkQG FRQW F

f

F FL HVWH R SURJUHVLH JHRPHWULF FX UD LD U

¦ U

QV

Q V

U RE LQHP

S

U UV ¦ V U Q Q V

Q

9DULDELOHDOHDWRDUH Q I FHUHSUH]LQW QXP UXOGHXQLW LGLQILUXOGHDúWHSWDUH ODXQPRPHQWGDWDUHUHSDUWL LD

§ Q I ¨¨ © S S SV

SV

"· ¸ SV "¸¹

úLDWXQFLQXP UXOPHGLXGHXQLW LvQILUXOGHDúWHSWDUHYDIL f

¦ Q V S

QI

Q V

UV Q V U Q V S ¦ V Q V f

Q

UV S U U V

UV U S V U

F FLDP LQXWVHDPDF

U U

G U U U GU

GHFL

G § U · ¨ ¸ G U ¨© U ¸¹

UV U S V U

QI

U

6HDUDW IRORVLQGVXPDUHDDFHORUDúLVHULLF QXP UXOPHGLXGHXQLW LGHFXUV GH VHUYLUH vQ PRGHOXO DFHVWD HVWH QV U GH XQGH QXP UXO PHGLX GH XQLW L GLQ VLVWHPXOGHDúWHSWDUHHVWH

Q

Q I QV

U V S U V V U

7LPSXOPHGLXGHDúWHSWDUHDXQHLXQLW LvQILUYDIL

WI

QI P QV

UV U S PU V U

LDUWLPSXOPHGLXGHDúWHSWDUHDXQHLXQLW LvQVLVWHPHVWH

WV

WI

P

· § UV U ¨¨ S ¸¸ P © U V U ¹

2EVHUYD LH'DF VHSUHVXSXQHF vQVLVWHPXOGHDúWHSWDUHSRWH[LVWDFHOPXOW 1 XQLW LODXQPRPHQWGDWúLF GHFLILUXOGHDúWHSWDUHHVWHOLPLWDWvQHOSXWkQGIL FHOPXOW 1 V XQLW LDWXQFL SQ SHQWUX Q ! 1 úLDYHP

Q ° U S ° Q ® ° UQ S °¯ V V Q V

SQ

3XQHPFRQGL LD

Q ° U S ° Q ® ° U V U Q V S °¯ V

SHQWUX d Q V SHQWUX V d Q d 1 1

¦S Q

Q

SHQWUX d Q V

SHQWUX V d Q d 1

úLRE LQHP

1 § V QV · S ¨ ¦ UQ ¦ U V U ¸ Q V V © Q Q ¹

GDU

V QV U U ¦ Q V V 1

DWXQFLYRPDYHD

S

V U 1 V U V U

Q V U 1 V U U ¦ V U Q Q V

3HQWUXDHYLWDFDOFXOHOHODERULRDVHQHFHVDUHGHWHUPLQ ULLLQGLFDWRULORU Q Q I

QV SXWHPIRORVLIRUPXOHOHGHUHFXUHQ SHQWUX SQ SQ úL

IRUPXOHOH

SHQWUX

° USQ SHQWUX d Q V ®Q °U SQ SHQWUX V d Q d 1 ¯ LQGLFDWRUL

Q

1

¦ QSQ Q

QV

V

¦ QS Q

QI

1

¦ Q V S Q V

Q

1

Q

V ¦ SQ Q V

([HPSOX/DRDJHQ LHGHYRLDMVXQWDPSODVDWHSDWUXFDVHGHELOHWH6HúWLHF VRVLUHDSDVDJHULORUHVWHSRLVVRQLDQ FXRPHGLHGH SDVDJHULSHRU LDUWLPSXO GHVHUYLUHDXQXLSDVDJHUHVWH GHVHFXQGH6 VHGHWHUPLQHQXP UXOPHGLXGH SDVDJHULFDUHDúWHDSW V LQWUHvQDJHQ LHúLWLPSXOGHDúWHSWDUHvQFRDG

P

cc c

6ROX LH V

O

$YHP S

§ UQ U · ¸¸ ¨¨ ¦ © Q Q U ¹

DJORPHUDUHD Q I

RUHUH]XOW P

UV U S V U

U

O VP

QV

U W I

úL U

O P

GHFLVHHYLW VXSUD QI P QV

RUH

&HOHSDWUXFDVHGHELOHWHVXQWIRORVLWHODvQWUHDJDFDSDFLWDWHF FLQXP UXOGH SDVDJHULVHUYL LvQXQLWDWHDGHWLPS P QV HVWHHJDOFXSRVLELOLW LOHGHVHUYLUH

