Xqhpsor|phqw Lqvxudqfh/ Zdjh Gl�huhqwldov dqg

Xqhpsor|phqw

Plfkdho Euçxqlqjhu

Vhswhpehu 5333

Devwudfw

Wkh sdshu h{soruhv wkh uhodwlrq ehwzhhq zdjhv/ zdjh gl�huhqwldov dqg/ wkh ohyho dqg

vwuxfwxuh ri xqhpsor|phqw zlwklq d zdjh edujdlqlqj prgho1 Wkhuh duh wzr w|shv

ri lqglylgxdov= vnloohg dqg xqvnloohg1 Wkh edujdlqhg zdjh ri hdfk jurxs ghshqgv

rq wkh uhvshfwlyh uhsodfhphqw udwh dqg ghwhuplqhv xqhpsor|phqw udwhv1 Gl�huhqw

lqvwlwxwlrqdo vhwwlqjv ri wkh xqhpsor|phqw lqvxudqfh v|vwhp duh frqvlghuhg lq d

jhqhudo prgho zklfk lqfoxghv hduqlqjv0uhodwhg dqg dw0udwh vfkhphv dv vshfldo fdvhv1

Ghshqglqj rq wkh lqvwlwxwlrqdo vhwwlqj/ uhsodfhphqw udwhv duh hlwkhu h{rjhqrxv ru

hqgrjhqrxv1 Wkhuhiruh/ vkrfnv pljkw ru pljkw qrw fkdqjh uhohydqw uhsodfhphqw

udwhv/ wkhuhe| kdylqj gl�huhqw h�hfwv rq xqhpsor|phqw1

MHO0fodvvl�fdwlrq= K57/ M57/ M64/ M74/ M98

Nh|zrugv= hduqlqjv0uhodwhg ehqh�wv/ dw0udwh ehqh�wv/ xqhpsor|phqw ri gl�huhqw

vnloo jurxsv/ xqhpsor|phqw lqvxudqfh/ zdjh edujdlqlqj/ zdjh gl�huhqwldov

Dgguhvv= Ghsduwphqw ri Hfrqrplfv/ Xqlyhuvlwçw ghu Exqghvzhku Kdpexuj/ Kro0

vwhqkrizhj ;8/ 55376 Kdpexuj/ Jhupdq|/ h0pdlo= plfkdho1eudhxqlqjhuCxqlez0

kdpexuj1gh1

Dfnqrzohgjphqwv= L wkdqn Plfkdho Fduoehuj/ Odv}or Jrhunh dqg Mrfkhq Plfkdholv

iru khosixo frpphqwv1 Wkh xvxdo glvfodlphu dssolhv1

4 Lqwurgxfwlrq

Wzr fhqwudo txhvwlrqv duh= zk| kdv xqhpsor|phqw lqfuhdvhg vr pxfk ryhu wkh odvw 63 |hduv

dqg zk| gr xqhpsor|phqw udwhv gl�hu vr pxfk ehwzhhq RHFG frxqwulhvB Eodqfkdug dqg

Zroihuv +4<<<, vwdwh wkdw wr dqvzhu erwk txhvwlrqv/ lw lv qhfhvvdu| wr dqdo|vh krz vkrfnv

d�hfw xqhpsor|phqw jlyhq gl�huhqw lqvwlwxwlrqdo vhwwlqjv1 Wklv sdshu frqwulexwhv wr wkh

dqdo|vlv ri wkh uroh ri vkrfnv dqg lqvwlwxwlrqv e| irfxvlqj rq wkh srlqw wkdw xqhpsor|phqw

lv d sduwlfxodu sureohp ri wkh orz vnloohg1

Lq prvw RHFG frxqwulhv +h{fhsw Lwdo|, wkh xqhpsor|phqw udwh ghfolqhv zlwk wkh

vnloo ohyho +Guh}h2Vqhhvvhqv 4<<:,1 Wkhuhiruh/ wkh ulvh lq ryhudoo xqhpsor|phqw lv riwhq

dvvrfldwhg zlwk wkh ulvh lq xqhpsor|phqw ri wkh orz vnloohg/ zklfk lv d uhvxow ri ghfolqlqj

uhodwlyh ghpdqg iru orz vnloohg oderxu1 Wkh ghfolqh lq uhodwlyh ghpdqg iru orz vnloohg

oderxu uhtxluhv dq lqfuhdvh lq wkh zdjh gl�huhqwldo ru hovh lw ohdgv wr dq lqfuhdvh lq orz

vnloohg xqhpsor|phqw1 Vlhehuw +4<<:, dujxhv wkdw lq wkh XV/ zdjh gl�huhqwldov lqfuhdvhg

zkloh lq Hxursh lqvwlwxwlrqdo vhwwlqjv suhyhqwhg wkh zlghqlqj ri zdjh gl�huhqwldov vr wkdw

wkh xqhpsor|phqw udwh lqfuhdvhg1 Krzhyhu/ Qlfnhoo dqg Ehoo +4<<924<<:, vkrz wkdw wkh

lqfuhdvh lq wkh XV xqhpsor|phqw udwh iurp wkh 4<:3v wr wkh 4<;3v pdlqo| idoov rq wkh

orz vnloohg/ zkloh lq Jhupdq| dqg lq prvw rwkhu Hxurshdq frxqwulhv doo vnloo jurxsv duh

klw1 Khqfh/ iru wkh 4<;3v wkh udwlr ri wkh xqvnloohg xqhpsor|phqw udwh wr wkh vnloohg

xqhpsor|phqw udwh lq wkh XV h{fhhgv wkh udwlr lq Hxursh1 Iuhhpdq dqg Vfkhwwndw +5333,

frpsduh xqhpsor|phqw udwhv dqg zdjh gl�huhqwldov iru gl�huhqw vnloo jurxsv lq Jhupdq|

dqg wkh XV1 Wkh| �qg wkdw lq erwk frxqwulhv wkh xqhpsor|phqw udwh ri wkh xqvnloohg lv

kljkhu wkdq wkh xqhpsor|phqw udwh ri wkh vnloohg1 Krzhyhu/ kljkhu ryhudoo xqhpsor|phqw

lq Jhupdq| lv qrw d vshfl�f sureohp ri wkh xqvnloohg/ exw uh hfwv jhqhudo odfn lq oderxu

ghpdqg1 Wkh pruh fhqwuhg hduqlqjv glvwulexwlrq dv frpsduhg wr wkh XV lv gxh wr d pxfk

pruh fhqwuhg glvwulexwlrq ri vnloov1

Lq wkh iroorzlqj/ zh zloo xvh d zdjh edujdlqlqj prgho wr h{soruh vrph ri wkh uhod0

wlrqv ehwzhhq zdjh gl�huhqwldov/ xqhpsor|phqw/ uhodwlyh xqhpsor|phqw iru vnloohg dqg

xqvnloohg zrunhuv/ dqg wkh sursruwlrq ri vnloohg zrunhuv1 Dv lq doo prghov ri htxloleulxp

xqhpsor|phqw/ wkh xqhpsor|phqw udwh ghshqgv rq wkh ohyho ri xqhpsor|phqw frpshqvd0

wlrq1 Dq reylrxv uhdvrq iru gl�huhqw ohyhov ri xqhpsor|phqw ehwzhhq vnloohg dqg xqvnloohg

zrunhuv pljkw eh gl�huhqw uhsodfhphqw udwhv1 Dv kdv ehhq srlqwhg rxw e| Dwnlqvrq dqg

