32'67$:2:(8.à$'<6(.:(1&<-1(
2*Ï/1$&+$5$.7(5<67<.$8.à$'Ï:
6(.:(1&<-1<&+
2PyZLRQH Z SRSU]HGQLP UR]G]LDOH EUDPNL QDOH* GR URG]LQ\
XNáDGyZ NRPELQDF\MQ\FK FKDUDNWHU\]XMF\FK VL W\P *H VWDQ\ LFK
Z\MFLD]DOH*W\ONRRGVWDQyZORJLF]Q\FKQDZHMFLDFKQDWRPLDVWQLH
]DOH*RGVWDQyZSRSU]HGQLFK
8NáDG\VHNZHQF\MQHREHMPXMV]HURNJUXSF\IURZ\FKXNáDGyZ
ORJLF]Q\FKNWyU\FKVWDQ]DOH*\QLHW\ONRRGV\JQDáyZGRSURZDG]RQ\FK
GRZHMüXNáDGXZGDQHMFKZLOLOHF]UyZQLH*RGZF]HQLHMV]\FKVWDQyZ
Z\MFLRZ\FK XNáDGX 3RQLHZD* VWDQ\ SRSU]HGQLH ]DOH* UyZQLH* RG
VHNZHQFML F]\OL NROHMQRFL VWDQyZ MHV]F]H GDZQLHMV]\FK
UHSUH]HQWRZDQ\FK SU]H] VWDQ\ SU]HU]XWQLNyZ W]Z ZHZQWU]QH VWDQ\
XNáDGXVWGQD]ZDXNáDG\VHNZHQF\MQH
3DPLWDQLHSRSU]HGQLFKVWDQyZXNáDGX]DFKRG]LZHOHPHQWDUQ\FK
NRPyUNDFKSDPLFLRZ\FKSU]HU]XWQLNDFKELVWDELOQ\FKEXGRZDQ\FK]
HOHPHQWDUQ\FK XNáDGyZ ORJLF]Q\FK WZRU]F\FK W]Z ]HVWDZ
IXQNFMRQDOQLHSHáQ\
-H*HOLVWDQZHMüXNáDGXVHNZHQF\MQHJRRNUHORQ\MHVWZHNWRUHP
;
(
)
=
∈
x x
x
x
n
i
1
2
,
,
,
,
% D VWDQ ZHZQWU]Q\ Z XNáDG]LH RNUHORQ\
MHVW ZHNWRUHP $ Z\QLNDMF\P ]H VWDQyZ ORJLF]Q\FK HOHPHQWyZ
SDPLFLRZ\FK $
(
)
Q Q
Q
Q
k
j
1
2
,
,
,
,
∈
% WR VWDQ Z\Mü XNáDGX
RNUHORQ\MHVWZHNWRUHP<
(
)
y y
y
y
m
i
1
2
,
,
,
,
∈
%
: XNáDGDFK VHNZHQF\MQ\FK RNUHOD VL ]ZL]NL PLG]\ VWDQDPL
;<$ZSRVWDFLGZyFKIXQNFML
)XQNFML SU]HMü
δ
RNUHODMFHM GOD ZHNWRUyZ $
W
;
W
QDVWSQ\
RSy(QLRQ\RSHZLHQF]DV
τ
VWDQZHZQWU]Q\$
W
τ
$
W
τ
δ
$
W
;
W
)XQNFMLZ\Mü
λ
RNUHODMFHMVWDQZ\Mü<
)XQNFMD Z\Mü MHVW IXQNFM SU]HáF]DMF L PR*H PLHü SRVWDü
RSLVXMFW]ZDXWRPDW0HDO\¶HJRU\VD
<
W
λ
$
W
;
W
OXERSLVXMFDXWRPDW0RRUH¶DU\VE
<
W
λ
$
W
a)
λ
δ
$
<
;
b)
λ
δ
$
<
;
5\V 3RGVWDZRZH PRGHOH XNáDGyZ VHNZHQF\MQ\FK D DXWRPDW 0HDO\¶HJR
EDXWRPDW0RRUH¶D
: ]DSLVLH W\P ND*G ]PLHQQ VWDQX F]\OL ND*G\ HOHPHQW
(
)
Q i
k
i
=
1 2
, ,
,
ZHNWRUD$RSLVXMHVLUyZQDQLHP
(
)
Q
Q Q
Q x x
x
i
i
k
n
=
δ
1
2
1
2
,
,
,
;
,
,
,
.D*GD]PLHQQDZ\MFLRZD
(
)
y
j
m
j
=
1 2
, ,
,
PR*HE\üRNUHORQDSU]H]
IXQNFMZ\Mü
ZDXWRPDFLH0HDO\¶HJR
(
)
Y
Q Q
Q x x
x
j
j
k
n
=
λ
1
2
1
2
,
,
,
;
,
,
,
D
ZDXWRPDFLH0RRUH¶D
(
)
Y
Q Q
Q
j
j
k
=
λ
1
2
,
,
,
E
%ORN UHDOL]XMF\ IXQNFM
δ
VNáDGD VL ] EORNX SDPLFL
]DZLHUDMFHJR]HVWDZSU]HU]XWQLNyZF]\OLW]ZUHMHVWUXRUD]]XNáDGX
NRPELQDF\MQHJR SU]\JRWRZXMFHJR V\JQDá\ ZHMFLRZH W]Z ZHNWRU
VWDQXZ]EXG]HHOHPHQWyZSDPLFLRZ\FK%ORNUHDOL]XMF\IXQNFM
λ
MHVWXNáDGHPNRPELQDF\MQ\P
'OD SHáQHJR RSLVX XNáDGX VHNZHQF\MQHJR NRQLHF]QH MHVW SHáQH
RNUHOHQLHSLFLXHOHPHQWyZ$;<
δ
λ
!:W\PFHOXVWRVXMHVL
RSLVJUDILF]Q\ZSRVWDFLJUDIX]RULHQWRZDQHJR]HW\NLHWQD]\ZDQHJR
JUDIHPSU]HMüLZ\MüWDEOLFHSU]HMüLZ\MüRUD]PDFLHU]HSU]HMüL
Z\Mü
3RGVWDZGRVWZRU]HQLDQSWDEOLF\VWDQyZZNWyUHMMHVW]DSLVDQ\
VWDQ Z\Mü SR WDNFLH ]HJDURZ\P GOD GDQHJR VWDQX SRSU]HGQLHJR L
GDQHJR VWDQX ZHMü MHVW Z\NUHV VWDQyZ 3RND]XMH RQ MDNLH V VWDQ\
Z\MFLRZH XNáDGX Z NROHMQ\FK F\NODFK ]HJDUD SU]\ GDQ\FK VWDQDFK
ZHMFLRZ\FK
1DU\VSU]HGVWDZLRQREDUG]RSURVW\SU]\NáDGZ\NUHVXVWDQyZ
XNáDGXVHNZHQF\MQHJR]MHGQ\PZHMFLHPLGZRPDZ\MFLDPL
3U]HMFLH GR NROHMQ\FK VWDQyZ Z\MFLRZ\FK SRGDQ\FK Z
NROHMQ\FK RNUJDFK ]DFKRG]L SU]\ VWDQLH ZHMFLD [ 3U]\ [
XNáDGSR]RVWDMHZVWDQLHSRSU]HGQLP
00
10
01
11
[
=
0
0
0
1
1
1
[
=
5\V 3U]\NáDG Z\NUHVX VWDQyZ
SURVWHJRXNáDGXVHNZHQF\MQHJR
=DOH*QLHRGWU\EXSUDF\XNáDG\VHNZHQF\MQHG]LHOLVLQDXNáDG\
DV\QFKURQLF]QHLV\QFKURQLF]QH
8NáDG\ DV\QFKURQLF]QH QLH PDM ZHMFLD VWHUXMFHJR
V\QFKURQL]XMFHJR]HJDURZHJR-DNDNROZLHN]PLDQDVWDQyZ<OXE$
ZW\FKXNáDGDFKPR*HZ\VWSLüMHG\QLHSR]PLDQLHVWDQXZHMFLRZHJR
;
8NáDG\ V\QFKURQLF]QH UHDJXM QD ]PLDQ VWDQX ZHMFLRZHJR ;
W\ONR Z G\VNUHWQ\FK FKZLODFK F]DVRZ\FK GHWHUPLQRZDQ\FK SU]H]
]HZQWU]Q\
V\JQDá
VWHUXMF\
&
QD]\ZDQ\
]HJDURZ\P
V\QFKURQL]XMF\PWDNWXMF\PNWyU\QLHZFKRG]LGRZHNWRUD;
-H*HOLZV]\VWNLHZ\VWSXMFHZXNáDG]LHSU]HU]XWQLNLELVWDELOQHV
V\QFKURQLF]QH WR XNáDG VHNZHQF\MQ\ MHVW V\QFKURQLF]Q\ :
SU]HFLZQ\PSU]\SDGNXJG\FKRüMHGHQSU]HU]XWQLNMHVWDV\QFKURQLF]Q\
WR XNáDG VHNZHQF\MQ\ MHVW DV\QFKURQLF]Q\ 8NáDG\ V\QFKURQLF]QH V
]QDF]QLH F]FLHM VWRVRZDQH Z V\VWHPDFK F\IURZ\FK QL* XNáDG\
DV\QFKURQLF]QH SRPLPR WHJR *H WH RVWDWQLH PRJ E\ü XNáDGRZR
SURVWV]H *áyZQ SU]\F]\Q WHJR MHVW Z\VWSRZDQLH Z XNáDGDFK
DV\QFKURQLF]Q\FK QLHSR*GDQ\FK ]MDZLVN RNUHODQ\FK MDNR Z\FLJL L
KD]DUG\ 2EMDZLDM VL RQH Z SRVWDFL SU]HMFLRZ\FK L VWDELOQ\FK
QLHSR*GDQ\FK UHDNFML QD ]PLHQQ VWDQX ZHMFLRZHJR ZVNXWHN
QLHMHGQDNRZ\FK RSy(QLH HOHPHQWyZ XNáDGX L Uy*Q\FK GUyJ
V\JQDáRZ\FK Z XNáDG]LH : XNáDGDFK V\QFKURQLF]Q\FK Z\FLJL L
KD]DUG\QLHZ\VWSXMDSRQDGWRV\QWH]DW\FKXNáDGyZMHVWSURVWV]D
:W\PUR]G]LDOH]RVWDQSU]HGVWDZLRQHSRGVWDZRZHSU]HU]XWQLNL
ELVWDELOQH]EXGRZDQH]EUDPHNRUD]OLF]QLNLLUHMHVWU\EGFHSURVW\PL
VHNZHQF\MQ\PL EORNDPL IXQNFMRQDOQ\PL UHDOL]RZDQ\PL Z RSDUFLX R
SU]HU]XWQLNL
35=(5=871,.,&<)52:(
3U]HU]XWQLNW\SX56
:]DMHPQLH VSU]*RQD SDUD IXQNWRUyZ 125 Z VSRVyE SRND]DQ\
QD U\VD WZRU]\ QDMSURVWV]\ SU]HU]XWQLN DQJ IOLS IORS W\SX
R
S
3RVLDGD RQ GZD GRSHáQLDMFH VL Z\MFLD Q i Q RUD] GZD ZHMFLD
VWHUXMFHXVWDZLDMFH
S
DQJVHWL]HUXMFH
R
DQJUHVHW
5
6
4
4
a)
b)
5\V 3U]HU]XWQLN 56 ]EXGRZDQ\ ] EUDPHN 125 D VFKHPDW XNáDGX E WDEOLFD
VWDQyZ
4
−
R]QDF]D
VWDQSRSU]HGQL
-H*HOL RED ZHMFLD V Z VWDQLH QLVNLP
R
S
= =
0
WR SU]HU]XWQLN
SR]RVWDMH Z VWDQLH ]DOH*Q\P RG SRSU]HGQLFK ZDUWRFL ORJLF]Q\FK QD
ZHMFLDFK
*G\ZHMFLDVZVWDQLH
S
=
0
R
WRREDZ\MFLDSU]\MPXM
VWDQ\ GRSHáQLDMFH VL Q
=
Q
=
3RGREQLH SU]\
S
R
RWU]\PXMHP\ Q
=
Q
=
'OD
R
S
= =
1
REDZ\MFLDVUyZQRF]HQLH
UyZQH ]HUX FR MHVW VSU]HF]QH ] R]QDF]HQLHP Z\Mü SU]HU]XWQLND ]
NWyU\FKMHGQR]DZV]HSRZLQQRE\üQHJDFMGUXJLHJRDSRQDGWRMH*HOL
ZQDVWSQHMVHNZHQFMLVWHUXMFHM
R
L
S
VWDQVLUyZQRF]HQLHUyZQH
]HUX WR VWDQ Z\Mü EG]LH QLHRNUHORQ\ 'ODWHJR VWDQ ZHMü
R
S
= =
1
MHVW Z W\P SU]\SDGNX QLHGR]ZRORQ\ =HVWDZLHQLH VWDQyZ SU]HU]XWQLND
]DPLHV]F]RQRZWDEOLF\VWDQyZQDU\VE
5
6
4
4
a)
b)
5\V3U]HU]XWQLN56]EXGRZDQ\]EUDPHN1$1'DVFKHPDWXNáDGXEWDEOLFD
VWDQyZ
7DEOLFD
6
5
4
4
4
−
4
−
7DEOLFD
6
5
4
4
4
−
4
−
1D U\VD SU]HGVWDZLRQR SU]HU]XWQLN
R
S
]EXGRZDQ\ ] EUDPHN
1$1' R WDNLHM VDPHM WDEOLF\ VWDQyZ MDN QD U\VE MHGQDN QDOH*\
]DXZD*\ü *H WHUD] PDP\ GR F]\QLHQLD ] ]DQHJRZDQ\PL ]PLHQQ\PL
ZHMFLRZ\PL R L S
6\QFKURQL]RZDQ\SU]HU]XWQLN56