VP

2EVHUYD LH 'DF QXP UXO SDVDJHULORU FH VRVHVF OD DJHQ LH DU IL O

SDVDJHUL SH RU DWXQFL VDU RE LQH U

QV

U

U

S

Q I

W I

LDU FDSDFLWDWHD GH VHUYLUH D VLVWHPXOXL QX DU IL IRORVLW GHFkWvQSURSRU LHGH F FLQXP UXOGHSDVDJHULVHUYL LvQXQLWDWHDGHWLPSHVWH P QV LDUSRVLELOLW LOHGHVHUYLUH VP

0RGHOXOGHDúWHSWDUHFXVRVLULSRLVVRQLHQHWLPSGH VHUYLUHH[SRQHQ LDOFXRVWD LHSRSXOD LHILQLW 0 0 ),)2 P P

0RGHOHOHDQWHULRDUHDXSUHVXSXVSRSXOD LDGLQVXUV LQILQLW ÌQSUDFWLF GH RELFHL VRVLULOH VXQW vQ QXP U PDUH GDU ILQLWH 0RGHOXO GH ID HVWH DúDQXPLWXO PRGHO DO UHSDUDWRUXOXL 6LVWHPXO DUH P ILQLW PDúLQL FX DFHOHDúL FDUDFWHULVWLFL WHKQRORJLFH úL FDUH IXQF LRQHD] LQGHSHQGHQW XQHOH GH DOWHOH 0DúLQLOH VH SRW GHIHFWD vQ PRG vQWkPSO WRU úL VRVHVF OD UHSDUDW GXS R OHJH SRLVVRQLDQ FX SDUDPHWUXO O SHQWUXDSXWHDILUHSDUDWHH[LVW XQVLQJXUPHFDQLFVWD LH LDUGXUDWD UHSDUD LHLXQHLPDúLQLXUPHD] RUHSDUWL LHH[SRQHQ LDO FXSDUDPHWUXO P 'HRDUHFH H[LVW R VLQJXU VWD LH SDUDPHWUXO P Q QX GHSLQGH GH QXP UXO GH XQLW LGLQVLVWHPHOYDILFRQVWDQWúLVHQRWHD] FX P 9RPGHWHUPLQDFDUDFWHULVWLFLOHDFHVWXLPRGHOREVHUYkQGF SUREDELOLWDWHDFD vQLQWHUYDOXOGHWLPS 'W V VRVHDVF vQVLVWHPRXQLWDWHFkQGvQVLVWHPVHDIO Q XQLW L GLQ FHOH P DOH VXUVHL HVWH FX DWkW PDL PLF FX FkW QXP UXO XQLW LORU U PDVHvQSRSXOD LHHVWHPDLPLF$VWIHOSXWHPVFULHDFHDVW SUREDELOLWDWHFDILLQG O Q 'W P Q O'W