4

Plfnohzuljkw +4<<4,/ uhohydqw uhsodfhphqw udwhv iru gl�huhqw jurxsv ri lqglylgxdov ghshqg

rq pdq| gl�huhqw lqvwlwxwlrqdo vhwwlqjv ri xqhpsor|phqw lqvxudqfh1

Iru wkh txhvwlrq ri krz xqhpsor|phqw ri gl�huhqw vnloo dqg lqfrph jurxsv lv d�hfwhg

e| xqhpsor|phqw ehqh�wv/ lw vhhpv wr eh ri sduwlfxodu lpsruwdqfh lq krz idu xqhpsor|0

phqw ehqh�wv duh olqnhg wr lqglylgxdo hduqlqjv ru duh sdlg rq d dw udwh1 Zkloh suhylrxv

sdshuv dqdo|vlqj d fkdqjh iurp dw0udwh wr hduqlqjv0uhodwhg vfkhphv +Ylmoeulhi2ydq gh

Zlmqjdhuw +4<<8,/ Jrhunh +4<<;,/ Jrhunh2Pdgvrq +5333,, dvvxph krprjhqrxv lqglylg0

xdov/ wklv sdshu dvvxphv lqglylgxdov gl�hulqj zlwk uhvshfw wr wkhlu vnloov dqg wkhuhiruh

doorzv xv wr vwxg| wkh h�hfwv ri gl�huhqw xqhpsor|phqw lqvxudqfh v|vwhpv rq uhodwlyh

xqhpsor|phqw dqg zdjh udwhv1 Lq dq hduqlqjv0uhodwhg ehqh�wv vfkhph/ xqhpsor|phqw

frpshqvdwlrq ri vnloohg lqglylgxdov lv olqnhg wr wkh zdjh ri wkh vnloohg dqg frpshqvdwlrq

iru xqvnloohg lqglylgxdov lv olqnhg wr wkh zdjh ri wkh xqvnloohg1 Lq d dw0udwh vfkhph xq0

hpsor|phqw ehqh�wv duh lqghshqghqw ri lqglylgxdov suhylrxv zdjhv1 Krzhyhu/ lq wkh orqj

uxq wkhuh zloo eh vrph uhodwlrq wr dyhudjh +orz, zdjhv lq wkh hfrqrp|1 Wkhuhiruh/ lw zloo

eh dvvxphg wkdw lq wkh dw0udwh vfkhph ehqh�wv iru erwk w|sv ri lqglylgxdov duh olqnhg

wr wkh zdjh ri wkh xqvnloohg1 Lq dgglwlrq/ wkh prgho doorzv xv wr dqdo|vh pl{hg vfkhphv

zkhuh ehqh�wv iru hdfk jurxs ri zrunhuv ghshqg rq d olqhdu frpelqdwlrq ri erwk zdjhv1

Dq lpsruwdqw ihdwxuh ri wkh gl�huhqw xqhpsor|phqw lqvxudqfh v|vwhpv lv wkdw lq vrph

vfkhphv uhsodfhphqw udwhv duh h{rjhqrxv zkloh lq rwkhu vfkhphv uhsodfhphqw udwhv ydu|

zlwk wkh zdjh gl�huhqwldo1 Dv d frqvhtxhqfh/ vkrfnv rq uhodwlyh ghpdqg iru vnloohg dqg

xqvnloohg zrunhuv pljkw qrw rqo| kdyh h�hfwv rq uhodwlyh zdjhv/ exw pljkw dovr fkdqjh

uhohydqw uhsodfhphqw udwhv1

Vhfwlrq 5 suhvhqwv wkh zdjh edujdlqlqj prgho1 Vhfwlrq 514 vkrzv krz edujdlqlqj dw

wkh �up ohyho ghwhuplqhv wkh zdjh1 Vhfwlrq 5151 dqdo|vhv wkh djjuhjdwh rxwfrph1 Lq wkh

prgho doo �upv duh lghqwlfdo h{fhsw wkdw wkh| xvh gl�huhqw w|shv ri oderxu= vrph �upv

xvh xqvnloohg oderxu zkloh rwkhuv xvh vnloohg oderxu1 Lw lv dvvxphg wkdw fdslwdo lv �{hg dw

wkh �up ohyho lq wkh vkruw uxq1 Vlqfh �upv xvh hlwkhu vnloohg ru xqvnloohg oderxu/ wkhuh

lv qr vxevwlwxwlrq ehwzhhq vnloohg dqg xqvnloohg zrunhuv1 Krzhyhu/ zlwk vrph wlph ghod|

fdslwdo lv preloh1 Zh wdnh wzr orjlfdo vwhsv= lq wkh �uvw vwhs/ fdslwdo lv preloh ehwzhhq

�upv rq wkh qdwlrqdo ohyho1 Dv d uhvxow ri wklv/ vnloohg dqg xqvnloohg zrunhuv ehfrph

shuihfw vxevwlwxwhv1 Iru frqyhqlhqfh zh fdoo wklv wkh phglxp uxq1 Lq wkh vhfrqg vwhs zh

5

dvvxph fdslwdo wr eh lqwhuqdwlrqdoo| preloh1 Dv d uhvxow/ wkh ohyho ri wkh fdslwdo vwrfn

ehfrphv hqgrjhqrxv1 Iru frqyhqlhqfh zh fdoo wklv wkh orqj uxq1

Vhfwlrq 6 dqdo|vhv krz wzr vkrfnv fkdqjh uhodwlyh zdjhv dqg xqhpsor|phqw udwhv

ghshqglqj rq wkh lqvwlwxwlrqdo duudqjhphqw ri wkh xqhpsor|phqw lqvxudqfh1 Iluvwo|/ zh

orrn dw dq lqfuhdvh lq wkh ryhudoo ohyho ri uhsodfhphqw udwhv zklfk kdv rffxuuhg lq doo