: V\QFKURQL]RZDQ\P SU]HU]XWQLNX 56 DQJ FORFNHG 56 IOLS
IORS ]PLDQD VWDQyZ QD Z\MFLDFK SU]HU]XWQLND QDVWSXMH GRSLHUR SR
GRSURZDG]HQLXLPSXOVXWDNWXMFHJRGRVSHFMDOQHJRZHMFLD]HJDURZHJR
&
U\V
5
6
4
4
5
6
&
%
1
%
2
%
3
%
4
5\V 6\QFKURQLF]Q\ SU]HU]XWQLN
56
'OD
C
=
0
QD Z\MFLDFK EUDPHN
B B
3
4
,
PDP\ R S
= =
1
L
SU]HU]XWQLNZW\PSU]\SDGNXSDPLWDVWDQSRSU]HGQL'OD
C
=
1
PDP\
R
R
S
S
=
=
',
'
L SU]HU]XWQLN ]DFKRZXMH VL ZWHG\ MDN QRUPDOQ\
SU]HU]XWQLN563U]\
C
=
1
SU]HU]XWQLNPR*H]PLHQLüVZyMVWDQQDZHW
ZLHORNURWQLHMH*HOL Z W\P F]DVLH Z\VWSL ]PLDQ\ QD ZHMFLDFK R S
,
2F]\ZLFLH WDN MDN Z SRSU]HGQLR RPDZLDQ\P QLHV\QFKURQL]RZDQ\P
XNáDG]LHU\VDVWDQZHMü
R
S
= =
1
MHVW]DEURQLRQ\
3U]HU]XWQLN'W\SXÄ]DWU]DVN´
-HGQ\P ]H VSRVREyZ XPR*OLZLDMF\FK Z\HOLPLQRZDQLH
]DEURQLRQHM V\WXDFML Z V\QFKURQL]RZDQ\P SU]HU]XWQLNX 56 MHVW
ZSURZDG]HQLH GRGDWNRZHJR LQZHUWHUD ]DSHZQLDMFHJR R S
=
8NáDG
WDNLPDMHGQRZHMFLHSURJUDPXMFHL MHVW QD]\ZDQ\SU]HU]XWQLNLHP '
W\SXÄ]DWU]DVN´DQJGDWDODWFKU\V
']LNL ZSURZDG]RQHPX LQZHUWHURZL
B
5
Z XNáDG]LH VSHáQLRQ\
MHVWZDUXQHN
S
D
=
L R=D=DWHPMDNGáXJRV\JQDá]HJDURZ\
C
=
1
Z
SU]HU]XWQLNXW\PPDP\ Q D
=
FRSRND]DQRUyZQLH*ZWDEOLF\SU]HMü
QDU\VE
5
6
4
4
'
&
%
4
%
2
%
1
%
3
a)
b)
%
5\V3U]HU]XWQLN'W\SXÄ]DWU]DVN´DVFKHPDWXNáDGXEWDEOLFDSU]HMü
-H*HOL
C
=
0
WR DNWXDOQ\ Z GDQHM FKZLOL VWDQ Z\Mü ]RVWDMH
]DSDPLWDQ\ -DN áDWZR PR*QD ]DXZD*\ü Z XNáDG]LH QD U\V GOD
C
=
1
EUDPND
B
4
GDMH QD Z\MFLX QHJDFM ]PLHQQHM
D
8PR*OLZLD WR
Z\HOLPLQRZDQLHLQZHUWHUD
B
5
LRV]F]GQLHMV]UHDOL]DFMSU]HU]XWQLND'
W\SXÄ]DWU]DVN´MDNQDU\V
4
4
'
&
4
4
'
&
'
&
a)
b)
%
2
%
1
%
3
%
4
5\V 3UDNW\F]QD UHDOL]DFMD SU]HU]XWQLND ' W\SX Ä]DWU]DVN´ D VFKHPDW XNáDGX
EV\PEROJUDILF]Q\SU]HU]XWQLND
3U]HU]XWQLNL WHJR W\SX V UHDOL]RZDQH Z SRVWDFL XNáDGyZ
VFDORQ\FKMDNQS/677/(&/&026
3U]HU]XWQLNL ' W\SX Ä]DWU]DVN´ V UHDOL]RZDQH Z WHFKQRORJLL
&026 SU]\ Z\NRU]\VWDQLX EUDPHN WUDQVPLV\MQ\FK OXE WUyMVWDQRZ\FK
FRSR]ZDODQDXSURV]F]HQLHVFKHPDWXHOHNWU\F]QHJRSU]HU]XWQLND
6WUXNWXU\ ORJLF]QH LOXVWUXMFH ]DVDG G]LDáDQLD WHJR W\SX
SU]HU]XWQLNyZSU]HGVWDZLRQRQDU\V
'
4
&
φ
7*
2
7*
1
φ
'
4
&
φ
φ
φ
1
2
3
2
1
a)
b)
φ
φ
φ
5\V 3U]HU]XWQLNL W\SX Ä]DWU]DVN´ D ] EUDPNDPL WUDQVPLV\MQ\PL
E]EUDPNDPLWUyMVWDQRZ\PL
7DEOLFD
&
'
4
4
−
4
−
*G\]HJDU]QDMGXMHVLZVWDQLH
C
=
0
WRZXNáDG]LHQDU\VD
EUDPNDWUDQVPLV\MQD7*MHVWZáF]RQDDEUDPND7*Z\áF]RQD6WDQ
ZHMFLD
D
ZSRVWDFL]DQHJRZDQHMMHVWRGWZDU]DQ\QDZ\MFLXXNáDGX
R]QDF]RQ\PMDNRQ 1DUDVWDMFH]ERF]HLPSXOVX]HJDURZHJRSRZRGXMH
Z\áF]HQLH EUDPNL WUDQVPLV\MQHM 7* D ZáF]HQLH 7* 1DVWSXMH
SU]HUZDQLH WUDQVPLVML GOD V\JQDáX ] ZHMFLD
D
RUD] SRGWU]\PDQLH
]DWU]DQLFLHVWDQXZ\MFLRZHJRXVWDORQHJRWX*SU]HG]PLDQVWDQyZ
QDZHMFLX
C
ZSWOLXWZRU]RQHMSU]H]LQZHUWHU\LEUDPN7*:
XNáDG]LH QD U\VE SU]\ QLVNLP VWDQLH ]HJDUD
C
=
0
DNW\ZQ\ MHVW
LQZHUWHU QDWRPLDVW Z\MFLH LQZHUWHUD ]QDMGXMH VL ZWHG\ Z VWDQLH
GX*HMLPSHGDQFML6WDQZHMFLD
D
ZSRVWDFLSURVWHMMHVWRGWZDU]DQ\QD
Z\MFLX Q 1DUDVWDMFH ]ERF]H LPSXOVX ]HJDUD SRZRGXMH SU]HMFLH
LQZHUWHUD GR VWDQX GX*HM LPSHGDQFML FR SRZRGXMH SU]HUZDQLH
WUDQVPLVML GOD V\JQDáX ] ZHMFLD
D
XDNW\ZQLHQLH LQZHUWHUD L
SRGWU]\PDQLH]DWU]DQLFLHVWDQXZ\MFLRZHJRXVWDORQHJRSU]\
C
=
0
3U]HU]XWQLNL'Z\]ZDODQH]ERF]HPLPSXOVX]HJDURZHJR
3U]HU]XWQLN ' Z\]ZDODQ\ QDUDVWDMF\P ]ERF]HP LPSXOVX
]HJDURZHJRDQJVLQJOHHGJHWULJJHUHGIOLSIORSFKDUDNWHU\]XMHVL
W\P *H LQIRUPDFMD ] ZHMFLD
D
MHVW SU]HQLHVLRQD L ]DSDPLW\ZDQD QD
Z\MFLX Q SU]\]PLDQLHVWDQX]HJDUD
C
]QDLSR]DW\PSU]HU]XWQLN
QLH UHDJXMH QD ]PLDQ\ VWDQX ZHMFLRZHJR Z SU]HU]XWQLNX ' W\SX
Ä]DWU]DVN´ ND*GD ]PLDQD VWDQX
D
SU]HQRVL VL QD Z\MFLH Q SU]\
C
=
1
3RQLHZD* LQIRUPDFMD QD Z\MFLX Q MHVW QLHFR RSy(QLRQD
Z]JOGHP QDUDVWDMFHJR ]ERF]D LPSXOVX ]HJDURZHJR F]VWR R MHGHQ
RNUHV V\JQDáX ]HJDURZHJR VWG SRFKRG]L V\PERO
D
DQJ GHOD\
6WUXNWXUDZHZQWU]QDSU]HU]XWQLND]DOH*\RGWHFKQRORJLLZ\WZDU]DQLD
1L*HM ]RVWDQ SU]HGVWDZLRQH W\SRZH UHDOL]DFMH SU]HU]XWQLNyZ
UHSUH]HQWXMFHURG]LQ\XNáDGyZ/677/L&026
3U]HU]XWQLN ' Z\]ZDODQ\ ]ERF]HP PR*QD ]UHDOL]RZDü áF]F
V]HUHJRZR GZD SU]HU]XWQLNL ' W\SX Ä]DWU]DVN´ ] NWyU\FK ND*G\
VWHURZDQ\MHVWGRSHáQLDMF\PLVLV\JQDáDPL]HJDURZ\PLU\V
*G\ ]HJDU MHVW Z VWDQLH
C
=
0
LQIRUPDFMD ] ZHMFLD
D
MHVW
SU]HQRV]RQD QD Z\MFLH
Q
1
SU]HU]XWQLND 0$67(5 ]D SU]HU]XWQLN
6/$9(MHVWZWHG\ZVWDQLH]DEORNRZDQLDQDZ\MFLDFK EUDPHN %
L
%
Z\VWSXMVWDQ\ SDPLWDMF VWDQ SRSU]HGQL 3U]\ ]PLDQLH VWDQX
]HJDUD]QDQDVWSXMHSU]HSLVDQLHVWDQX
Q
1
QDZ\MFLH Q ]DZW\P
F]DVLHSU]HU]XWQLN0$67(5MHVWZVWDQLH]DEORNRZDQLDQDZ\MFLDFK
EUDPHN%
L%
Z\VWSXMVWDQ\
4
4
'
&
%
23
%
21
%
22
%
24
&
&
2
=
'
2
%
11
%
12
%
14
%
13
&
&
1
=
'
1
0$67(5
6/$9(
5\V3U]HU]XWQLNL'W\SX0DVWHU6ODYH]UHDOL]RZDQ\]GZyFKSU]HU]XWQLNyZ'
W\SXÄ]DWU]DVN´
6WUXNWXUZHZQWU]QSU]HU]XWQLND'W\SX/6Z\]ZDODQHJR
GRGDWQLP]ERF]HP]HJDURZ\PZUD]]WDEOLFVWDQyZSU]HGVWDZLRQRQD
U\V
5
6
4
4
a)
b)
'
&
1
2
3
4
5
6
,
,,
,,,
c)
'
'
&
&
5
6
4
4
5
6
4
4
5\V3U]HU]XWQLN'W\SX/6DVWUXNWXUDZHZQWU]QDEWDEOLFDVWDQyZ
FV\PEROORJLF]Q\
3U]HU]XWQLNPDZHMFLHLQIRUPDF\MQH
D
ZHMFLH]HJDURZH
C
RUD]GZD
ZHMFLD XVWDZLDMFH R L S NWyUH G]LDáDM QLH]DOH*QLH RG ZHMFLD
]HJDURZHJR :\VWSLHQLH RGSRZLHGQLFK VWDQyZ QD ZHMFLX R DOER S
Z\PXV]D RGSRZLHGQLR VWDQ DOER QD Z\MFLX Q 8NáDG MHVW
]EXGRZDQ\ ] WU]HFK SU]HU]XWQLNyZ 56 : F]DVLH ]PLDQ\ V\JQDáX
7DEOLFD
5 6 ' & 4
4
+
/ [
[ +
/
/ +
[
[
/ +
/
/ [
[ + +
+ +
/
/ +
+ + +
+
/
+
+
[
[ 4
−
4
−
+
+
[
4
−
4
−
8ZDJL ]ERF]H QDUDVWDMFH ]HJDUD
]ERF]H RSDGDMFH ]HJDUD
[
VWDQ GRZROQ\
+
OXE
/
]HJDURZHJR ]H VWDQX QD LQIRUPDFMD SRGDQD QD ZHM FLH
D
MHVW
ZSLV\ZDQDGRSU]HU]XWQLND,MH*HOL
D
=
1
OXEGRSU]HU]XWQLND,,MH*HOL
D
=
0
:\MFLD EUDPHN L W\FK SU]HU]XWQLNyZ VWHUXM XVWDZLDQLHP
EUDPHNLSU]HU]XWQLNDZ\MFLRZHJR3RZUyWGRVWDQXQDZHMFLX
V\QFKURQL]XMF\PSRZRGXMHZ\PXV]HQLHVWDQXQDZ\MFLDFKLD
W\PVDP\PSU]HU]XWQLNZ\MFLRZ\SRGWU]\PXMHVWDQSRSU]HGQL
*G\QDZHMFLH
D
SRGDQ\MHVWVWDQLZHMFLH]HJDURZHMHVWZ
VWDQLHZyZF]DVQDZ\MFLXEUDPNLSRMDZLVLVWDQDQDZ\MFLX
EUDPNLSRMDZLVLVWDQ:\MFLDEUDPHNL]QDMGXMVLZVWDQLH
=PLDQD V\JQDáX ]HJDURZHJR ]H VWDQX QD Z FKZLOL RVL JQLFLD
ZDUWRFLQDSLFLDSURJRZHJREUDPNLSRZRGXMHSRMDZLHQLHVL QDMHM
Z\MFLXVWDQXQDZ\MFLDFK]D Q L Q SU]HU]XWQLND,,,RGSRZLHGQLR
VWDQyZL