GHFL O Q P Q O Q P &X DOWH FXYLQWH UDWD VRVLULORU HVWH SURSRU LRQDO FXQXP UXOGHXQLW LU PDVHvQVLVWHP P Q

ÌQORFXLP O Q úL P Q

SQ

P vQUHOD LD 9RPDYHD

PO P O P Q O

P P P DVWIHOF SHQWUX Q P P

S

$PQ UQ S

SQ ùWLLQGF

Q

§O· P P P Q ¨ ¸ S ©P¹

P

¦ SQ

RE LQHP ¦ $PQ UQ S

Q

GHXQGH

Q

S

P

¦$ U Q P

Q

Q

1XP UXOPHGLXGHXQLW LvQVLVWHPVHFDOFXOHD] DVWIHO

Q

Q

Q

GHXQGH

P

P

P

P

¦ QS ¦ P P Q S ¦ PS ¦ P Q S Q

Q

Q

P

P

Q

Q

Q

Q

Q

P¦ SQ ¦ P Q SQ

vQORFXLPSQFXH[SUHVLDRE LQXW DQWHULRUúL LQHPFRQWF

P

¦S

Q

9RPRE LQH

P

P ¦ P Q $PQ UQ S

Q

Q

GDU

P Q $PQ

úLDWXQFL

Q

PP P Q P Q P

P ¦ $PQ UQ S

P

Q

P

¦S Q

Q

S U

P

S U

1XP UXOPHGLXGHXQLW LvQFXUVGHVHUYLUHHVWH QV S LDUQXP UXOPHGLXGHXQLW LvQILUXOGHDúWHSWDUHHVWH

QI

$PQ

S GHFL

Q

Q

F FL

Q

Q QV

P

U S U

7LPSXOPHGLXGHDúWHSWDUHDXQHLXQLW LvQILUHVWH

WI

QI

§ P · ¨¨ ¸¸ P © S U ¹

P QV

LDUWLPSXOPHGLXGHDúWHSWDUHvQVLVWHPYDIL

§ P · ¨¨ ¸¸ P © S U ¹ P S GHFL OP Q P S DWXQFL 'LQ RE LQHP P Q O QI WV

WI

OP Q

WI

P

([HPSOXÌQH[HPSOXFRQVLGHUDWvQDFHVWPRGHOV SUHVXSXQHPF PDúLQLOH DSDU LQXQXLDWHOLHUGHVWUXQJ ULHvQFDUHDYHP VWUXQJXULGHDFHODúLIHOFHSRWIL UHSDUDWHvQFD]GHGHIHFWDUHGHXQVLQJXUPHFDQLFùWLLQGF vQ RUHPDúLQLOHVH GHIHFWHD] FX UHSDUWL LD SRLVVRQLDQ FX O PDúLQLK LDU PXQFLWRUXO UHSDU R PDúLQ vQWUXQWLPSH[SRQHQ LDOFXPHGLD PLQXWH6 VHGHWHUPLQH D SHULRDGDGHLQDFWLYLWDWHDPHFDQLVPXOXL E SUREDELOLWDWHDFD VWUXQJXULV ILHGHIHFWH F FHOHODOWHFDUDFWHULVWLFLDOHPRGHOXOXL 6ROX LH

D 3HULRDGD GH LQDFWLYLWDWH HVWH DFHHD FkQG vQ VLVWHP QX H[LVW QLFL XQ VWUXQJGHFLWUHEXLHFDOFXODWSFXDMXWRUXOUHOD LHL úWLLQGF O PDúLQLK P PDúLQLK U S E ÌQORFXLQGGDWHOHvQUHOD LD RE LQHP § · S $ ¨ ¸ ©¹ F 'LQUHOD LD DYHP Q úLGLQUHOD LD RE LQHP

QI

7LPSXOPHGLXGHDúWHSWDUHDXQXLVWUXQJvQILUHVWH W I

RUHLDUWLPSXO

PHGLXGHDúWHSWDUHvQVLVWHP W V RUH 0RGHOGHDúWHSWDUHFXVRVLULSRLVVRQLHQHWLPSGHVFULHUH H[FHS LRQDOFXVVWD LLLGHQWLFHSRSXOD LDILQLW 0 0 V ),)2 P V P $FHVWPRGHOGLIHU GHFHODQWHULRUSULQIDSWXOF VHUYLUHDHVWHDVLJXUDW GH V VWD LGHVHUYLUHLGHQWLFH(YLGHQW V P DOWIHOQXDUH[LVWDDúWHSWDUHD &D úL OD PRGHOXO DQWHULRU SRSXOD LD GLQ VXUV HVWH ILQLW SDUDPHWUXO O Q UHSUH]HQWkQG QXP UXO PHGLX DO VRVLULORU SH XQLWDWHD GH WLPS GHSLQGH GH QXP UXO XQLW LORUU PDVHvQVXUV O Q P Q O

P Q VH YD VFULH FD úL 0 0 V ),)2 f f FX V ! úLDQXPH QP SHQWUX d Q V PQ ® ¯VP SHQWUX V d Q d P ÌQ vQORFXLP O Q úL P Q vQFHOHVWD LLúLRE LQHP GDF d Q V DWXQFL &HO ODOW

SDUDPHWUX

vQ

PRGHOXO

PO P O P Q O $PQ § O · S S ¨¨ ¸¸ S &PQ UQ S P P QP Q © P ¹ GDF V d Q d P DWXQFL PO P O P Q O $PQ OQ $PQ Q SQ S S U S P P >V P@ VP VP VV Q VP Q VV Q V