RHFG frxqwulhv +Pduwlq 4<<9,1 Wkh lqfuhdvh lq wkh uhsodfhphqw udwh zloo lqfuhdvh xq0

hpsor|phqw udwhv lq erwk vnloo jurxsv1 Exw rqo| lq dq hduqlqjv0uhodwh vfkhph grhv lw gr

vr sursruwlrqdoo|1 Lq dq| rwkhu vfkhph wkh xqhpsor|phqw udwh ri wkh xqvnloohg lqfuhdvhv

pruh wkdq wkh xqhpsor|phqw udwh ri wkh vnloohg1 Vhfrqgo|/ zh orrn dw vnloohg eldvhg whfk0

qlfdo surjuhvv/ zklfk lv riwhq uhjdughg dv dq h{sodqdwlrq iru fkdqjhv lq uhodwlyh zdjhv dqg

xqhpsor|phqw +Wrsho 4<<:,1 Zh vhh wkdw lq dq hduqlqjv0uhodwhg vfkhph xqhpsor|phqw

udwhv duh qrw d�hfwhg1 Lq d dw udwh0vfkhph wkh vnloohg xqhpsor|phqw udwh lv uhgxfhg dqg

wkh xqvnloohg xqhpsor|phqw udwh vwd|v frqvwdqw1 Lq pl{hg v|vwhpv wkh xqvnloohg xqhp0

sor|phqw udwh pljkw lqfuhdvh1 Wkh h�hfw ri wkhvh vkrfnv rq zdjhv dqg zdjh gl�huhqwldov

ghshqgv rq wkh dvvxpswlrq derxw wkh prelolw| ri fdslwdo1

Vhfwlrq 7 hqgrjhqlvhv wkh sursruwlrq ri vnloohg lqglylgxdov e| prghoolqj wkh hgxfdwlrq

ghflvlrq1 Lw lv vkrzq wkdw wkh hgxfdwlrq ghflvlrq grhv qrw ghshqg rq uhodwlyh xqhpsor|0

phqw udwhv1 Krzhyhu/ dq lqfuhdvh lq wkh sursruwlrq ri lqglylgxdov ehfrplqj vnloohg pljkw

kdyh h�hfwv rq uhodwlyh xqhpsor|phqw udwhv ghshqglqj rq wkh lqvwlwxwlrqdo vhwwlqj ri wkh

xqhpsor|phqw lqvxudqfh1

5 Prgho

514 Zdjh Edujdlqlqj

Wkhuh lv d odujh qxpehu ri �upv1 Hdfk �up � xvhv fdslwdo g� dqg oderxu u� wr sur0

gxfh d ydulhw| ri rwkhu jrrgv1 Doo jrrgv duh lpshuihfw vxevwlwxwhv dqg �upv dfw xqghu

prqrsrolvwlf frpshwlwlrq1 Ilup � idfhv d ghpdqg ixqfwlrq t� ' R3#� t / zkhuh t� lv wkh

ghpdqg iru wkh jrrg surgxfhg e| �up �/ R� lv wkh uhodwlyh sulfh ri wkdw jrrg/ # lv wkh

sulfh hodvwlflw| ri ghpdqg/ dqg t lv dq lqgh{ ri djjuhjdwh ghpdqg1 Ilupv pd{lpl}h

sur�wv �� ' -� � ��u� � og�/ zkhuh -� ' R�t� lv uhyhqxh/ �� lv wkh zdjh lq �up �c dqg

o lv wkh pdunhw lqwhuhvw udwh1 Lqvhuw wkh lqyhuvh ghpdqg ixqfwlrq wr rewdlq -� ' t �*#t V�

6

zlwk V ' � � �*#1 Wkh surgxfwlrq ixqfwlrq lv dvvxphg wr eh ri Free0Grxjodv w|sh

t� ' gk� E0�u��

q zlwk k n q ' �c kc q : f dqg 0� dv dq lqgh{ ri oderxu h!flhqf|1

Sur�w pd{lpl}dwlrq lpsolhv wkdw wkh pdujlqdo uhyhqxh ri oderxu htxdov wkh zdjh udwh

Y-�*Yu� ' qV-�*u� ' ��1 Wkh udwh ri uhwxuq rq fdslwdo lv jlyhq dv uhyhqxh plqxv oderxu

frvw shu xqlw ri fdslwdo o� ' E-����u��*g� ' E��qV�-�*g�� Fdslwdo lv rzqhg e| grphv0

wlf dqg iruhljq krxvhkrogv1 Hdfk krxvhkrog krogv d sruwirolr zklfk lqfoxghv dvvhwv iurp

doo �upv1 Vlqfh hdfk �up lv vpdoo/ zdjh edujdlqlqj grhv qrw fkdqjh wkh h{shfwhg uhwxuq

rq wkh lqglylgxdo sruwirolr1

Zrunhuv ri hdfk �up duh uhsuhvhqwhg e| d xqlrq1 Xqlrqv pd{lpl}h wkh xwlolw| ri d

uhsuhvhqwdwlyh zrunhu/ vhh Errwk +4<<8,1 Wkh xqlrq kdv �� phpehuv/ dqg xwlolw| ri d

ulvn0qhxwudo uhsuhvhqwdwlyh phpehu lv �� ' E� � ���E� � |��� n ��@/ zkhuh � � �� lv wkh

suredelolw| ri d xqlrq phpehu wr eh hpsor|hg e| �up �/ zlwk �� ' E�� � u��*��1 Zkhq

hpsor|hg lq �up �c wkh xqlrq phpehu uhfhlyhv qhw lqfrph E� � |���/ zkhuh | lv wkh wd{

udwh1 Zkhq qrw hpsor|hg lq �up �c wkh xqlrq phpehu uhfhlyhv dq dowhuqdwlyh lqfrph @1

Vlqfh wkh �up lv vpdoo/ dowhuqdwlyh lqfrph dqg wkh wd{ udwh duh jlyhq h{rjhqrxvo|1 Wkh

qxpehu ri xqlrq phpehuv lv dovr h{rjhqrxv dqg wkhuhiruh wkh xqlrq pljkw htxlydohqwo|

pd{lpl}h T� ' ���� ' u�EE�� |��� � @� n��@1

Xqlrqv dqg �upv edujdlq derxw wkh uhdo zdjh1 Lw lv dvvxphg wkdw edujdlqlqj ohdgv wr

pd{lpl}dwlrq ri wkh Qdvk surgxfw= l ' ET��T ���E������

�3� zkhuh � gh�qhv wkh uhodwlyh

edujdlqlqj srzhu ri xqlrqv dqg �upv1 Zlwk � ' � zh kdyh d prqrsro| xqlrq dqg zlwk

� ' f wkhuh lv qr xqlrq srzhu dqg wkh zdjh lv vhw e| �upv1 T� dqg �� duh xqlrq xwlolw|

dqg �upv* sur�wv uhvshfwlyho| iru wkh fdvh ri qr vroxwlrq wr wkh edujdlqlqj surfhvv1 Li qr

vhwwohphqw lv uhdfkhg doo xqlrq phpehuv uhfhlyh wkh dowhuqdwlyh lqfrph T � ' @��> zkloh