-H*HOLQDZHMFLH
D
SRGDQ\MHVWVWDQLZHMFLH]HJDURZHMHVWZ
VWDQLH WR Z WDNLP SU]\SDGNX Z\MFLH EUDPNL SU]\MPXMH VWDQ
Z\MFLH EUDPNL VWDQ 3U]\ ]PLDQLH V\JQDáX ] QD QD ZHM FLX
]HJDURZ\P QD Z\MFLX EUDPNL SRMDZL VL VWDQ L Z\MFLH Q
SU]\MPXMHVWDQ 3U]HU]XWQLNL'UHDOL]RZDQHZWHFKQLFH&026PRJ
PLHü Uy*QH VWUXNWXU\ FR ]DOH*\ RG SURGXFHQWD MHGQDN ZV]\VWNLH RQH
RSDUWHVQDNRQFHSFMLPDVWHUVODYHSU]HGVWDZLRQHMQDU\V3HZQH
XSURV]F]HQLH VFKHPDWX HOHNWU\F]QHJR SU]HU]XWQLND Z SRUyZQDQLX GR
RSLVDQHJR UR]ZL]DQLD Z WHFKQLFH 77/ X]\VNXMH VL G]LNL SURVWHM
VWUXNWXU]H SU]HU]XWQLND W\SX Ä]DWU]DVN´ PR *OLZHM GR UHDOL]DFML Z WHM
WHFKQRORJLL SU]\ Z\NRU]\VWDQLX EUDPHN WUDQVPLV\MQ\FK OXE
WUyMVWDQRZ\FK
1D U\V SU]HGVWDZLRQR VWUXNWXU ZHZQWU]Q SU]HU]XWQLND '
Z\]ZDODQHJR GRGDWQLP ]ERF]HP LPSXOVX ]HJDUD Z\NRQDQHJR Z
WHFKQRORJLL&026W\SX%ILUP\0RWRUROD
-HJR ]DVDGD G]LDáDQLD MHVW EDUG]R SRGREQD GR G]LDáDQLD
SU]HU]XWQLND ] U\V SU]\ F]\P SU]HU]XWQLNL ' W\SX Ä]DWU]DVN´
UHDOL]RZDQH V SU]\ Z\NRU]\VWDQLX EUDPHN WUDQVPLV\MQ\FK MDN QD
U\VD
=PLDQD VWDQX Z\Mü SU]HU]XWQLND Z\QLNDMFD ] GRSURZDG]HQLD
LPSXOVX]PLHQLDMFHJRMHJRVWDQGRMHGQHJR]ZHMüDV\QFKURQLF]Q\FK
( )
R R
OXE
( )
S S
EG(GRV\QFKURQLF]QHJRZHMFLD
C
QDVWSXMH]DZV]H]
SHZQ\P RSy(QLHQLHP Z]JOGHP FKZLOL RVLJQLFLD ZDUWRFL SURJRZHM
QDSLFLDSU]H]]ERF]HLPSXOVXLQLFMXMFHJR]PLDQVWDQX
'
4
&
φ
φ
a)
b)
7*
1
7*
2
%
1
%
2
6
5
φ
7*
3
7*
4
%
3
%
4
φ
4
'
&
5
6
4
4
%
%
φ
φ
5\V D 6WUXNWXUD ZHZQWU]QD SU]HU]XWQLND ' W\SX % ILUP\ 0RWRUROD
EV\PEROORJLF]Q\SU]HU]XWQLND
'ODWHJR GOD ND*GHJR SU]HU]XWQLND GHILQLXMH VL QDVWSXMFH SDUDPHWU\
G\QDPLF]QH
−
F]DV\SURSDJDFMLV\JQDáyZRGZHMFLD]HJDURZHJRGRZ\MüQ
Q
L
−
F]DV\ SURSDJDFML V\JQDáyZ RG ZHMü DV\QFKURQLF]Q\FK GR Z\Mü
Q
Q
L
−
F]DVXVWDODQLD
t
s
DQJVHWXSWLPH
−
F]DVSU]HWU]\P\ZDQLD
t
h
DQJKROGWLPH
−
PLQLPDOQ\F]DVWUZDQLDRNUHORQ\FKV\JQDáyZQS
t
w
−
PDNV\PDOQDF]VWRWOLZRüSU]HELHJXV\QFKURQL]XMFHJR
1DU\VDSU]HGVWDZLRQRLOXVWUDFMGHILQLFMLF]DVyZSURSDJDFML
V\JQDáyZ RG ZHMFLD ]HJDURZHJR
C
GR Z\MFLD Q GOD QDUDVWDMFHJR
]ERF]D]HJDUDDQDU\VESU]HGVWDZLRQRLOXVWUDFM GHILQLFMLF]DVyZ
XVWDODQLD
t
s
LSU]HWU]\P\ZDQLD
t
h
&]DVXVWDODQLD
t
s
MHVW WR PLQLPDOQ\ F]DV Z NWyU\P V\JQDá
ZHMFLRZ\ PXVL E\ü REHFQ\ QD ZHMFLDFK LQIRUPDF\MQ\FK
V\QFKURQL]RZDQ\FK SU]HU]XWQLND SU]HG QDGHM FLHP Z\]ZDODMFHJR
]ERF]DLPSXOVX]HJDUDU\V
&]DV SU]HWU]\P\ZDQLD
t
h
MHVW WR PLQLPDOQ\ F]DV Z NWyU\P V\JQDá
ZHMFLRZ\
PXVL
SR]RVWDü
QD
ZHMFLX
LQIRUPDF\MQ\P
V\QFKURQL]RZDQ\P SR Z\VWSLHQLX Z\]ZDODMFHJR ]ERF]D V\JQDáX
]HJDUD
'
&
a)
b)
4
W
K
W
V
W
Z
W
3+/
+
+
+
/
/
/
W
W
W
W
3/+
50
50
50
'
&
W
K
W
V
+
+
/
/
W
W
50
50
5\V,OXVWUDFMDGHILQLFMLDF]DVyZSURSDJDFMLV\JQDáXV\QFKURQL]XMFHJR
&
GR
Z\MFLD
4
EF]DVyZXVWDODQLD
W
V
LSU]HWU]\PDQLD
t
h
3U]HU]XWQLN56PDVWHUVODYH
1D U\V SU]HGVWDZLRQR VWUXNWXU ORJLF]Q SU]HU]XWQLND 56
PDVWHU VODYH SRZVWDMF ] GZX NDVNDGRZR SRáF]RQ\FK
SU]HU]XWQLNyZ 56 2ED SU]HU]XWQLNL V EORNRZDQH QD SU]HPLDQ
V\JQDáHP]HJDURZ\P
C
4
4
6
5
0$67(5
6/$9(
&
5\V 3U]HU]XWQLN
56PDVWHUVODYH
*G\ V\JQDá ]HJDUD
C
=
1
LQIRUPDFMD ZHMFLRZD ] ZHMü R S
,
MHVW ZF]\W\ZDQD GR SU]HU]XWQLND JáyZQHJR 6WDQ Z\Mü QLH XOHJD
]PLDQLH SRQLHZD* SU]HU]XWQLN SRPRFQLF]\ MHVW ]DEORNRZDQ\
]DQHJRZDQ\PV\JQDáHP C
=
0
*G\LPSXOV]HJDUD]PLHQLVZyMVWDQQD
C
=
0
SU]HU]XWQLNJáyZQ\
]RVWDMH ]DEORNRZDQ\ D UyZQRF]HQLH SU]HU]XWQLN SRPRFQLF]\ ]RVWDMH
RGEORNRZDQ\ L Z PRPHQFLH XMHPQHJR ]ERF]D LPSXOVX ]HJDUD VWDQ
SU]HU]XWQLNDJáyZQHJR]RVWDMHSU]HND]DQ\QDZ\MFLH3RGREQLHMDNZ
V\QFKURQL]RZDQ\PSU]HU]XWQLNX56WDNLWXWDMNRPELQDFMD]PLHQQ\FK
ZHMFLRZ\FK
R
S
= =
1
SU]\
C
=
1
MHVW QLHGR]ZRORQD SRQLHZD*
SURZDG]LGRQLHRNUHORQHJR]DFKRZDQLDVLSU]HU]XWQLNDSU]\SU]HMFLX
]HJDUDGRVWDQX
3U]HU]XWQLN-.L-
.
PDVWHUVODYH
.ODV\F]Q\SU]HU]XWQLN -. Z\NRU]\VWXMH RE\GZD ]ERF]D LPSXOVX
VWHUXMFHJR GR ]PLDQ\ VWDQX SU]HU]XWQLND 3URVW UHDOL]DFM WDNLHJR
SU]HU]XWQLND VWDQRZL X*\FLH GZyFK ]DWU]DVNRZ\FK SU]HU]XWQLNyZ 56
SRáF]RQ\FKNDVNDGRZRZVSRVyESRND]DQ\QDU\VD
5
6
4
4
-
&
a)
b)
.
7DEOLFD7DEOLFHVWDQyZSU]HU]XWQLND-.
W
Q
t
n
+
1
W
Q
t
n
+
1
-
.
4
4
4
-
.
4
4
4
Q
4
Q
[
[
[
4
Q
4
Q
[
[
VWDQGRZROQ\
5\V 3U]HU]XWQLN -. PDVWHUVODYH D VFKHPDW ORJLF]Q\ XNáDGX E WDEOLFD
VWDQyZ
-HVW RQ Z\SRVD*RQ\ Z ZHMFLD SURJUDPXMFH
J
L
K
ZHMFLH
V\QFKURQL]XMFH ]HJDURZH
C
RUD] GZD ZHMFLD DV\QFKURQLF]QH
XVWDZLDMFH S L ]HUXMFH R =ZURWQH SRGDQLH GRSHáQLDMF\FK VL
V\JQDáyZ Z\MFLRZ\FK SU]HU]XWQLND QD MHJR ZHMFLD SU]\ F]\P
]HZQWU]QH ZHMFLD QRV] QD]Z ZHMü J K
,
SR]ZDOD UyZQLH* QD
Z\NRU]\VWDQLHNRPELQDFML]PLHQQ\FKZHMFLRZ\FK
J
K
= =
1
:HMFLD
DV\QFKURQLF]QH R L S XPR*OLZLDM ]PLDQ VWDQX SU]HU]XWQLND
QLH]DOH*QLH RG VWDQX QD ZHMFLX ]HJDUD
C
']LDáDQLH ORJLF]QH
SU]HU]XWQLND -.06 PR*QD RSLVDü SU]\ SRPRF\ MHGQHM ] GZyFK WDEHO
QDU\VE]NWyU\FKND*GDVDPRG]LHOQLHLMHGQR]QDF]QLHRSLVXMH
G]LDáDQLH SU]HU]XWQLND .ROXPQ\
t
n
Z WDEOLFDFK RNUHODM V\WXDFM
LVWQLHMF SU]HG GRSURZDG]HQLHP LPSXOVX ]HJDUD QDWRPLDVW Z
NROXPQDFK
t
n
+
1
MHVWRSLVDQDV\WXDFMDLVWQLHMFDSR]DNRF]HQLXLPSXOVX
]HJDUD 6WDQ Z MDNLP XVWDZLD VL SU]HU]XWQLN ]DOH*\ RG VWDQyZ ZHMü
SURJUDPXMF\FK J K
,
RUD] RG SRSU]HGQLHJR VWDQX SU]HU]XWQLND *G\
MHGQR ] ZHMü SURJUDPXMF\FK SU]\MPXMH ZDUWRü G]LDáDQLH
SU]HU]XWQLND-.MHVWDQDORJLF]QHGRG]LDáDQLDSU]HU]XWQLND56DJG\QD
REXZHMFLDFK
J
L
K
Z\VWSXMHVWDQZyZF]DVSU]HU]XWQLN ]PLHQLD
VWDQ SR ND*G\P LPSXOVLH ]HJDUD :SURZDG]RQH VSU]*HQLH ]ZURWQH
SRZRGXMH RJUDQLF]HQLH SUDF\ SU]HU]XWQLND -. WDEOLFH SU]HM ü ]
U\VERERZL]XMW\ONRZyZF]DVJG\SU]\VWDQLH]HJDUD
C
=
1
VWDQ
ZHMüSURJUDPXMF\FK
J
L
K
QLHXOHJD]PLDQLH:SU]HFLZQ\PUD]LH
G]LDáDQLH SU]HU]XWQLND PR*H E\ü QLHSUDZLGáRZH :DG\ WHM QLH PDM
SU]HU]XWQLNL Z\]ZDODQH ]ERF]HP Z NWyU\FK ZSURZDG]HQLH GDQ\FK ]
ZHMü SURJUDPXMF\FK L RGSRZLHGQLD ]PLDQD VWDQX Z\Mü QDVWSXMH
V\QFKURQLF]QLH ] MHGQ\P ]ERF]HP LPSXOVX ]HJDUD : WDNLFK
SU]HU]XWQLNDFK -. Z\]ZDODQ\FK ]ERF]HP ]PLDQ\ VWDQyZ
J
L
K
SRGF]DVWUZDQLDLPSXOVX]HJDURZHJRVGRSXV]F]DOQH
6FKHPDW\ ORJLF]QH VFDORQ\FK SU]HU]XWQLNyZ -. Z\]ZDODQ\FK
LPSXOVHP PDM QLHFR LQQ EXGRZ RG SU]HGVWDZLRQHM QD U\V
]DOH*QLHRGVWRVRZDQHMWHFKQRORJLL
1D U\VD SU]HGVWDZLRQR VWUXNWXU ORJLF]Q SU]HU]XWQLND -
.