Q

Q V RUL

$VWIHODPRE LQXW

SQ

&PQ UQ S ° Q ® $P Q ° Q V U S ¯ VV

LQkQG FRQW GH IDSWXO F P

¦S Q

SHQWUX V d Q d P P

¦S Q

$YHP

GHXQGH

SHQWUX d Q V

Q

Q

RE LQHP YDORDUHD SUREDELOLW LL S

§ V Q Q P $PQ Q · ¨¨ ¦ &PU ¦ Q V U ¸¸ S Q V V V ©Q ¹

· § V $Q S ¨¨ ¦ &PQ UQ ¦ PQ V UQ ¸¸ Q V V ¹ ©Q U O úLGDF QRW PFX U IDFWRUXOGHVHUYLUHJOREDODYHP V VP

· § V VV P S ¨¨ ¦ &PQ UQ ¦ $PQ U Q ¸¸ V Q V ¹ ©Q LDUH[SUHVLDRE LQXW SHQWUXSUREDELOLW LOH SQ VHYDVFULH

&PQ UQ S ° ® Q VV Q ° $P U S ¯ V

SQ

SHQWUX d Q V SHQWUX V d Q d P

LQkQG VHDPD F DX ORF UHOD LLOH &PN SXWHPVFULHRUHOD LHGHUHFXUHQ SHQWUX SQ

SQ

P Q USQ ° ® Q °P Q U SQ ¯

PN N &P úL $PN N

SHQWUX d Q V

P N $PN

SHQWUX V d Q d P

&DUDFWHULVWLFLOHPRGHOXOXLVHFDOFXOHD] SRUQLQGGHODGHILQL LL Q

P

¦ QS Q

QI

P

¦ Q V S

Q V

Q

QV

Q Q I W I

QI P QV

úL W V

WI

Q

P

([HPSOX ÌQWUR IDEULF GH SLHVH WXUQDWH VXQW PDúLQL GH WXUQDW FRQWLQXX GHVHUYLWH GH HOHFWULFLHQL FDUH LQWHUYLQ QXPDL vQ FD] GH GHIHF LXQH ùWLLQG F GXUDWDUHSDUD LHLXQHLPDúLQLGHWXUQDWHVWHRYDULDELO H[SRQHQ LDO FXSDUDPHWUXO

P

PDúLQLRU úLF GXUDWDGHIXQF LRQDUHDXQHLPDúLQLI U GHIHFWHVWH RUH

V VHGHWHUPLQH D SUREDELOLWDWHD FD OD XQ PRPHQW GDW vQ VLVWHPXO GH DúWHSWDUH V VH J VHDVF PDúLQL E QXP UXOPHGLXGHPDúLQLGHIHFWHFHDúWHDSW ODXQPRPHQWGDWV ILHUHSDUDWH F WLPSXOGHDúWHSWDUHvQILUúLWLPSXOGHDúWHSWDUHvQVLVWHP