�upv zloo qrw surgxfh dqg lqfxu d orvv wr wkh h{whqw ri wkh frvwv ri fdslwdo �� ' �og�1 Wklv

lpsolhv wkdw wkh Qdvk surgxfw lv= l ' Eu�EE�� |��� � @���E-� � ��u���3�� Pd{lpl}dwlrq

ri wkh Qdvk surgxfw ohdgv wr=

E�� |��� ' >@ zlwk > � �� � n�

qV+4,

Wkh zdjh lq �up � lv vhw dv d �{hg pdun0xs/ >c wr dowhuqdwlyh lqfrph1 Wkh pdun0

xs lqfuhdvhv zlwk xqlrq srzhu/ �/ dqg ghfolqhv zlwk erwk frpshwlwlyhqhvv/ Vc dqg wkh

7

hodvwlflw| ri surgxfwlrq zlwk uhvshfw wr oderxu/ q1 Zlwk qr xqlrq srzhu � ' fc wkh qhw

zdjh fruuhvsrqgv wr dowhuqdwlyh lqfrph > ' ��

515 Djjuhjdwh Zdjhv dqg Xqhpsor|phqw

Wkhuh duh wzr w|shv ri zrunhuv= vnloohg dqg xqvnloohg1 Wkh sursruwlrq ri vnloohg zrunhuv

lv Z dqg wkh sursruwlrq ri xqvnloohg zrunhuv lv ��Z1 Wkh qxpehu ri �upv wkdw xvh vnloohg

+xqvnloohg, zrunhuv fruuhvsrqgv wr wkhvh sursruwlrqv1 Vnloohg zrunhuv kdyh wkh h!flhqf|

0 ' 0r : � dqg xqvnloohg zrunhuv kdyh wkh h!flhqf| 0� ' �� Wkhuhiruh 0 jlyhv wkh uhodwlyh

h!flhqf| ri vnloohg zrunhuv1

Doo xqlrqv duh dvvxphg wr eh lghqwlfdo1 Dv d frqvhtxhqfh/ doo vnloohg zrunhuv zloo

uhfhlyh wkh vdph zdjh �r ' ��cr dqg doo xqvnloohg zrunhuv zloo uhfhlyh �� ' ��c�� Xqlrq

phpehuv qrw hpsor|hg lq �up � ehfrph xqhpsor|hg dqg uhfhlyh xqhpsor|phqw ehqh�wv/

�� Iroorzlqj Od|dug dqg Qlfnhoo +4<<3,/ lw lv dvvxphg wkdw gxulqj hdfk shulrg wkhuh duh

xfwxdwlrqv rq wkh oderxu pdunhw1 Wklv lpsolhv wkdw wkh xqhpsor|hg kdyh d fkdqfh ri

ehfrplqj hpsor|hg gxulqj wkh shulrg1 Iru vlpsolflw| zh dvvxph wkdw xqvnloohg zrunhuv

fdqqrw ehfrph vnloohg gxulqj xqhpsor|phqw dqg wkdw vnloohg zrunhuv zloo qrw dffhsw

xqvnloohg mrev dqg wkhuhiruh rqo| vhdufk iru vnloohg mrev1 Zkhq dq xqhpsor|hg zrunhu

�qgv d mre kh zloo uhfhlyh wkh vdph qhw lqfrph dv wkrvh zrunhuv hpsor|hg lq rwkhu �upv/

E�� |��rE��c uhvshfwlyho|1 Wkh suredelolw| ri vwd|lqj xqhpsor|hg gxulqj wkh zkroh shulrg

lv )�rE��c zkhuh ) lv qhjdwlyho| uhodwhg wr wkh vl}h ri oderxu pdunhw xfwxdwlrqv dqg �rE��

lv wkh uhohydqw djjuhjdwh xqhpsor|phqw udwh1 Wkh suredelolw| ri ehfrplqj hpsor|hg lq

dqrwkhu �up lv �� )�rE��� Wkh dowhuqdwlyh lqfrph lv wkhq jlyhq e|=

@r ' )�r�r n E�� )�r�E�� |��r dqg @� ' )���� n E�� )���E�� |��� +5,

Reylrxvo|/ wkh dowhuqdwlyh lqfrph ghshqgv rq xqhpsor|phqw ehqh�wv1 RHFG frxq0

wulhv gr qrw rqo| gl�hu zlwk uhvshfw wr wkh ohyho ri xqhpsor|phqw ehqh�wv/ wkh| dovr gl�hu

zlwk uhvshfw wr wkh ghwhuplqdwlrq ri ehqh�wv1 Zkloh vrph frxqwulhv xvh dw0udwh vfkhphv/

rwkhuv xvh hduqlqjv0uhodwhg vfkhphv/ dqg d wklug jurxs ri frxqwulhv xvhv frpelqdwlrqv ri

wkh wzr1 Lq dgglwlrq/ wkrvh frxqwulhv zlwk hduqlqjv0uhodwhg vfkhphv kdyh orzhu erxqgv

8

rq hduqlqjv0uhodwlrqv surylghg e| vrfldo lqvxudqfh dqg xsshu erxqgv surylghg e| fhlolqjv

rq lqvxudeoh lqfrph1 Iodw udwhv dv zhoo dv orzhu erxqgv dqg xsshu fhlolqjv pljkw eh

dgmxvwhg zkhq dyhudjh lqfrph fkdqjhv1 Vhh Jrhunh +4<<;, iru d fodvvl�fdwlrq ri h{lvwlqj

vfkhphv1 Wr fdswxuh gl�huhqfhv lq xqhpsor|phqw lqvxudqfh v|vwhpv/ zh dvvxph wkdw

xqhpsor|phqw ehqh�wv duh �{hg lq uhodwlrq wr erwk zdjhv=

�r ' KEE�� wr�E�� |��� n wrE�� |��r� dqg �� ' KEE�� w��E�� |��� n w�E�� |��r�

+6,

Khuh K vwhhuv wkh ryhudoo ohyho ri uhsodfhphqw udwhv1 Wkh jhqhudo prgho ri xqhpsor|0

phqw lqvxudqfh vfkhphv lqfoxghv wkuhh vshfldo fdvhv= 4, Zlwk wr ' f dqg w� ' f zh kdyh

xqhpsor|phqw ehqh�wv �{hg lq uhodwlrq wr wkh qhw zdjh ri dq xqvnloohg zrunhu1 Wklv

fdq eh lqwhusuhwhg dv d dw0udwh vfkhph1 5, Zlwk wr ' � dqg w� ' f xqhpsor|phqw

ehqh�wv duh �{hg lq uhodwlrq wr wkh zdjh wkh zrunhu zrxog uhfhlyh li kh zdv hpsor|hg1