W\SX /6 L MHJR WDEOLF VWDQyZ 6WUXNWXUD ORJLF]QD WHJR
SU]HU]XWQLND MHVW Z\QLNLHP PRG\ILNDFML VWUXNWXU\ SU]HU]XWQLND W\SX '
SU]\SRáF]HQLX J K
=
RWU]\PXMHVLSU]HU]XWQLN':\]ZDODQ\MHVW
RQQDUDVWDMF\P]ERF]HPLPSXOVX]HJDUD
5
6
4
4
a)
b)
-
&
1
2
3
4 1
5
6
4 2
4 3
.
5\V 3U]HU]XWQLN - . W\SX /6 D VWUXNWXUD SU]HU]XWQLND E WDEOLFD
VWDQyZ
5yZQLH* Z WHFKQRORJLL &026 VWUXNWXU ORJLF]Q SU]HU]XWQLND
-
.
RWU]\PXMHVLZZ\QLNXSURVWHJRSU]HNV]WDáFHQLDSU]HU]XWQLNDW\SX
'Z\]ZDODQHJR]ERF]HPMDNWRSU]HGVWDZLRQRQDU\V
6
6
OXE
4
4
-
&
.
6WUXNWXUD
SU]HU]XWQLND
'
'
5
5
OXE
5\V 6WUXNWXUD SU]HU]XWQLND
- . UHDOL]RZDQHJR Z WHFKQRORJLL
&026
)XQNFMD ORJLF]QD QD ZHMFLX LQIRUPDF\MQ\P SU]HU]XWQLND
D
UHDOL]RZDQDSU]H]ZHMFLRZ\XNáDGNRPELQDF\MQ\PDSRVWDü
(
) (
) (
)
(
)
D
J
Q
K Q
J
Q
K
Q
=
+
+
⋅
=
+
+
7DNVWUXNWXUSRVLDGDMQSSU]HU]XWQLNLVFDORQH+&-H*HOL
] ZHMFLD K ]RVWDQLH XVXQLW\ LQZHUWHU RWU]\PXMH VL ZyZF]DV
SU]HU]XWQLN -.06 D SU]\NáDGHP WDNLHM UHDOL]DFML PR *H E\ü XNáDG
%3URGXNRZDQHVUyZQLH*SU]HU]XWQLNL-.Z\]ZDODQHXMHPQ\P
7DEOLFD
5 6 - . & 4 4
+ / [ [ [ + /
/ + [ [ [ / +
/ / [ [ [ + +
+ + / /
/ +
+ + + +
+ /
+ + + /
4
Q
4
Q
+ + / +
4
Q
4
Q
+ + [ [
E] E]
8ZDJD
4
Q
VWDQ QD Z\MFLX
4
EH]SRUHGQLR SU]HG SRMD
ZLHQLHP
VL QDUDVWDMFHJR
]ERF]D LPSXOVX ]HJDUD
E]
EH] ]PLDQ
]ERF]HP]HJDUD3U]\NáDGHPWHJRW\SXSU]HU]XWQLNyZPRJE\üXNáDG\
+& Z WHFKQRORJLL +&026 L /6 Z WHFKQRORJLL /677/
SURGXNXMHVLUyZQLH*$&$&7$/6$)LWS
-DN SRND]DQR QD U\V VWUXNWXU ORJLF]Q SU]HU]XWQLND
+& RWU]\PXMHP\ Z Z\QLNX PRG\ILNDFML XNáDGX ] U\V
SROHJDMFHM QD SU]HVXQLFLX LQZHUWHUD ] ZHMFLD K QD ZHMFLH
C
L
UHDOL]DFMDSU]HU]XWQLND'MDNZXNáDG]LH+&
6
4
4
-
&
.
6WUXNWXUD
SU]HU]XWQLND
+&4
'
5
5
6
&
4
4
5\V6WUXNWXUDSU]HU]XWQLND+&RUD]WDEOLFDMHJRVWDQyZ
/,&=1,.,
.ODV\ILNDFMDLSRGVWDZRZHSDUDPHWU\OLF]QLNyZ
/LF]QLNL V VHNZHQF\MQ\PL XNáDGDPL F\IURZ\PL ]OLF]DMF\PL
OLF]E LPSXOVyZ SRGDQ\FK Z RNUHORQ\P SU]HG]LDOH F]DVX QD LFK
ZHMFLH =EXGRZDQH V ] SHZQHM OLF]E\ n
≥
1
V\QFKURQLF]Q\FK
SU]HU]XWQLNyZ RGSRZLHGQLR ]H VRE SRáF]RQ\FK 2SUyF] ZHMFLD GOD
LPSXOVyZ ]OLF]DQ\FK OLF]QLN SRVLDGD ZHMFLH DV\QFKURQLF]QH
XVWDZLDMFH MHJR VWDQ SRF]WNRZ\ 8VWDZLHQLH ZV]\VWNLFK
SU]HU]XWQLNyZOLF]QLNDZVWDQQD]\ZDVL]HURZDQLHPOLF]QLND
:OLF]QLNDFKGZyMNRZ\FK n VWDQRZLOLF]EELWyZOLF]QLNDF]\OL
OLF]E]QDNyZZOLF]ELHGZyMNRZHMUHSUH]HQWXMFHMVWDQOLF]QLND
/LF]E VWDQyZ SU]\MPRZDQ\FK SU]H] OLF]QLN Z MHGQ\P SHáQ\P
F\NOX QD]\ZD VL GáXJRFL F\NOX OXE SRMHPQRFL OLF]QLND -H*HOL
OLF]QLN VNáDGD VL ] Q SU]HU]XWQLNyZ WR MHJR SRMHPQRü ]DOH*QD RG
7DEOLFD
5 6 - . & 4 4
+ / [ [ [ + /
/ + [ [ [ / +
/ / [ [ [ + +
+ + / +
/ +
+ + + /
+ /
+ + + +
4
Q
4
Q
+ + / /
4
Q
4
Q
+ + [ [
E] E]
+ + [ [ [ E] E]
E]EH]]PLDQ
SRáF]H ORJLF]Q\FK PLG]\ SRV]F]HJyOQ\PL SU]HU]XWQLNDPL ]DZLHUD
VLZSU]HG]LDOH
<
>
1 2
,
n
-H*HOL OLF]QLN PD p Uy*Q\FK VWDQyZ SU]H] NWyUH SU]HFKRG]L
F\NOLF]QLHWRRNUHODVLJRMDNROLF]QLNPRGXORS
.D*GHPX RNUHORQHPX VWDQRZL OLF]QLND RGSRZLDGD MHGQD
RNUHORQD NRPELQDFMD VWDQyZ SU]HU]XWQLNyZ WZRU]F\FK OLF]QLN
/LF]QLNGZyMNRZ\RSRMHPQRFLQD]\ZDVLOLF]QLNLHPG]LHVLWQ\P
OXEGHNDGRZ\P3HáQ\F\NOSUDF\WDNLHJROLF]QLNDREHMPXMHVWDQyZ
=DZDUWRü OLF]QLND G]LHVLWQHJR Z\UD*D VL Z ]DSLVLH G]LHVLWQ\P
NRGRZDQ\PGZyMNRZR%&'DQJ%LQDU\&RGHG'HFLPDO
'RNRQXMF SRG]LDáX OLF]QLNyZ SRG Z]JOGHP GáXJRFL F\NOX
PR*HP\Z\Uy*QLü
OLF]QLNLRVWDáHMGáXJRFLF\NOX
OLF]QLNLRSURJUDPRZDOQHMGáXJRFLF\NOX
-H*HOL NROHMQH OLF]E\ UHSUH]HQWXMFH VWDQ\ OLF]QLND Z]UDVWDM Z
WUDNFLH OLF]HQLD LPSXOVyZ WR WDNLH OLF]QLNL QD]\ZDP\ OLF]QLNDPL
]OLF]DMF\PLZSU]yG:SU]HFLZQ\PUD]LHMHOLPDOHMWRQD]\ZDP\
MH OLF]QLNDPL ]OLF]DMF\PL ZVWHF] /LF]QLNL NWyUH SRVLDGDM ]GROQRü
]OLF]DQLD LPSXOVyZ ]DUyZQR Z SU]yG MDN L ZVWHF] RNUHOD VL MDNR
OLF]QLNLGZXNLHUXQNRZHOXEUHZHUV\MQH
%DUG]RLVWRWQ\PNU\WHULXPSRG]LDáXOLF]QLNyZPR*HE\üVSRVyE
RGG]LDá\ZDQLDLPSXOVyZ]OLF]DQ\FKQDVWDQSU]HU]XWQLNyZOLF]QLND=H
Z]JOGXQDWRNU\WHULXPOLF]QLNLPR*QDVNODV\ILNRZDüMDNR
V\QFKURQLF]QH
DV\QFKURQLF]QH
DV\QFKURQLF]QRV\QFKURQLF]QH
:OLF]QLNXV\QFKURQLF]Q\PDQJV\QFKURQRXVFRXQWHULPSXOV\
]OLF]DQH V SRGDQH QD ZHMFLD ]HJDURZH ZV]\VWNLFK SU]HU]XWQLNyZ
QDWRPLDVW Z OLF]QLNX DV\QFKURQLF]Q\P DQJ ULSSOH FRXQWHU RUD]
DV\QFKURQLF]QRV\QFKURQLF]Q\PLPSXOV\]OLF]DQHSRGDMHVLW\ONRQD
MHGQROXEQLHNWyUH]ZHMü]HJDURZ\FKSU]HU]XWQLNyZOLF]QLND
3U]\GDWQRü OLF]QLND GR SUDF\ Z RNUHORQ\FK V\VWHPDFK
F\IURZ\FKPR*HE\üRFHQLDQDZRSDUFLXRMHJRSRGVWDZRZHSDUDPHWU\
V]\ENRüG]LDáDQLD
F]DVXVWDODQLD]DZDUWRFLOLF]QLND
6]\ENRü G]LDáDQLD RNUHOD VL SU]H] SRGDQLH PDNV\PDOQHM
GRSXV]F]DOQHM F]VWRWOLZRFL
f
max
LPSXOVyZ ]OLF]DQ\FK 1DMSURVWV]\P
OLF]QLNLHP LPSXOVyZ MHVW OLF]QLN PRGXOR PRG NWyU\ PR*QD
]UHDOL]RZDü SU]\ X*\FLX SU]HU]XWQLND ' OXE -. MDN WR SRND]DQR QD
U\V 3U]HU]XWQLN NWyU\ ]PLHQLD VZyM VWDQ SR ND*G\P LPSXOVLH
]HJDUDQD]\ZDQ\MHVWSU]HU]XWQLNLHPW\SX7
a)
b)
'
&
&
+
4
4
4
4
+
-
&
5
6 4
4
.
+
+
+
&
4
4
6
5
5\V/LF]QLNPRG]UHDOL]RZDQ\SU]\X*\FLXSU]HU]XWQLNDDW\SX'E-.