6ROX LH 'LQ GDWHOH SUREOHPHL GHGXFHP F V PDúLQL SH RU

U

O VP

O

GH XQGH O

VWD LL P PDúLQL P

PDúLQL SH RU DVWIHO F U

O P

D $SOLFkQGIRUPXOD YRPDYHD

§ Q § · Q Q § ·Q · ¨ ¦ & ¨ ¸ ¦ $ ¨ ¸ ¸ ¨Q © ¹ Q © ¹ ¸¹ ©

S

§· & ¨ ¸ S ©¹

úL S E Q I F W V

¦ Q S

Q

QI P QV

Q

Q

# VHFXQGHúL W V

¦ QS Q

WI

P

Q

úL QV

RUH

Q QI

úL

%,%/,2*5$),(

>@ >@ >@ >@ >@ >@ >@ >@ >@ >@ >@ >@ >@ >@ >@ >@ >@ >@ >@ >@

%RUHO ( 6XU OHV SUREDELOLWpV GHQRPHUDEOHV HW OHXUV DSSOLFDWLRQV DULWPpWLTXHV 5HQGGHO&HUF0DWGL3DOHUPR( %ODVFKNH : 9RUOHVXQJHQ EHU ,QWHJUDO JHRPHWULH HG 9(% 'HXWVFKHU 9HUODJGHU:LVV%HUOLQ % GLX 9 5DLVFKL & &XUV GH PDWHPDWLFL DSOLFDWH vQ HFRQRPLH /LWR $6( %XFXUHúWL &DQWHOOL)3&RQVLGpUDWLRQVVXUODFRQYHUJHQFHGDQVOHFDOFXOGHVSUREDELOLWpV $QQ,QVW03RLQFDUp &LXFX * 6LPERDQ * 7HRULD SUREDELOLW LORU úL VWDWLVWLFD PDWHPDWLF (GLWXUD 7HKQLF %XFXUHúWL &LXFX*&UDLX96 FXLX,&XOHJHUHGHSUREOHPHGHWHRULDSUREDELOLW LORU (GLWXUD7HKQLF %XFXUHúWL &LXFX * &UDLX 9 3UREOHPH GH VWDWLVWLF PDWHPDWLF (GLWXUD 'LGDFWLF úL 3HGDJRJLF %XFXUHúWL &UDPpU+0DWKHPDWLFDOPHWKRGVRIVWDWLVWLFV3ULQFHWRQ *PXUPDQ 9( 3UREOHPDV GH OD WHRULD GH ORV SUREDELOLGDGHV \ GH HVWDGLVWLFD PDWHPDWLFD(GLWRULDO0LU8566 ,RVLIHVFX00LKRF*K7HRULDSUREDELOLW LORUúLVWDWLVWLFDPDWHPDWLF (GLWXUD 7HKQLF %XFXUHúWL .HQGDOO 0* 0RUDQ 3$3 *HRPHWULFDO 3UREDELOLW\ &KDUOHV *ULJJLQ FRPS /LP/RQGRQ .RORPRJRURY $1 'HWHUPLQD]LRQH HPSLULFD GL XQD OHJJH GL GLVWULEX]LRQH *LRUQDOH6HW+DO$+XDUL /HY\33UREDELOLW\7KHRU\HGD1HZ

>@ 2QLFHVFX 2 0LKRF * úD &DOFXOXO SUREDELOLW LORU úL DSOLFD LL (GLWXUD $FDGHPLHL565%XFXUHúWL >@ 3RSHVFX2úD0DWHPDWLFLDSOLFDWHvQHFRQRPLH(GLWXUD'LGDFWLF úL3HGDJRJLF %XFXUHúWL >@ 5pQ\L$2QWKHWKHRU\RIRUGHUVWDWLVWLFV$FWD0DWHPDWLFD$FDG6FLHQWLDUXP 6WXQJDULFRO >@ 6DQWDOy/$hEHUGDVNLQHPDWLVFKH0DVVLP5DXP* $FW6FLHW,QG +HUPDQQ3DULV >@ 6vPERDQ * úD 7HRULD SUREDELOLW LORU (GLWXUD 'LGDFWLF úL 3HGDJRJLF %XFXUHúWL >@ 7UDQGDILU5&XOHJHUHGHSUREOHPHPDWHPDWLFLSHQWUXLQJLQHULHG$,,D(GLWXUD 7HKQLF >@ 7RUWUDW$&DOFXOGHVSUREDELOLWpV3DULV >@ $OOHQ 5*' $QDOL] PDWHPDWLF SHQWUX HFRQRPLúWL (GLWXUD ùWLLQ LILF %XFXUHúWL >@ 'XGD , $QDOL] PDWHPDWLF SDUWHD , (GLWXUD )XQGD LHL 5RPkQLD GH 0kLQH%XFXUHúWL >@ 'XGD,7UDQGDILU5$QDOL] PDWHPDWLF FXOHJHUHGHSUREOHPH(GLWXUD )XQGD LHL5RPkQLDGH0kLQH%XFXUHúWL >@ 'XGD , (OHPHQWH GH DOJHEU SHQWUX HFRQRPLúWL (GLWXUD )XQGD LHL 5RPkQLDGH0kLQH%XFXUHúWL >@ .DXIPDQ 9 0HWRGH úL PRGHOH DOH FHUFHW ULL RSHUD LRQDOH YRO , úL ,, (GLWXUDùWLLQ LILF %XFXUHúWL >@ 0LKRF *K ùWHI QHVFX $ 3URJUDPDUH PDWHPDWLF (GLWXUD 'LGDFWLF úL 3HGDJRJLF %XFXUHúWL >@ 0LK LO 13RSHVFX20DWHPDWLFLVSHFLDOHDSOLFDWHvQHFRQRPLH(GLWXUD 'LGDFWLF úL3HGDJRJLF %XFXUHúWL >@ 2SUHVFX*K0DWHPDWLFLSHQWUXHFRQRPLúWL(GLWXUD)XQGD LHL5RPkQLDGH 0kLQH%XFXUHúWL >@ 3XUFHUX,0DWHPDWLFLILQDQFLDUHúLGHFL]LLvQDIDFHUL(GLWXUD(FRQRPLF >@ 3RSHVFX 3 úL FRODERUDWRUL 0DWHPDWLFL DSOLFDWH vQ HFRQRPLH YRO , úL ,, (GLWXUD'LGDFWLF úL3HGDJRJLF 5$%XFXUHúWL