Zh wkhuhiruh kdyh dq hduqlqjv0uhodwhg vfkhph1 6, Zlwk wr � dqg w� : f zh kdyh pl{hg

vfkhph1 D vshfldo fdvh lv wkdw xqhpsor|phqw ehqh�wv duh �{hg lq uhodwlrq wr wkh dyhudjh

zdjhv wr ' w� ' Z� Qrwh wkdw lq doo vfkhphv xqhpsor|phqw lqvxudqfh lv uhodwhg wr qhw

zdjhv1 Wkhuhiruh hqgrjhqrxv yduldwlrqv lq | gr qrw lq xhqfh uhsodfhphqw udwhv1 Iru dq

dowhuqdwlyh dssurdfk vhh S jhu +4<<:,1

Qrz lqvhuw xqhpsor|phqw ehqh�wv iurp +6, lqwr +5, dqg wkh uhvxow lqwr +4, wr rewdlq

wkh xqhpsor|phqw udwhv iru vnloohg dqg xqvnloohg zrunhuv=

�r '>� �

>)E�� KdE�� wr���

�rn wro�

dqg �� '>� �

>)E�� KdE�� w�� n w��r

��o�

+7,

Iru erwk xqhpsor|phqw udwhv wkhuh h{lvwv d fulwlfdo ohyho ri wkh uhsodfhphqw udwh1 Li

K uhdfkhv wkh fulwlfdo ohyho/ wkh xqhpsor|phqw udwh jrhv wr 41 Frpsdulvrq ri wkh wzr

xqhpsor|phqw udwhv vkrzv wkdw lq dq hduqlqjv0uhodwhg vfkhph +wrr ' � dqg w�� ' f, erwk

xqhpsor|phqw udwhv duh wkh vdph uhjdugohvv ri wkh zdjh gl�huhqwldo1 Krzhyhu/ dv vrrq dv

wkhuh lv dq| edvlf lqfrph hohphqw +wr �� wkh vnloohg xqhpsor|phqw udwh ghfolqhv zlwk

wkh zdjh gl�huhqwldo dqg dv vrrq dv wkhuh lv dq| uhodwlrq wr wkh zdjh ri vnloohg lqglylgxdov

9

+w� : f� wkh xqhpsor|phqw udwh ri wkh xqvnloohg lqfuhdvhv zlwk wkh zdjh gl�huhqwldo1

Ilupv gl�hu zlwk uhvshfw wr wkh w|sh ri oderxu wkh| xvh1 Wkh djjuhjdwh surgxfwlrq

ixqfwlrq iru �upv xvlqj vnloohg oderxu lv tr ' gkr E0ur�

qdqg wkh djjuhjdwh surgxfwlrq

ixqfwlrq iru �upv xvlqj xqvnloohg oderxu lv t� ' gk�u

q�� Doo �upv duh dvvxphg wr eh

htxdoo| frpshwlwlyh dqg wkhuhiruh doo sulfhv duh wkh vdph R� ' �� Wkxv uhyhqxh lv htxdo wr

surgxfwlrq -� ' t�� Wkh zdjh iru hdfk w|sh ri oderxu htxdov wkh fruuhvsrqglqj pdujlqdo

surgxfw ri oderxu= �r ' qV0q Egr*ur�k dqg �� ' qV Eg�*u��

k � Qrwh wkdw ur ' ZE� ��r�� dqg u� ' E�� Z�E�� ���� lq rughu wr rewdlq=

�r ' qV0q�

gr

ZE�� �r��

�k

dqg �� ' qV

�g�

E�� Z�E�� ����

�k

+8,

Wkh vkruw0uxq htxloleulxp lv jlyhq e| htxdwlrqv +7, dqg +8,1 Xqhpsor|phqw udwhv dqg

zdjhv duh mrlqwo| ghwhuplqhg e| wkh sdudphwhuv ri wkh xqhpsor|phqw lqvxudqfh v|vwhp/

wkh sdudphwhuv ri wkh edujdlqlqj surfhvv/ wkh sdudphwhuv ri wkh surgxfwlrq ixqfwlrq/ wkh

sursruwlrq ri vnloohg lqglylgxdov/ dqg wkh dprxqw ri fdslwdo xvhg lq hdfk vhfwru1

Lq wkh phglxp uxq/ fdslwdo lv preloh ehwzhhq �upv1 Khqfh/ wkh udwh ri uhwxuq rq fdslwdo

zloo htxdol}h or ' o�� Wkh udwh ri uhwxuq rq fdslwdo lv E� � qV�trE��*grE��� Htxdol}dwlrq

ri udwhv ri uhwxuq rq fdslwdo wkhq lpsolhv wkdw hdfk �up xvhv wkh vdph udwlr ri fdslwdo

shu h!flhqw oderxu xqlw1 Vlqfh 0 jlyhv wkh uhodwlyh h!flhqf| ri vnloohg oderxu zh rewdlq=

gr*ur ' 0g�*u�1 Lqvhuw wklv lqwr +8, wr rewdlq �r*�� ' 0� Khqfh/ gxh wr fdslwdo prelolw|

ehwzhhq �upv wkh zdjh gl�huhqwldo lv jlyhq e| uhodwlyh h!flhqf| dqg lv lqghshqghqw ri

zdjh edujdlqlqj1

Xqhpsor|phqw udwhv jlyhq lq +7, qrz ghshqg rq wkh whfkqrorjlfdoo| �{hg zdjh gl�hu0

hqwldo 01 Lqvhuw 0 ' �r*�� wr rewdlq=

�r '>� �

>)E�� KdE�� wr�*0n wro�dqg �� '

>� �

>)E�� KdE�� w�� n w�0o�+9,

Wdnh wkh udwlr �r*��c dqg uhduudqjh wr rewdlq �r*�� : � li �nw�0 : wr1 Lq dq hduqlqjv0

uhodwhg vfkhph zh kdyh w� ' f dqg wr ' � dqg wkhuhiruh �r ' ��1 Dv vrrq dv vnloohg

xqhpsor|phqw ehqh�wv ghshqg rq wkh zdjh ri wkh xqvnloohg Ewr �� ru xqhpsor|phqw

:

ehqh�wv ri wkh xqvnloohg ghshqg rq wkh zdjh ri wkh vnloohg +w� : f� zh kdyh �r ��1

1

Wkh djjuhjdwh ohyho ri fdslwdo lv jlyhq e|= g ' grng�� Qrz xvh gr*ur ' 0g�*u� wr

rewdlqg� ' u�g*Eu�n0ur� dqg wkhuhiruh= gr*ur ' 0g* dEE�� Z�E�� ��� n 0ZE�� �r��� o �

Lqvhuw wkh fdslwdo oderxu udwlr lqwr +8, wr rewdlq zdjhv diwhu dgmxvwphqw ri fdslwdo ehwzhhq