1D U\V SU]HGVWDZLRQR RJyOQ\ VFKHPDW ORJLF]Q\ OLF]QLND
DV\QFKURQLF]QHJR
&
4
4
4
4
4
&
&
&
&
1
3
2
:HMFLH GOD
LPSXOVyZ
]OLF]DQ\FK
:\MFLD
Q
−
Q
5\V6FKHPDWORJLF]Q\OLF]QLNDDV\QFKURQLF]QHJR
: OLF]QLNX DV\QFKURQLF]Q\P QD U\V PDNV\PDOQD
F]VWRWOLZRü LPSXOVyZ Z\MFLRZ\FK Z\VWSXMH W\ONR Z SLHUZV]\P
SU]HU]XWQLNX L QLH PR*H SU]HNURF]\ü GRSXV]F]DOQHM ZDUWRFL
f
max
3RQLHZD*PDNV\PDOQ\F]DVXVWDODQLDVL]DZDUWRFLOLF]QLNDMHVWVXP
F]DVyZ SURSDJDFML t
p
ZV]\VWNLFK SU]HU]XWQLNyZ WR PDNV\PDOQD
F]VWRWOLZRüZHMFLRZDQLHSRZLQQDSU]HNURF]\üZDUWRFL
(
)
f
n t
t
p
max
max
≤
+
−
0
1
JG]LHn OLF]EDSU]HU]XWQLNyZZFKRG]F\FKZVNáDGOLF]QLND
t
p
F]DVSURSDJDFMLMHGQHJRSU]HU]XWQLND
t
0
F]DVSRWU]HEQ\QDXVWDOHQLHVL]DZDUWRFLOLF]QLNDSRND*G\P
LPSXOVLH]OLF]DQ\P
: OLF]QLNX V\QFKURQLF]Q\P ZHMFLD ]HJDURZH ZV]\VWNLFK
SU]HU]XWQLNyZVSRáF]RQHFR]DSHZQLDMHGQRF]HVQRü]PLDQVWDQyZ
SU]HU]XWQLNyZ &]DV XVWDODQLD ]DZDUWRFL OLF]QLND GHWHUPLQRZDQ\ MHVW
VXP F]DVyZ SURSDJDFML V\JQDáX SU]H] XNáDG\ NRPELQDF\MQH
UHDOL]XMFH ]ELyU IXQNFML SU]HáF]DMF\FK GOD ZHMü LQIRUPDF\MQ\FK
SU]HU]XWQLNyZ OLF]QLND =H Z]JOGX QD VSRVyE UHDOL]DFML W\FK IXQNFML
Z\Uy*QLDVL
±
OLF]QLNLV\QFKURQLF]QH]SU]HQLHVLHQLDPLUyZQROHJá\PLDQJ SDUDOOHO
FDUU\OXEORRNDKHDG
±
OLF]QLNL V\QFKURQLF]QH ] SU]HQLHVLHQLDPL V]HUHJRZ\PL DQJ VHULDO
FDUU\OXEULSSOHFDUU\
1D U\V SU]HGVWDZLRQR WHQ VDP OLF]QLN V\QFKURQLF]Q\ Z
GZyFK ZHUVMDFK ] SU]HQLHVLHQLDPL UyZQROHJá\PL RUD] V]HUHJRZ\PL
-DN PR*QD ZQLRVNRZDü QD SRGVWDZLH WHJR U\VXQNX UyZQROHJá\ XNáDG
SU]HQLHVLH ]DSHZQLD QDMNUyWV]\ F]DV SURSDJDFML F]\OL QDMZL NV]
F]VWRWOLZRü LPSXOVyZ ]OLF]DQ\FK OHF] MHJR ]áR*RQRü Z]UDVWD
SURSRUFMRQDOQLHGROLF]E\SU]HU]XWQLNyZELWyZOLF]QLND
%
&
4
:HMFLH GOD
LPSXOVyZ
]OLF]DQ\FK
7
&
4
7
&
4
7
&
4
7
&
4
7
&
4
7
&
4
7
&
4
7
&
4
7
&
4
7
(
'
&
$
%
$
(
'
&
:HMFLH GOD
LPSXOVyZ
]OLF]DQ\FK
a)
b)
5\V 6FKHPDW\ ORJLF]QH OLF]QLNyZ V\QFKURQLF]Q\FK ] SU]HQLHVLHQLDPL
DUyZQROHJá\PLEV]HUHJRZ\PL
/LF]QLNLDV\QFKURQLF]QH
$V\QFKURQLF]Q\ OLF]QLN GZyMNRZ\ PR*QD ]UHDOL]RZDü WZRU]F
áDFXFK V]HUHJRZ\ GZyMHN OLF]F\FK Z NWyU\P ZHMFLH ]HJDURZH
C
ND*GHJRSU]HU]XWQLNDSRáF]RQHMHVW]Z\MFLHP Q SRSU]HGQLHJRMDNWR
SRND]DQRQDU\V
$E\ RWU]\PDü ]OLF]DQLH Z SU]yG SU]HU]XWQLNL PXV] ]PLHQLDü
VZyMVWDQSU]\]PLDQLHLPSXOVX]HJDURZHJR]QD:DUXQHNWHQMHVW
VSHáQLRQ\ SU]\ ]DVWRVRZDQLX SU]HU]XWQLNyZ -. PDVWHU VODYH SU]\
XVWDZLRQ\FK
J
K
= =
1
/LF]QLN WHQ PR*QD GRZROQLH UR]V]HU]Dü
:SU]HGVWDZLRQ\P XNáDG]LH PR*QD UyZQLH* ]DVWRVRZDü SU]HU]XWQLNL
Z\]ZDODQHGRGDWQLP]ERF]HPLPSXOVX]HJDUDF]\OLQSSU]HU]XWQLNL'
Z\]ZDODQH]ERF]HP
&
4
&
4
-
&
4
%
$
&
&/.
1
1
1
.
-
.
.
-
&/.
%
$
&
a)
b)
c)
5\V$V\QFKURQLF]Q\OLF]QLNGZyMNRZ\DVFKHPDWORJLF]Q\EWDEOLFDVWDQyZ
FSU]HELHJLF]DVRZH
-HGQDN Z WDNLP SU]\SDGNX SU]\ SRáF]HQLDFK WDNLFK MDN QD U\V
RWU]\PDP\ OLF]QLN ]OLF]DMF\ ZVWHF] $E\ ]UHDOL]RZDü ]OLF]DQLH Z
SU]yG QDOH*\ GRNRQDü LQZHUVML V\JQDáX ]HJDURZHJR OXE SURFLHM
ZHMFLD ]HJDURZH SU]HU]XWQLNyZ SRáF]\ü ] Z\MFLDPL Q
SRSU]HG]DMF\FKSU]HU]XWQLNyZ=OLF]DQLHZVWHF]R]QDF]D *H ZDUWRFL
OLF]ERZHRGSRZLDGDMFHNROHMQ\PVWDQRPVPDOHMFH
-DNSRND]DQRQDU\VFOLF]QLNMHVWUyZQRF]H QLHG]LHOQLNLHP
F]VWRWOLZRFL SRQLHZD* F]VWRWOLZRü QD Z\MFLX NROHMQHJR
SU]HU]XWQLND MHVW UyZQD SRáRZLH F]VWRWOLZRFL QD MHJR ZHMFLX
]HJDURZ\PF]\OLQDZ\MFLXSRSU]HG]DMFHJRSU]HU]XWQLND
: FHOX ]GHNRGRZDQLD SRV]F]HJyOQ\FK VWDQyZ OLF]QLND QDOH *\
]DVWRVRZDü GHNRGHU 3RQLHZD* ]PLDQ\ VWDQyZ SU]HU]XWQLNyZ OLF]QLND
QDVWSXM ] SHZQ\P RSy(QLHQLHP GODWHJR QD Z\MFLX GHNRGHUD PRJ
SRMDZLüVLIDáV]\ZHVWDQ\:FHOXZ\HOLPLQRZDQLDW\FKVWDQyZQDOH *\
]DVWRVRZDüGHNRGHU]HVWURERZDQLHPLPSXOVyZZHM FLRZ\FK
0DNV\PDOQD ZDUWRü F]VWRWOLZRFL LPSXOVyZ ZHMFLRZ\FK GOD
OLF]QLNDDV\QFKURQLF]QHJR]GHNRGRZDQLHPVWDQyZZ\QRVL
1
f
n t
t
p
s
max
≥
+
SU]\F]\P
n
OLF]EDSU]HU]XWQLNyZ
t
p
F]DVRSy(QLHQLDSURSDJDFMLMHGQHJRSU]HU]XWQLND
t
s
F]DVVWURERZDQLDF]DVWUZDQLDLPSXOVXQDZ\M FLXGHNRGHUD
$ % &
']LHOQLN F]VWRWOLZRFL ]UHDOL]RZDQ\ ] NDVNDGRZR SRáF]RQ\FK
SU]HU]XWQLNyZW\SX7PR*HPLHüZVSyáF]\QQLNSRG]LDáXF]VWRWOLZRFL
UyZQ\ W\ONR SRWG]H OLF]E\ 8]\VNDQLH LQQHJR ZVSyáF]\QQLND MHVW
PR*OLZH MH*HOL ]RVWDQ ]DVWRVRZDQH VSU]*HQLD ]ZURWQH NWyUH XVXQ
QDGPLDU VWDQyZ OLF]QLND 1D U\V SU]HGVWDZLRQR DV\QFKURQLF]Q\
OLF]QLNG]LHVLWQ\]HVSU]*HQLHP]HUXMF\P
&
4
&
4
-
&
4
&/.
1
1
1
.
-
.
.
-
&
4
-
.
1
5
5
5
5
5\V$V\QFKURQLF]Q\
OLF]QLN
G]LHVLWQ\
]H
VSU]*HQLHP]HUXMF\P
/LF]QLNL DV\QFKURQLF]QH ]DSURMHNWRZDQH Z WHQ VSRVyE PRJ G]LDáDü
QLHSUDZLGáRZRZSU]\SDGNXJG\F]DVRSy(QLHQLDSURSDJDFMLPLG]\
ZHMFLHP]HUXMF\PSU]HU]XWQLNDDMHJRZ\MFLHPPDUy*QZDUWRüGOD
SRV]F]HJyOQ\FK SU]HU]XWQLNyZ :yZF]DV LPSXOV ]HUXM F\ UyZQ\
QDMPQLHMV]HPX ] F]DVyZ RSy(QLH PR*H WUZDü ]E\W NUyWNR DE\
Z\]HURZDü FDá\ OLF]QLN : FHOX Z\HOLPLQRZDQLD WHJR QLHSR *GDQHJR
]MDZLVND QDOH*\ ]DVWRVRZDü GRGDWNRZR SU]HU]XWQLN 56 XVWDZLDQ\ Z
VWDQ ]GHNRGRZDQ\P VWDQHP OLF]QLND D ]HURZDQ\ LPSXOVDPL
ZHMFLRZ\PLU\V
&
4
&
4
-
&
4
&/.
1
1
1
.
-
.
.
-
&
4
-
.
1
5
5
5
5
4
4
5\V$V\QFKURQLF]Q\
OLF]QLN
G]LHVLWQ\
]
]HUXMF\P XNáDGHP VSU]
*HQLD ]DZLHUDMF\P SU]H
U]XWQLN56
:LHOHUy*Q\FKW\SyZOLF]QLNyZDV\QFKURQLF]Q\FKMHVWGRVW SQ\FK
Z SRVWDFL XNáDGyZ VFDORQ\FK 'OD SU]\NáDGX QL *HM ]RVWDá\
SU]HGVWDZLRQH VFKHPDW\ ORJLF]QH MHGQ\FK ] SLHUZV]\FK VFDORQ\FK
OLF]QLNyZDV\QFKURQLF]Q\FK/6+&L/6+&
/LF]QLN¶U\VVNáDGDVL]F]WHUHFKSU]HU]XWQLNyZ$%&
' W\SX 06 SRáF]RQ\FK Z WHQ VSRVyE *H WZRU] GZD OLF]QLNL MHGHQ
]OLF]DMF\PRGSU]HU]XWQLN$LGUXJL]OLF]DMF\PRGSU]HU]XWQLNL
% & L ' :\MFLH SU]HU]XWQLND $ QLH MHVW SRáF]RQH ZHZQWU]QLH
]ZHMFLHP QDVWSQHJR SU]HU]XWQLND FR VWZDU]D PR*OLZRü
Z\NRU]\VWDQLDXNáDGXMDNROLF]QLNDG]LHOFHJRSU]H]RUD]SU]H]
&
4
&
4
-
&
4
.
-
.
.
-
&
4
5
6
$
ZH
%'
ZH
( )
50 1
( )
50 2
( )
59 2
( )
59 1
$
%
&
'
a)
c)
b)
90
( )
50 1
( )
50 2
( )
59 1
( )
59 2
%'
ZH
$
ZH
$
%
&
'
5\V 6FDORQ\ OLF]QLN DV\QFKURQLF]Q\ ¶ D VFKHPDW ORJLF]Q\ E V\PERO
JUDILF]Q\FNRGOLF]QLND
/LF]QLN PD GZD EUDPNRZDQH ZHMFLD ] NWyU\FK MHGQR ZHMFLH
( )
R0 1
L
( )
R0 2
VáX*\ GR XVWDZLHQLD OLF]QLND Z VWDQ ]HURZ\ D GUXJLH
ZHMFLD
( )
R9 1
L
( )
R9 2
VáX*\ GR XVWDZLHQLD OLF]QLND Z VWDQ
RGSRZLDGDMF\ OLF]ELH /LF]QLN XPR*OLZLD X]\VNDQLH SRG]LDáX
SU]H]WDN*HZSU]\SDGNXJG\MHVWZ\PDJDQHZ\SHáQLHQLHSU]HELHJX
Z\MFLRZHJR
/LF]QLN¶U\VVNáDGDVL]F]WHUHFKSU]HU]XWQLNyZ$%
&L'W\SX06SRáF]RQ\FKZWHQVSRVyE*HWZRU]OLF]QLNL]OLF]DMFH
PRG L PRG /LF]QLN PD EUDPNRZDQH ZHM FLH ]HUXMFH ZHMFLH
( )
R0 1
L
( )
R0 2
:\MFLHSU]HU]XWQLND$QLHMHVWSRáF]RQHZHZQWU]QLH
]ZHMFLHPQDVWSQHJRSU]HU]XWQLND
2SUyF] RSLVDQ\FK F]WHURELWRZ\FK OLF]QLNyZ ELQDUQ\FK
/6+&/6+&Z\WZDU]DQHVZVNDOLSU]HP\VáRZHMOLF]QLNL
DV\QFKURQLF]QH /6+& SRGZyMQH VLHGPLRELWRZH
0& GZXQDVWRELWRZH +& RUD] F]WHUQDVWRELWRZH
+&
:UyGDV\QFKURQLF]Q\FKELQDUQ\FKG]LHOQLNyZF] VWRWOLZRFLQD
XZDJ ]DVáXJXM XNáDG\ /6+& XPR*OLZLDMFH SRG]LDá
:\MFLD
' & % $
2EMDQLHQLH :\MFLH
$
MHVW SRáF]RQH ]
ZHMFLHP
%'
F]VWRWOLZRFL V\JQDáX ZHMFLRZHJR Z ]DNUHVLH
RUD] XNáDG\
/6+&XPR*OLZLDMFHSRG]LDáF]VWRWOLZRFLZ]DNUHVLH
&
4
&
4
-
&
4
.
-
.
.
-
&
4
5
6
$
ZH
%
ZH
( )
50 1
( )
50 2
$
%
&
'
a)
c)
b)
( )
50 1
( )
50 2
%
ZH
$
ZH
$
%
&
'
5\V 6FDORQ\ OLF]QLN ¶ D VFKHPDW ORJLF]Q\ E V\PERO JUDILF]Q\ F NRG
OLF]QLND
/LF]QLNLV\QFKURQLF]QH
/LF]QLNL V\QFKURQLF]QH FKDUDNWHU\]XM VL W\P *H ]OLF]DQH
LPSXOV\VSRGDZDQHUyZQRF]HQLHQDZV]\VWNLHZHMFLD]HJDURZH
C
SU]HU]XWQLNyZ
5R]ZD*P\ V\QFKURQLF]Q\ OLF]QLN PRG ]OLF]DMF\ Z SU]yG Z
QDWXUDOQ\PNRG]LHGZyMNRZ\P]UHDOL]RZDQ\ZRSDUFLXRSU]HU]XWQLNL
-.061DSRGVWDZLHWDEOLF\Z]EXG]HSU]HU]XWQLND-.06U\VE
L WDEOLF\ VWDQyZ OLF]QLND U\VD RWU]\PXMH VL WDEOLFH .DUQDXJKD
U\VE L F XPR*OLZLDMFH Z\]QDF]HQLH IXQNFML SU]HáF]DMF\FK GOD
SRV]F]HJyOQ\FKZHMü
J
K
L
SU]HU]XWQLNyZ
:\MFLD
' & % $
2EMDQLHQLH :\MFLH
$
MHVW SRáF]RQH ]
ZHMFLHP
%
a)
b)
1
0 0
%$
0 1
0 0
0 1
1 1
1 1 1 0
1 0
1
1
1
1
1
1
1
'&
-
$
[
[
[
[
[
[
[
[
0
0 0
%$
0 1
0 0
0 1
1 1
1 1 1 0
1 0
0
0
0
1
1
1
1
'&
-
%
[
[
[
[
[
[
[
[
0 0
%$
0 1
0 0
0 1
1 1
1 1 1 0
1 0
1
'&
-
&
[
[
[
[
[
[
[
0 0
%$
0 1
0 0
0 1
1 1
1 1 1 0
1 0
1
'&
-
'
[
[
[
[
[
[
[
[
-
$
%
=
-
$
=
1
1
0 0
%$
0 1
0 0
0 1
1 1
1 1 1 0
1 0
1
1
1
1
1
1
1
'&
.
$
[
[
[
[
[
[
[
[
0
0
0
0
0
0
[
0
0
0
0
0
0
0
-
$%&
%
=
-
$%
%
=
0 0
%$
0 1
0 0
0 1
1 1
1 1 1 0
1 0
1
1
1
1
'&
.
%
[
[
[
[
[
[
[
[
0 0
%$
0 1
0 0
0 1
1 1
1 1 1 0
1 0
0
1
1
'&
.
&
[
[
[
[
[
[
[
[
0 0
%$
0 1
0 0
0 1
1 1
1 1 1 0
1 0
0
1
'&
.
'
[
[
[
[
[
[
[
[
0
0
0
0
.
$
%
=
.
$
=
1
0
0
0
0
0
0
0
0
0
0
0
c)
.
$%&
'
=
.
$%
'
=
1
5\V /LF]QLN V\QFKURQLF]Q\ ]OLF]DMF\ Z SU]yG Z QDWXUDOQ\P NRG]LH
GZyMNRZ\P D WDEOLFD VWDQyZ E WDEOLFH .DUQDXJKD GOD ZHMü
-
FWDEOLFH.DUQDXJKDGODZHMü
.
= WDEOLF .DUQDXJKD RWU]\PXMHP\ QDVWSXMFH IXQNFMH GOD ZHMü
J K
,
' & % $
' & % $
J
K
J
K
A
J
K
A B
J
K
A B C
A
A
B
B
C
C
D
D
=
=
=
=
=
=
=
=
1
=DWHPSU]HU]XWQLNZFKRG]F\ZVNáDGOLF]QLNDGZyMNRZHJRPR*H
]PLHQLüVZyMVWDQW\ONRZWHG\NLHG\ZV]\VWNLHSU]HU]XWQLNLSRSU]HGQLH
V Z VWDQLH MHGHQ -DN MX* RPyZLRQR Z UR]G] ]H Z]JOGX QD
VSRVyE UHDOL]DFML IXQNFML Z\Uy*QLD VL OLF]QLNL V\QFKURQLF]QH ]
SU]HQLHVLHQLDPL UyZQROHJá\PL OXE V]HUHJRZ\PL 6FKHPDW\ ORJLF]QH
OLF]QLNyZGODRE\GZXURG]DMyZSU]HQLHVLHSU]HGVWDZLRQRQDU\V
: XNáDG]LH ] SU]HQLHVLHQLDPL UyZQROHJá\PL Z PLDU ]ZLNV]HQLD
SRMHPQRFL OLF]QLND Z\VWSXMH SRWU]HED VWRVRZDQLD EUDPHN R
]ZLNV]DMFHM VL OLF]ELH ZHMü RUD] ]ZLNV]D VL REFL*HQLH Z\Mü
SU]HU]XWQLNyZ = NROHL V]\ENRü G]LDáDQLD OLF]QLND ] SU]HQLHVLHQLDPL
V]HUHJRZ\PL MHVW ]QDF]QLH PQLHMV]D RG V]\ENR FL OLF]QLND ]
SU]HQLHVLHQLDPLUyZQROHJá\PL]HZ]JOGXQDVSRVyEUHDOL]DFMLIXQNFML
SU]HáF]DMF\FK J K
,
SRV]F]HJyOQ\FKSU]HU]XWQLNyZ
: SRGREQ\ VSRVyE MDN GOD OLF]QLND GZyMNRZHJR PR *QD
Z\]QDF]\ü IXQNFMH SU]HáF]DMFH QD ZHMFLDFK LQIRUPDF\MQ\FK
SU]HU]XWQLNyZ RUD] VWUXNWXU ORJLF]Q OLF]QLNyZ V\QFKURQLF]Q\FK R
PQLHMV]HM SRMHPQRFL QL* OLF]ED VWDQyZ Z\QLNDMFD ] OLF]E\
]DVWRVRZDQ\FKSU]HU]XWQLNyZ p
n
<
2
5R]ZD*P\ GOD SU]\Ná DGX GHNDG OLF]F Z NRG]LH 1D
U\VDSU]HGVWDZLRQRWDEOLFVWDQyZOLF]QLNDPRGDQDU\VEL
F WDEOLFH .DUQDXJKD RGSRZLHGQLR GOD ZHMü
J
L
K
SU]HU]XWQLNyZ
.ODWNL SXVWH RGSRZLDGDM VWDQRP QLHZ\NRU]\VW\ZDQ\P ]DWHP SU]\
]DSLVLHIXQNFMLSU]HáF]DMF\FKQLHPDMRQH]QDF]HQLD
)XQNFMH SU]HáF]DMFH GOD SRV]F]HJyOQ\FK ZHMü J K
,
SU]HU]XWQLNyZPDMSRVWDü
J
K
J
A D
K
A
J
A D
K
A B
J
A B C
K
A
A
A
B
B
C
C
D
D
=
=
=
=
=
=
=
=
1
1
6FKHPDWORJLF]Q\GHNDG\OLF]FHMZNRG]LHSU]HGVWDZLRQR
QDU\V
b)
1
0 0
%$
0 1
0 0
0 1
1 1
1 1 1 0
1 0
1
1
1
1
'&
-
$
[
[
[
[
[
0
0 0
%$
0 1
0 0
0 1
1 1
1 1 1 0
1 0
0
0
1
1
'&
-
%
[
[
[
[
0 0
%$
0 1
0 0
0 1
1 1
1 1 1 0
1 0
'&
-
&
[
[
[
[
0 0
%$
0 1
0 0
0 1
1 1
1 1 1 0
1 0
1
'&
-
'
[
[
-
$'
%
=
-
$
=
1
1
0 0
%$
0 1
0 0
0 1
1 1
1 1 1 0
1 0
1
1
1
1
'&
.
$
[
[
[
[
[
0
0
0
0
0
0
0
0
0
0
0
0
-
$%&
%
=
-
$%
%
=
0 0
%$
0 1
0 0
0 1
1 1
1 1 1 0
1 0
1
1
'&
.
%
[
[
[
[
[
[
0 0
%$
0 1
0 0
0 1
1 1
1 1 1 0
1 0
1
'&
.
&
[
[
[
[
[
[
0 0
%$
0 1
0 0
0 1
1 1
1 1 1 0
1 0
'&
.
'
[
[
[
[
[
[
[
[
0
0
.
$
%
=
.
$
=
1
0
0
0
0
c)
.
$
'
=
.
$%
'
=
0
1
5\V'HNDGDOLF]FDZNRG]LHDWDEOLFDVWDQyZEWDEOLFH.DUQDXJKDGOD
ZHMü
-
FWDEOLFH.DUQDXJKDGODZHMü
.
3U]\NáDGHP VHU\MQLH SURGXNRZDQ\FK OLF]QLNyZ V\QFKURQLF]Q\FK
PRJ E\ü OLF]QLNL F]WHURELWRZH /6$ &026
RPLRELWRZH /6 RUD] Z Z\NRQDQLX VSHFMDOQ\P XNáDG\
+& +& LWS MDNR SURJUDPRZDQH OLF]QLNL
RPLRELWRZH]SRMHG\QF]\PZHMFLHP
a)
' & % $
' & % $
%
.
=HU
&
4
-
1
-
2
-
3
5
4
&
4
-
1
-
2
-
3
.
1
.
2
.
3
5
4
&
4
-
1
-
2
-
3
.
1
.
2
.
3
5
4
'
'
&
&
%
.
&
4
-
5
4
$
$
&/.
5\V'HNDGDOLF]FDZNRG]LH
6SHF\ILF]Q\P OLF]QLNLHP V\QFKURQLF]Q\P UHDOL]RZDQ\P SU]\
X*\FLXUHMHVWUXSU]HVXZQHJRMHVWW]ZOLF]QLN-RKQVRQD
1DU\VDSU]HGVWDZLRQRVFKHPDW ORJLF]Q\ GHNDG\ OLF]FHM Z
NRG]LH -RKQVRQD ]EXGRZDQHM Z RSDUFLX R SU]HU]XWQLNL -.06 D QD
U\VEZRSDUFLXRSU]HU]XWQLNL'
&
4
&
4
-
&
4
.
-
.
.
-
&
4
$
%
&
'
a)
b)
&
4
.
-
$
5
5
5
5
5
-
.
4
4
4
4
4
(
(
'
&
%
&
4
&
4
&
4
&
4
$
%
&
'
&
4
$
5
5
5
5
5 4
4
4
4
4
(
(
'
&
%
'
'
'
'
'
&/.
&/.