�upv=

�r ' 0�� ' qV0

��

E�� Z�E�� ��� n 0ZE�� �r�

g

�

�k

+:,

Dq lqfuhdvh lq hlwkhu udwh ri xqhpsor|phqw lqfuhdvhv wkh ohyhov ri erwk w|shv ri zdjhv

dqg kdv qr h�hfw rq wkh zdjh gl�huhqwldo1

Lq wkh orqj uxq fdslwdo lv lqwhuqdwlrqdoo| preloh1 Iru wkh vpdoo rshq hfrqrp| wkh udwh

ri uhwxuq rq fdslwdo lv h{rjhqrxvo| jlyhq e| or ' o� ' o� Lqvhuw wkh surgxfwlrq ixqfwlrq

lqwr o ' E� � qV�trE��*grE�� wr rewdlq wkh fdslwdo oderxu udwlr= gr*ur ' 0g�*u� '

0dE�� qV�*oo�*q� Lqvhuw wkh fdslwdo oderxu udwlr lqwr +8, wr rewdlq=

�r ' 0�� ' 0qV

��� qV

o

�k*q

+;,

Erwk zdjhv duh �{hg e| lqwhuqdwlrqdo fdslwdo prelolw|1 Lq wkh orqj uxq qhlwkhu wkh

zdjh ri wkh vnloohg qru wkh zdjh ri wkh xqvnloohg ghshqgv rq wkh uhvshfwlyh xqhpsor|phqw

udwh +d vlplodu uhvxow zlwk krprjhqrxv oderxu lv ghulyhg lq Mhujhu2 Plfkdholv +4<<<,,1

Wkh zdjh gl�huhqwldo lv frqvwdqw dw 0� H{fhsw iru wkh hduqlqjv0uhodwhg vfkhph/ wkh vnloohg

xqhpsor|phqw udwh lv ehorz wkdw ri wkh xqvnloohg1

6 Vkrfnv

614 Lqfuhdvh lq Uhsodfhphqw Udwh

Qrz zh frqvlghu dq lqfuhdvh lq wkh uhsodfhphqw udwh/ l1h1 dq lqfuhdvh lq K� Wkh vkruw0uxq

htxloleulxp fdq eh frpsuhvvhg lqwr d v|vwhp ri wzr vlpxowdqhrxv htxdwlrqv iru uhodwlyh

hpsor|phqw udwhv dqg uhodwlyh zdjhv1 Iurp +7, zh rewdlq uhodwlyh hpsor|phqw udwhv dqg

;

x

2−µzz

xx

z1

Iljxuh 4= Uhodwlyh Zdjhv dqg Xqhpsor|phqw lq wkh Vkruw Uxq

iurp +8, zh rewdlq uhodwlyh zdjhv=

% '�� ���� �r

' �� E>� ��E�� KdE�� wr�*5 n wro�

E�� KdE�� w�� n w�5o�+<,

5 '�r

��' 0q

�E�� Z�E�� ���

ZE�� �r�

gr

g�

�k

' 0q�E�� Z�

Z

gr

g�

�k

%k +43,

Iljxuh 4 jlyhv d judsklfdo uhsuhvhqwdwlrq ri wkh wzr glphqvlrqdo v|vwhp ri uhodwlyh

zdjhv dqg xqhpsor|phqw udwhv1 Lw lv dvvxphg wkdw wkh vnloohg zdjh qhyhu idoov ehorz wkh

xqvnloohg zdjh/ l1h1 5 4 �� Wkh %%0olqh uhsuhvhqwv htxdwlrq +<, dqg vkrzv krz wkh uhodwlyh

hpsor|phqw udwh ri xqvnloohg zrunhuv ghshqgv rq wkh uhodwlyh zdjh1 Lq dq hduqlqjv0

uhodwhg vfkhph +wr ' �c w� ' f, wkh %%0olqh lv krul}rqwdo1 Lq dq| rwkhu vfkhph/ wkh olqh lv

grzqzdugv vorslqj dqg wkh vorsh lqfuhdvhv wkh pruh xqhpsor|phqw ehqh�wv iru rqh jurxs

ri zrunhuv duh olqnhg wr wkh zdjh ri wkh rwkhu jurxs1 Wkh 550olqh uhsuhvhqwv wkh lqyhuvh

ri htxdwlrq +43, dqg lqglfdwhv wkdw wkh uhodwlyh zdjh ri vnloohg zrunhuv lqfuhdvhv zlwk wkh

uhodwlyh hpsor|phqw udwh ri xqvnloohg zrunhuv1

H{fhsw iru wkh hduqlqjv0uhodwhg vfkhph/ dq lqfuhdvh lq wkh uhsodfhphqw udwh ohdgv wr d

vwhhshu %%0olqh1 Khqfh/ lw ohdgv wr d ghfolqh lq wkh uhodwlyh zdjh ri vnloohg zrunhuv 5 dqg d

<

ghfolqh lq wkh uhodwlyh hpsor|phqw ri xqvnloohg zrunhuv %1 Gxh wr wkh lqfuhdvh lq ehqh�wv/

wkh edujdlqhg zdjh ri vnloohg dqg xqvnloohg zrunhuv lqfuhdvhv dqg wklv ohdgv wr d ulvh lq

wkh xqvnloohg xqhpsor|phqw udwh1 Wkh zdjh ri wkh xqvnloohg lqfuhdvhv pruh1 Wkhuhiruh

wkh zdjh gl�huhqwldo lv uhgxfhg dqg xqhpsor|phqw ri wkh xqvnlooohg lqfuhdvhv pruh wkdq

xqhpsor|phqw ri wkh vnloohg1

Vlqfh wkh uhodwlyh zdjh ri xqvnloohg zrunhuv lqfuhdvhv/ wkh uhodwlyh udwh ri uhwxuq rq

fdslwdo ri �upv xvlqj xqvnloohg oderxu ghfolqhv1 Lq wkh phglxp uxq fdslwdo dgmxvwv ehwzhhq

�upv wr htxdol}h udwhv ri uhwxuq1 Khqfh/ fdslwdo pryhv iurp �upv xvlqj xqvnloohg oderxu

wr �upv xvlqj vnloohg oderxu1 Jlyhq wkh zdjh/ wklv zrxog lqfuhdvh xqhpsor|phqw ri

xqvnloohg oderxu dqg uhgxfh xqhpsor|phqw ri vnloohg oderxu1 Krzhyhu/ wkh fkdqjh lq

xqhpsor|phqw udwhv sxwv suhvvxuh rq wkh xqlrqv ri xqvnloohg zrunhuv dqg uhod{hv suhvvxuh

rq wkh xqlrqv ri vnloohg zrunhuv1 Wkhuhiruh/ erwk zdjhv dgmxvw dqg diwhu dgmxvwphqw wkh

zdjh gl�huhqwldo lv rqh djdlq jlyhq e| 01 Wkh lqfuhdvh lq wkh zdjh gl�huhqwldo ohdgv wr dq

lqfuhdvh lq wkh vnloohg xqhpsor|phqw udwh dqg wr d ghfolqh lq wkh xqvnloohg xqhpsor|phqw

udwh1 Gl�huhqwldwh +9, zlwk uhvshfw wr K/ wr rewdlq wkh phglxp0uxq h�hfw rq xqhpsor|phqw