=HU
=HU
5\V 'HNDGD OLF]FD Z NRG]LH -RKQVRQD ]EXGRZDQD D Z RSDUFLX
RSU]HU]XWQLNL-.06EZRSDUFLXRSU]HU]XWQLNL'
&HFKFKDUDNWHU\VW\F]QOLF]QLND-RKQVRQD]OLF]DMFHJRPRGXORQQ
MHVWX*\FLHQSU]HU]XWQLNyZSRáF]RQ\FKZNDVNDGLSRáF]HQLH
Z\MFLD Q
n
RVWDWQLHJR SU]HU]XWQLND ] ZHMFLHP
D
1
SLHUZV]HJR
SU]HU]XWQLND RGSRZLHGQLR Q
J
n
]
1
RUD]
Q
K
n
]
1
SU]\ UHDOL]DFML
OLF]QLND QD SU]HU]XWQLNDFK -.06 .D*GH ] SR]RVWDá\FK Z\Mü
(
)
Q i
n
i
<
MHVWSRáF]RQH]QDVWSXMF\PSRQLPZHMFLHP
D
i
+
1
-DN SRND]DQR Z WDEOLF\ VWDQyZ OLF]QLND -RKQVRQD QDVW SQH
LPSXOV\ZSLVXMNROHMQHMHG\QNLGRFKZLOLZNWyUHMUHMHVWUX]\VNDVWDQ
2G WHM FKZLOL QD ZHMFLX SLHUZV]HJR SU]HU]XWQLND SRMDZLD VL
VWDQ L QDVWSQH LPSXOV\ Z\]ZDODMFH SRZRGXM NROHMQH ]HURZDQLH
SU]HU]XWQLNyZWDN *HSRLPSXOVDFKXNáDGSRQRZQLH]QDMGXMHVLZ
VWDQLH
7DEOLFD7DEOLFDVWDQyZG]LHVLWQHJROLF]QLND-RKQVRQD
(
' &
%
$
(
' &
%
$
%DUG]RLVWRWQFHFKOLF]QLND-RKQVRQDMHVWWR*H]ERF]HND*GHJR
NROHMQHJR LPSXOVX ]HJDUD SRZRGXMH SU]HáF]HQLH W\ONR MHGQHJR
SU]HU]XWQLND'ODWHJRSU]\GHNRGRZDQLXVWDQyZOLF]QLNDQLHZ\VW SXM
]DNáyFDMFH LPSXOV\ V]SLONRZH MDN WR PD PLHMVFH Z OLF]QLNDFK
V\QFKURQLF]Q\FKRPyZLRQ\FKZF]HQLHMZNWyU\FKSU]\GHNRGRZDQLX
VWDQyZ Z\MFLRZ\FK PRJ SRMDZLDü VL NUyWNLH LPSXOV\ V]SLONRZH
EGFHUH]XOWDWHPV]\ENRQDVWSXMF\FKSRVRELHQLHFRSU]HVXQLW\FK
Z F]DVLH SU]HáF]H NLONX SU]HU]XWQLNyZ 3RQDGWR GHNRGHU OLF]QLND
-RKQVRQD MHVW EDUG]R SURVW\ SRQLHZD* ND*G\ VWDQ OLF]QLND PR*QD
]GHNRGRZDü QD SRGVWDZLH VWDQX W\ONR GZyFK SU]HU]XWQLNyZ /LF]QLN
-RKQVRQD MHVW OLF]QLNLHP V\QFKURQLF]Q\P ] SU]HQLHVLHQLDPL
UyZQROHJá\PL QLH Z\PDJDMF\ VWRVRZDQLD *DGQ\FK GRGDWNRZ\FK
IXQNFML SU]HáF]DMF\FK QD ZHMFLDFK SURJUDPXMF\FK SU]HU]XWQLNyZ
-HVW ]DWHP OLF]QLNLHP R HNVWUHPDOQHM V]\ENRFL ]OLF]DQLD LPSXOVyZ
ZHMFLRZ\FK 1DMEDUG]LHM ]QDQ\PL OLF]QLNDPL -RKQVRQD V OLF]QLN
PRGXOR W\SX +& L OLF]QLN PRGXOR W\SX
+&
/LF]QLNLGZXNLHUXQNRZHUHZHUV\MQH
:\Uy*QLüPR*QDGZDW\S\OLF]QLNyZUHZHUV\MQ\FKDQJXSGRZQ
FRXQWHUV
±
OLF]QLNLRMHGQ\PZHMFLXGODLPSXOVyZ]OLF]DQ\FKLGUXJLPZHMFLX
RNUHODMF\PNLHUXQHN]OLF]DQLD
±
OLF]QLNLRGZyFKZHMFLDFKGODLPSXOVyZ]OLF]DQ\FK]NWyU\FKMHGQR
SRZRGXMH]ZLNV]DQLHDGUXJLH]PQLHMV]DQLDVWDQXOLF]QLND
-DNR SU]\NáDG V\QWH]\ GZXNLHUXQNRZHJR OLF]QLND GZyMNRZHJR
]RVWDQLH UR]SDWU]RQ\ OLF]QLN ELWRZ\ ]DSURMHNWRZDQ\ SU]\ X *\FLX
SU]HU]XWQLNyZ-.06:WDEOLF\VWDQyZ]HVWDZLRQRNROHMQHVWDQ\
MDNLH SU]\MPXMH F]WHURELWRZ\ OLF]QLN UHZHUV\MQ\ R MHGQ\P ZHM FLX GOD
LPSXOVyZ ]OLF]DQ\FK L GUXJLP ZHMFLX
X
K
RNUHODMF\P NLHUXQHN
]OLF]DQLD SU]\ F]\P
X
K
=
1
R]QDF]D GRGDZDQLH ]D
X
K
=
0
R]QDF]D
RGHMPRZDQLH
7DEOLFD7DEOLFDVWDQyZF]WHURELWRZHJROLF]QLNDUHZHUV\MQHJR
X
K
' & %
$
X
K
'
&
%
$
1D SRGVWDZLH WDEOLF\ Z]EXG]H GOD SU]HU]XWQLND -.06
U\VE L WDEOLF\ VWDQyZ OLF]QLND RWU]\PXMH VL WDEOLFH
.DUQDXJKDU\VD]NWyU\FKZ\]QDF]DVL IXQNFMHSU]HáF]DMFHGOD
SRV]F]HJyOQ\FK SU]HU]XWQLNyZ OLF]QLND GOD XSURV]F]HQLD ZSLVDQR Z
SRV]F]HJyOQ\FK WDEOLFDFK VWDQ\ ]HUR MHG\QNRZH GOD ZHM ü
J
L
K
áF]QLH)XQNFMHWHPDMSRVWDü
J
K
J
K
X
A
X A
J
K
X
A B
X
A B
J
K
X
A B C
X
A B C
A
A
B
B
K
K
C
C
K
K
D
D
K
K
=
=
=
=
+
=
=
+
=
=
+
1
6FKHPDW ORJLF]Q\ V\QFKURQLF]QHJR GZyMNRZHJR OLF]QLND
GZXNLHUXQNRZHJRMHVWSU]HGVWDZLRQ\QDU\VE
b)
a)
0 0
%$
0 1
0 0
0 1
1 1
1 1 1 0
1 0
'&
[
[
[
[
[
[
[
[
0 0
0 1
1 1
1 0
[
[
[
[
[
[
[
[
[
[
[
[
[
[ [
[
[
[ [
[
[
[
[
[
;
.
=
;
.
=
0 0
%$
0 1
0 0
0 1
1 1
1 1 1 0
1 0
'&
[ [
0 0
0 1
1 1
1 0
;
.
=
;
.
=
0 0
%$
0 1
0 0
0 1
1 1
1 1 1 0
1 0
'&
[
0 0
0 1
1 1
1 0
[
;
.
=
;
.
=
0 0
%$
0 1
0 0
0 1
1 1
1 1 1 0
1 0
'&
0 0
0 1
1 1
1 0
[
[
[
[
;
.
=
;
.
=
[
[
[
[
[ [
[
[ [
[
[
[
[
[
φ
φ
φ
φ
φ
φ
φ
φ
φ
φ
φ
φ
φ
φ
φ
φ
[ [
[
[
[
[
[
[
[ [
[ [
[
[
[
[
[ [
[ [ [
[
[
[ [ [ [
[ [ [
[
[
[
[
[
[ [
[
[
[
[
[ [ [
[
[
[
[
[
[
[
[ [ [
[
[ [
[
-
.
$%&;
$%& ;
'
'
.
.
=
=
+
+
-
.
$%;
$% ;
&
&
.
.
=
=
+
-
.
$;
$ ;
%
%
.
.
=
=
+
-
.
$
$
=
=
$
%
-
&
.
4
4
-
&
.
4
4
-
&
.
4
4
-
&
.
4
4
'
&
&/.
;
.
;
.
5\V 6\QFKURQLF]Q\ UHZHUV\MQ\ OLF]QLN GZyMNRZ\ D WDEOLFH .DUQDXJKD
EVFKHPDWORJLF]Q\
1D U\V SU]HGVWDZLRQR VSRVyE GZXNDQDáRZHJR SRGDZDQLD
LPSXOVyZ]OLF]DQ\FKGROLF]QLNDUHZHUV\MQHJR.DQDáHP$V SRGDZDQH
LPSXOV\ NWyUH ]ZLNV]DM ]DZDUWRü OLF]QLND QDWRPLDVW NDQDáHP %
LPSXOV\NWyUH]PQLHMV]DM]DZDUWRüOLF]QLND
;
.
;
.
( )
−
( )
+
( )
+
( )
−
$
%
6WHURZDQLH
NLHUXQNLHP
]OLF]DQLD
&/.
,PSXOV\
]OLF]DQH
5\V 8NáDG GR GZXNDQDáRZHJR
ZSURZDG]DQLD LPSXOyZ GR OLF]QLND
UHZHUV\MQHJR
%UDPND (;25 QLH UHDJXMH JG\ UyZQRF]HQLH SRMDZL VL
LPSXOV\ QD ZHMFLDFK
A
B
L
%UDPNL %
L %
ZQRV] GRGDWNRZH
RSy(QLHQLHDE\ZF]HQLHMXVWDOLá\VLSR]LRP\QDSLüQDZHMFLDFK
X
K
X
K
RNUHODMF\FK NLHUXQHN ]OLF]DQLD ]DQLP SRMDZL VL LPSXOV QD
ZHMFLDFK]HJDURZ\FK&/.
3U]\NáDGHP EDUG]R SRSXODUQ\FK V\QFKURQLF]Q\FK OLF]QLNyZ
UHZHUV\MQ\FK V XNáDG\ W\SX ¶ L ¶ SU]\ F]\P DSRVWURI R]QDF]D
URG]LQ\ XNáDGyZ VFDORQ\FK /6 +& L LQQH /LF]QLN ¶ MHVW
UHZHUV\MQ GHNDG OLF]F Z NRG]LH ]D OLF]QLN ¶ MHVW
F]WHURELWRZ\PUHZHUV\MQ\POLF]QLNLHPELQDUQ\P
2E\GZD XNáDG\ V SU]\VWRVRZDQH GR NDVNDGRZHJR áF]HQLD Z
FHOX UHDOL]DFML OLF]QLNyZ R GRZROQLH GX*HM SRMHPQRFL : W\P FHOX
SRVLDGDMQDVWSXMFHZHMFLDLZ\MFLDU\V
ZHMFLHUyZQROHJáH A B C D
', ', ',
',
Z\MFLDUyZQROHJáH A B C D
, , ,
,
ZHMFLH
C
+
GODLPSXOVyZGRGDZDQ\FKGR]DZDUWRFLOLF]QLND
ZHMFLH
C
−
GODLPSXOVyZRGHMPRZDQ\FKRG]DZDUWRFLOLF]QLND
Z\MFLHSU]HQLHVLHQLD
P
+
Z\MFLHSR*\F]NL
P
−
ZHMFLH]HUXMFH
Zer
ZHMFLHVWHUXMFHZSLV\ZDQLHPUyZQROHJá\PLQIRUPDFML WR
&
+
&
−
3
+
3
−
=HU
:5
:\MFLD
'DQH ZHMFLRZH
SRGDZDQH UyZQROHJOH
:H ]HURZDQLD
:H VWHUXMFH
ZSURZDG]DQLHP
UyZQROHJ á \P
GDQ\FK
ZHMFLRZ\FK
5\V 6\JQDá\ ZHMFLRZH L
Z\MFLRZH OLF]QLNyZ UHZHUV\MQ\FK
¶¶
: OLF]QLNX ¶ SU]HQLHVLHQLH
P
+
JHQHURZDQH MHVW SU]\
]GHNRGRZDQLXVWDQXL
C
+
]DSR*\F]ND
P
−
SU]\]GHNRGRZDQLX
VWDQXL
C
−
=DWHPOLF]QLNWHQMHVWGHNDGVáX*FGREXGRZ\
G]LHVLWQ\FKOLF]QLNyZZNRG]LH%&'/LF]QLN ¶SRVLDGDWDNVDP
VWUXNWXU OHF] SU]HQLHVLHQLH
P
+
MHVW JHQHURZDQH SU]\ ]GHNRGRZDQLX
VWDQX L
C
+
]D SR*\F]ND
P
−
SU]\ ]GHNRGRZDQLX VWDQX
L
C
−
0R*H ]DWHP VáX*\ü GR EXGRZ\ ELQDUQ\FK OLF]QLNyZ
UHZHUV\MQ\FK
5(-(675<
2JyOQDFKDUDNWHU\VW\NDLSRG]LDáUHMHVWUyZ
5HMHVWU VWDQRZL SHZQHJR URG]DMX QLHDGUHVRZDOQ SDPLü R
VWRVXQNRZR PDáHM SRMHPQRFL 3RGREQLH MDN SDPLFL DGUHVRZDQH
UHMHVWU\ PRJ E\ü VWDW\F]QH OXE G\QDPLF]QH 5HMHVWU VWDW\F]Q\ MHVW
]áR*RQ\]QSU]HU]XWQLNyZL]DSLVDQDZQLPLQIRUPDFMDZSRVWDFLVáRZD
Q ELWRZHJR PR*H Z QLP SR]RVWDZDü GRZROQLH GáXJR ,QIRUPDFMD
]DSLVDQD Z UHMHVWU]H G\QDPLF]Q\P ]PLHQLD VL VDPRLVWQLH ] ELHJLHP
F]DVXLSRGREQLHMDNZSDPLFLDFKG\QDPLF]Q\FKZ\PDJDRGZLH*DQLD
]DZDUWRFL UHMHVWUX =H Z]JOGX QD VSRVyE ZSURZDG]DQLD L
Z\SURZDG]DQLDLQIRUPDFMLUHMHVWU\G]LHOVLQD
±
V]HUHJRZHXPR*OLZLDMFHV]HUHJRZHZSURZDG]DQLHLZ\SURZDG]DQLH
LQIRUPDFMLW]QNROHMQRELWSRELFLH
±
UyZQROHJáH XPR*OLZLDMFH UyZQROHJáH ZSURZDG]DQLH L Z\SUR
ZDG]DQLH LQIRUPDFML MHGQRF]HQLH GR ZV]\VWNLFK L ]H ZV]\VWNLFK
SR]\FMLUHMHVWUX
±
V]HUHJRZR UyZQROHJáH XPR*OLZLDMFH V]HUHJRZH ZSURZDG]DQLH L
UyZQROHJáHZ\SURZDG]DQLHLQIRUPDFML
UyZQROHJáR V]HUHJRZH XPR*OLZLDMFH UyZQROHJáH ZSURZDG]DQLH L
V]HUHJRZHZ\SURZDG]DQLHLQIRUPDFML
5HMHVWU\ ] ZHMFLHP V]HUHJRZ\P SRVLDGDM PR*OLZRü SU]HVXZDQLD
ZSURZDG]RQHM LQIRUPDFML Z SUDZR OXE Z OHZR UHMHVWU\
MHGQRNLHUXQNRZH EG( WH* ]DUyZQR Z SUDZR MDN L Z OHZR UHMHVWU\
GZXNLHUXQNRZH QD]\ZDQH WH* UHMHVWUDPL UHZHUV\MQ\PL = ]HVSRáX
UHMHVWUyZ UyZQROHJá\FK EXGRZDQH V F]VWR W]Z SDPLFL EXIRURZH
VáX*FH GR SU]HFKRZ\ZDQLD LQIRUPDFML SRGDZDQHM Z VSRVyE
UyZQROHJá\
5HMHVWU\UyZQROHJáH
5HMHVWU\ UyZQROHJáH RNUHODQH UyZQLH* MDNR UHMHVWU\ EXIRURZH
UHDOL]RZDQH V Z SRVWDFL VFDORQHM MDNR ]HVSRá\ OXE QDMF]FLHM
SU]HU]XWQLNyZ ]DWU]DVNRZ\FK OXE SU]HU]XWQLNyZ ' Z\]ZDODQ\FK
]ERF]HP1DMEDUG]LHMSRSXODUQ\PLUHMHVWUDPL]DWU]DVNRZ\PLV XNáDG\
F]WHURELWRZH ¶ ¶ ¶ RUD] RPLRELWRZH W\SX ¶ L
SRFKRGQH1DU\VSU]HGVWDZLRQRVFKHPDWORJLF]Q\R PLRELWRZHJR
UHMHVWUX]DWU]DVNRZHJR¶]Z\MFLHPWUyMVWDQRZ\P
*G\ZHMFLH
LE
DQJODWFKHQDEOHMHVWZVWDQLHZ\VRNLPLQIRUPDFMD]
ZHMü
D
i
L MHVWSU]HQRV]RQDQDZ\MFLD
Q
i
SU]HU]XWQLNyZ
D QDVWSQLH MHVW SDPLWDQD WDN GáXJR MDN GáXJR WUZD QLVNL VWDQ QD
ZHMFLX
LE
'RVWS GR ]DSDPLWDQHM LQIRUPDFML MHVW PR*OLZ\ SRSU]H]
EUDPNLEXIRURZHZ ND*GHM FKZLOL SU]\ Z\PXV]HQLX QLVNLHJR VWDQX QD
ZHMFLX OE DQJ RXWSXW HQDEOH 1DWRPLDVW JG\ ZHMFLH OE MHVW Z
VWDQLHZ\VRNLPZV]\VWNLHZ\MFLDUHMHVWUX
(
)
Q Q
Q
0
1
7
,
,
]QDMGXMVLZ
VWDQLHGX*HMLPSHGDQFML
4
'
/
4
4
2(
/(
'
/
4
4
'
/
4
4
4
4
'
'
'
5\V6WUXNWXUDUHMHVWUX]DWU]DVNRZHJRW\SX¶
7UyMVWDQRZH Z\MFLD UHMHVWUX XPR*OLZLDM EH]SRUHGQLH SU]\áF]HQLH
W\FKZ\MüGRPDJLVWUDOLV\VWHPRZHM
'UXJDJUXSDUHMHVWUyZUyZQROHJá\FKWR]HVSRá\SU]HU]XWQLNyZ'
Z NWyU\FK ]DSDPLWDQLH LQIRUPDFML ZHMFLRZHM RGE\ZD VL
V\QFKURQLF]QLH]GRGDWQLP]ERF]HPLPSXOVX]HJDUD5HSUH]HQWDQWHPWHM
JUXS\UHMHVWUyZPRJE\üQSF]WHURELWRZ\XNáDG¶OXERPLRELWRZ\
¶1DU\VSU]HGVWDZLRQRVWUXNWXUUHMHVWUX¶
05
4
'
&
4
5
4
2(
&
2(
,(
,(
4
'
&
5
4
'
'
4
5\V6WUXNWXUDUHMHVWUXW\SX¶
,QIRUPDFMDZHMFLRZD
D
i
L ZSURZDG]RQDMHVWGRZ\Mü
SU]HU]XWQLNyZ GRGDWQLP ]ERF]HP LPSXOVX ]HJDUD MH*HOL ZHMFLD
IE
1
RUD]
IE
2
DQJ LQSXWHQDEOHVZVWDQLHQLVNLP*G\FKRFLD*MHGQR ]
ZHMü
IE
MHVWZVWDQLHZ\VRNLPZHMFLH
D
i
SU]HU]XWQLNDMHVWGRáF]RQH
GR MHJR Z\MFLD
Q
i
L WD VDPD LQIRUPDFMD MHVW FLJOH SU]HSLV\ZDQD ]
ZHMFLDQDZ\MFLHSU]H]ND*GHGRGDWQLH]ERF]HLPSXOVX]HJDUD5HMHVWU
SRVLDGD Z\MFLD WUyMVWDQRZH NWyU\FK XDNW\ZQLHQLH XPR*OLZLDM QLVNLH
SR]LRP\ V\JQDáyZ OE
1
OXE OE
2
5HMHVWU ¶ PD ]Z\NáH Z\MFLD
GZXVWDQRZH
5HMHVWU\SU]HVXZQH
5HMHVWU SU]HVXZQ\ VWDQRZL JUXS SU]HU]XWQLNyZ ' -. OXE
G\QDPLF]Q\FK 65 SRáF]RQ\FK NDVNDGRZR Z WHQ VSRVyE *H
V\QFKURQLF]QLH ] LPSXOVDPL ]HJDURZ\PL VWDQ ORJLF]Q\ ND*GHJR
SU]HU]XWQLND]RVWDMHSU]HVXQLW\GRQDVWSQHJRSU]HU]XWQLNDZáDFXFKX
OXE QD ]HZQWU] XNáDGX 3U]\NáDG UHDOL]DFML UHMHVWUX SU]HVXZQHJR
SU]HGVWDZLRQRQDU\V
5
6
4
'
&
4
5
4
'
&
4
5
4
'
&
4
5
4
6
&
4
4
5\V5HMHVWUSU]HVXZQ\6,32W\SX¶
1DMSURVWV]\P UHMHVWUHP SU]HVXZQ\P MHVW WDNL UHMHVWU Z NWyU\P
]DUyZQRZSURZDG]DQLHMDNLZ\SURZDG]DQLHLQIRUPDFMLMHVWV]HUHJRZH
5HMHVWU WDNL QD]\ZDQ\ MHVW V]HUHJRZ\P L R]QDF]DQ\ DNURQLPHP 6,62
DQJ VHULDO LQ VHULDO RXW UHJLVWHU 5HMHVWU ¶ SU]HGVWDZLRQ\ QD
U\V PR*H SUDFRZDü MDNR UHMHVWU 6,62 MH*HOL Z\NRU]\VWDP\
V]HUHJRZH ZHMFLH LQIRUPDF\MQH
S
S
1
2
L
RUD] V]HUHJRZH Z\MFLH
Q
7
0R*OLZRüZ\NRU]\VWDQLDW\ONRRVWDWQLHJR]Z\Mü
Q
7
UyZQROHJá\FK
UHMHVWUX SU]HGVWDZLRQHJR QD U\V R]QDF]D *H UHMHVWU\ V]HUHJRZH
6,62VV]F]HJyOQ\PSU]\SDGNLHPUHMHVWUyZV]HUHJRZRUyZQROHJá\FK
6,32DQJVHULDOLQSDUDOOHORXWUHJLVWHU5HMHVWU\SU]HVXZQH6,32
VáX*JáyQLHGR]DPLDQ\LQIRUPDFML]SRVWDFLV]HUHJRZHMQDUyZQROHJá
.RQZHUVML Z RGZURWQ VWURQ WM ]DPLDQ\ LQIRUPDFML ] SRVWDFL
UyZQROHJáHM QD V]HUHJRZ PR*QD GRNRQDü ]D SRPRF UHMHVWUX
SU]HVXZQHJRUyZQROHJáRV]HUHJRZHJR3,62DQJSDUDOOHOLQVHULDO
RXW UHJLVWHU 3U]\NáDGHP WDNLHJR UHMHVWUX MHVW XNáDG ¶ NWyUHJR
VFKHPDWORJLF]Q\SU]HGVWDZLRQRQDU\V
&,
&
'6
&
4
5
'3
/
'6
&
4
5
'3
/
'6
&
4
5
'3
/
/
5
6
'
'
'
4
5\V5HMHVWUSU]HVXZQ\3,62W\SX¶
1DMEDUG]LHM XQLZHUVDOQ JUXS UHMHVWUyZ SU]HVXZQ\FK VWDQRZL
UHMHVWU\UyZQROHJáH3,32DQJ SDUDOOHOLQSDUDOOHORXWUHJLVWHUZ
NWyU\FK G]LNL RGSRZLHGQLP SRáF]HQLRP ZHMü L Z\Mü PR*OLZ\ MHVW
]DUyZQRV]HUHJRZ\MDNLUyZQROHJá\]DSLVRUD]RGF]\WLQIRUPDFMLMDN
UyZQLH* SU]HVXZDQLH LQIRUPDFML Z SUDZR OXE Z OHZR UHMHVWU
UHZHUV\MQ\3U]\NáDGHPWDNLHJRUHMHVWUXPR*HE\üXNáDG¶NWyUHJR
VFKHPDWORJLF]Q\SU]HGVWDZLRQRQDU\V
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
4
4
3
65
4
4
4
3
3
3
4
4
4
4
4
6/
'
&
4
5
'
&
4
5
'
&
4
5
'
&
4
5
4
4
4
4
4
4
4
4
05
&
6
6
5\V6FKHPDWORJLF]Q\UHMHVWUXSU]HVXZQHJR3,32W\SX¶
$V\QFKURQLF]QH ]HURZDQLH UHMHVWUX MHVW PR*OLZH SU]H] GRSURZDG]HQLH
LPSXOVX R QLVNLP SR]LRPLH GR ZHMFLD MR DQJ PDVWHU UHVHW *G\
ZHMFLH MR MHVW Z VWDQLH Z\VRNLP NRQWURO QDG IXQNFMRQRZDQLHP
UHMHVWUXSU]HMPXMZHMFLD
S
0
L
S
1
7DEOLFD)XQNFMHUHMHVWUXSU]HVXZQHJR3,32W\SXµ
]U\V
)XQNFMD
05
6
6
2WZDUWDEUDPND
=HURZDQLH
/
[
[
=DWU]\PDQLHSU]HVXZXLZSLVX
+
/
/
%
3U]HVXZZOHZR
+
/
+
%
3U]HVXZZSUDZR
+
+
/
%
:SLVUyZQROHJá\
+
+
+
%
=DOH*QLH RG SR]LRPyZ ORJLF]Q\FK ZHMü
S
0
L
S
1
RUD] LFK QHJDFML
RWZDUWDMHVWMHGQD]EUDPHN$1'%
%
SRZRGXMF]JRGQLH]WDEOLF
IXQNFMLMHGQ]Z\V]F]HJyOQLRQ\FKRSHUDFMLJG\
S
L S
H
0
1
=
=
,
WRRWZDUWHVEUDPNL%
LLQIRUPDFMDGRVWDUF]RQDZSRVWDFLV]HUHJRZHM
GR ZHMFLD
SL
SU]HVXZDQD MHVW Z OHZR = NROHL SU]\
S
H
S
L
0
1
=
=
,
RWZDUWHVEUDPNL%
LLQIRUPDFMDGRVWDUF]DQDZSRVWDFLV]HUHJRZHMGR
ZHMFLD
SR
MHVWSU]HVXZDQDZSUDZR
3U]\
S
S
H
0
1
= =
RWZDUWH V EUDPNL
B
2
L LQIRUPDFMD ] ZHMü
UyZQROHJá\FK
P
P
0
4
MHVW ZSLV\ZDQD GR UHMHVWUX 3U]\
S
S
L
0
1
= =
RWZDUWHVEUDPNL
B
3
LZHMFLH
D
i
ND*GHJRSU]HU]XWQLNDSRáF]RQHMHVW]
MHJRZ\MFLHP
Q
i
LND*G\LPSXOV]HJDUDSRGWU]\PXMHVWDQUHMHVWUX
3RGREQLH MDN UHMHVWU ¶ ]EXGRZDQH V RPLRELWRZH UHMHVWU\
3,32W\SX¶L+&