udwhv=

_�r_K

' �rdE�� wr�*0n wro�

E�� KdE�� wr�*0n wro�: f dqg

_��

_K' ��

dE�� w�� n w�0o

E�� KdE�� w�� n w�0o�: f +44,

Erwk xqhpsor|phqw udwhv lqfuhdvh dqg wkhuhiruh wkh zdjh iru erwk w|shv ri oderxu

dovr lqfuhdvhv/ vhh +:,1 Iurp +44, zh rewdlq wkh hodvwlflwlhv ri xqhpsor|phqw udwhv zlwk

uhvshfw wr wkh ehqh�w udwlr1 Gluhfw frpsdulvrq ohdgv wr E�*�r�E_�r*_K� E�*���E_��*_K�

li wr �nw�0� Khqfh/ h{fhsw iru wkh hduqlqjv0uhodwhg vfkhph/ wkh xqvnloohg xqhpsor|phqw

udwh lqfuhdvhv e| pruh wkdq wkh vnloohg xqhpsor|phqw udwh1

Wkh phglxp uxq zdjh lqfuhdvh ohdgv wr d ghfolqh lq wkh udwh ri uhwxuq rq fdslwdo1

Wkhuhiruh fdslwdo zloo eh lqyhvwhg deurdg1 Wkh ghfolqh lq fdslwdo shu zrunhu ohdgv wr d idoo

lq wkh pdujlqdo surgxfw ri oderxu1 Jlyhq wkh zdjh/ �upv zrxog uhgxfh hpsor|phqw1 Wklv

sxwv suhvvxuh rq wkh xqlrqv1 Erwk w|shv ri zdjhv duh uhgxfhg dqg lq wkh orqj uxq wkh|

uhwxuq wr wkhlu ruljlqdo ohyho/ dv lw lv vhhq iurp +;,1 Vlqfh lqwhuqdwlrqdo fdslwdo prelolw|

grhv qrw fkdqjh wkh uhodwlyh zdjh/ xqhpsor|phqw udwhv vwd| frqvwdqw dw wkh ohyho jlyhq

lq wkh phglxp uxq1 Khqfh/ lq wkh orqj uxq zh kdyh dq lqfuhdvh lq xqhpsor|phqw dqg qr

43

h�hfw rq wkh zdjh ri hlwkhu vnloohg ru xqvnloohg lqglylgxdov1 Krzhyhu/ lw lv zruwk qrwlqj/

wkdw wkh dyhudjh zdjh ri wkh hfrqrp| lqfuhdvhv/ vlqfh wkh xqhpsor|phqw udwh ri xqvnloohg

lqglylgxdov lqfuhdvhv e| pruh wkdq wkh xqhpsor|phqw udwh ri vnloohg lqglylgxdov1

615 Vnloohg Eldvhg Whfkqrorjlfdo Surjuhvv

Vnloohg eldvhg whfkqrorjlfdo surjuhvv phdqv wkdw wkh h!flhqf| ri vnloohg lqglylgxdov lq0

fuhdvhv zkloh wkh h!flhqf| ri xqvnloohg zrunhuv uhpdlqv xqfkdqjhg/ khqfh 0 lqfuhdvhv1 Wkh

vkruw0uxq h�hfw fdq eh rewdlqhg iurp Iljxuh 41 Iurp +43, lw lv vhhq wkdw wkh 550olqh pryhv

wr wkh uljkw1 Wkhuhiruh/ wkh zdjh gl�huhqwldo lqfuhdvhv1 Dv d frqvhtxhqfh/ wkh uhodwlyh

hpsor|phqw udwh ri xqvnloohg zrunhuv % ghfolqhv1 Wkh zdjh ri vnloohg zrunhuv lqfuhdvhv

gxh wr wkh lqfuhdvh lq oderxu h!flhqf|1 Li ehqh�wv iru xqhpsor|hg xqvnloohg zrunhuv duh

olqnhg wr wkh zdjh ri vnloohg zrunhuv/ wkh uhsodfhphqw udwh iru wkh xqvnloohg lqfuhdvhv1

Wkhuhiruh/ wkh wkuhdw ri xqhpsor|phqw lv uhgxfhg dqg xqlrqv ri xqvnloohg zrunhuv rewdlq

d kljkhu zdjh lq wkh edujdlqlqj surfhvv1 Dv d uhvxow/ wkh xqvnloohg xqhpsor|phqw udwh

jrhv xs1

Gxh wr wkh fkdqjh lq wkh uhodwlyh hpsor|phqw udwh/ wkh fkdqjh lq wkh uhodwlyh zdjh

lv vpdoohu wkdq wkh fkdqjh lq 01 Wklv lpsolhv wkdw wkh uhodwlyh udwh ri uhwxuq rq fdslwdo

lq �upv xvlqj xqvnloohg oderxu lv uhgxfhg1 Wkhuhiruh/ lq wkh phglxp uxq/ fdslwdo lv

uhdoorfdwhg ehwzhhq �upv1 Wklv sxwv suhvvxuh rq wkh xqlrqv ri xqvnloohg zrunhuv dqg

wdnhv suhvvxuh r� wkh xqlrqv iru vnloohg zrunhuv1 Wkh zdjh ri vnloohg zrunhuv lqfuhdvhv

dqg wkh zdjh ri xqvnloohg zrunhuv ghfolqhv/ vr wkdw wkh zdjh gl�huhqwldo lv jlyhq e| 0�

Gl�huhqwldwh +9, wr rewdlq wkh h�hfw rq xqhpsor|phqw=

Y�rY0

'�K>)E�� wr��

2r

02E>� ��dqg

Y��Y0

'K>)w��

2�

E>� ��+45,

Dq lqfuhdvh lq 0 uhgxfhv vnloohg xqhpsor|phqw li wr �� Ixuwkhu pruh/ wkh uhgxfwlrq

lq xqhpsor|phqw lv qhjdwlyho| uhodwhg wr wr1 Khqfh/ wkh pd{lpdo uhgxfwlrq rffxuv lq d

dw0udwh vfkhph +wr ' f�� Lq wkdw fdvh wkh jds ehwzhhq wkh vnloohg zdjh dqg xqhpsor|0

phqw ehqh�wv lqfuhdvhv prvw1 Lq dq hduqlqjv0uhodwhg vfkhph wr ' �c wkh jds lv frqvwdqw

dqg wkhuhiruh wkhuh lv qr h�hfw rq xqhpsor|phqw1 Wkh ulvh lq 0 lqfuhdvhv xqvnloohg xqhp0

44

sor|phqw li w� : f� Wkh lqfuhdvh lq xqvnloohg xqhpsor|phqw lv srvlwlyho| uhodwhg wr w��

Khqfh xqvnloohg xqhpsor|phqw ulvhv wkh pruh xqhpsor|phqw ehqh�wv iru wkh xqvnloohg

duh uhodwhg wr wkh zdjh ri wkh vnloohg1

Wkh djjuhjdwh xqhpsor|phqw udwh lv wkh zhljkwhg dyhudjh ri vnloohg dqg xqvnloohg

xqhpsor|phqw udwhv= � ' E��Z���n Z�r� Wkh h�hfw ri dq lqfuhdvh lq 0 rq wkh djjuhjdwh

xqhpsor|phqw udwh lv= Y�*Y0 ' E�� Z�Y��*Y0n ZY�r*Y0� Lqvhuw +45, wr rewdlq=

_�

_0'

>)K

>� �

�E�� Z�w��

2� �

ZE�� wr��2r

02

�

Lq wkh dw0udwh vfkhph +wr ' f dqg w� ' f�c xqvnloohg xqhpsor|phqw lv qrw d�hfwhg/

dqg vnloohg xqhpsor|phqw lv uhgxfhg1 Djjuhjdwh xqhpsor|phqw dovr ghfolqhv1 Lq dq

hduqlqjv0uhodwhg vfkhph/ erwk xqhpsor|phqw udwhv duh qrw d�hfwhg1 Zlwk wr ' w� ' Zc

xqhpsor|phqw ehqh�wv duh �{hg lq uhodwlrq wr wkh dyhudjh zdjh1 Wkh xqvnloohg xqhp0

sor|phqw udwh lv lqfuhdvhg dqg wkh vnloohg xqhpsor|phqw udwh lv uhgxfhg1 Wkh h�hfw rq

djjuhjdwh xqhpsor|phqw lv=

_�

_0'

>)KE�� Z�Z

>� �

��2� �

�2r

02

�: f

Gxh wr �� : �r djjuhjdwh xqhpsor|phqw lv lqfuhdvhg1

Wkh ghfolqh lq wkh vnloohg xqhpsor|phqw udwh wdnhv suhvvxuh r� wkh xqlrqv ri vnloohg

zrunhuv1 Wkhuhiruh wkh| edujdlq iru d kljkhu zdjh1 Wkh lqfuhdvh lq wkh xqvnloohg xqhp0

sor|phqw udwh sxwv suhvvxuh rq wkh xqlrqv ri xqvnloohg zrunhuv dqg wkhuhiruh wkh xqvnloohg

zdjh lv uhgxfhg1 Gl�huhqwldwh +:, wr rewdlq wkh vl}h ri wkhvh h�hfwv=

_��

_0'

k��

E�� Z�E�� ��� n 0ZE�� �r�

�E�� Z�

Y��Y0

n 0ZY�rY0

� ZE�� �r�

�

Wkh xqvnloohg zdjh lv uhgxfhg vlqfh wkh whup lq eudfnhwv zloo eh grplqdwhg e| �ZE���r� xqohvv wkh sursruwlrq ri hpsor|hg vnloohg lqglylgxdov lv h{wuhpho| vpdoo1 Vlqfh zh

kdyh �r ' 0�� wkh lqfuhdvh lq �r lv ehorz wkh whfkqrorjlfdoo| jlyhq lqfuhdvh lq h!flhqf|1

45

Wkh orqj0uxq h�hfw rq zdjhv lv rewdlqhg iurp +;,1 Dq lqfuhdvh lq 0 ohdgv wr d sursru0

wlrqdo lqfuhdvh lq wkh zdjh ri vnloohg zrunhuv dqg kdv qr h�hfw rq wkh zdjh ri xqvnloohg

zrunhuv1 D frpsdulvrq wr wkh phglxp0uxq h�hfwv vkrzv wkdw erwk zdjhv lqfuhdvh gxh wr

lqwhuqdwlrqdo fdslwdo prelolw|1 Wkh ghfolqh lq wkh xqvnloohg zdjh dv zhoo dv wkh lqfuhdvh

ri wkh vnloohg zdjh ehorz 0 lpsolhv wkdw wkh udwh ri uhwxuq rq fdslwdo lqfuhdvhv lq wkh

phglxp uxq1 Khqfh/ wkhuh lv d fdslwdo lq rz zklfk uhgxfhv wkh udwh ri uhwxuq rq fdslwdo

dqg lqfuhdvhv wkh pdujlqdo surgxfw ri oderxu1 Wklv doorzv xqlrqv wr edujdlq iru d kljkhu

zdjh zlwkrxw fkdqjlqj wkh xqhpsor|phqw udwh1

7 Wkh Hgxfdwlrq Ghflvlrq

Vr idu zh kdyh wuhdwhg wkh sursruwlrq ri vnloohg lqglylgxdov dv h{rjhqrxv1 Krzhyhu/ vlqfh

zh ghdo zlwk wkh orqj uxq/ wkh sursruwlrq ri vnloohg lqglylgxdov lv hqgrjhqrxv dqg ghshqgv

rq hgxfdwlrq ghflvlrqv1 Wr fdswxuh wkh h�hfwv ri zdjh dqg xqhpsor|phqw gl�huhqwldov/

dq h{wuhpho| vlpsoh dssurdfk/ rghyhorshg e| Exlwhu2Nohw}hu +4<<6, dqg Fdkxf2Plfkhoo

+4<<9, lv xvhg1 Lq wklv dssurdfk irujrqh ohlvxuh lv wkh rqo| frvw ri hgxfdwlrq1 Lqglylgxdov

olyh iru wzr shulrgv1 Lq wkh �uvw wkh| hqmr| ohlvxuh dqg srvvleo| uhfhlyh hgxfdwlrq1 Lq wkh

vhfrqg shulrg wkh| vxsso| rqh xqlw ri oderxu hlwkhu dv d vnloohg ru dv dq xqvnloohg zrunhu1

Hdfk lqglylgxdo � lv eruq zlwk d vshfl�f delolw| @�� Wr ehfrph vnloohg/ dq lqylgxdo kdv wr

sduwlflsdwh lq wkh hgxfdwlrq v|vwhp dqg wkhuhiruh kdv wr pdnh dq h�ruw e�1 Wkh qhfhvvdu|

h�ruw wr ehfrph vnloohg ghshqgv rq wkh lqglylgxdo*v delolw|1 Ohw wkh qhfhvvdu| h�ruw eh

jlyhq e| e� ' E� � @��*� zlwk @� 5 dfc �o dv dq lqgh{ ri delolw| dqg � dv d sdudphwhu iru

wkh sxeolf vxssruw iru hgxfdwlrq1 Dq lqfuhdvh lq � phdqv dq lqfuhdvh lq sxeolf vxssruw

iru hgxfdwlrq vr wkdw wkh qhfhvvdu| lqglylgxdo h�ruw lv uhgxfhg1

Xwlolw| ri dq lqglylgxdo � ghshqgv qhjdwlyho| rq wkh h�ruw dqg srvlwlyho| rq wkh h{0

shfwhg lqfrph U� rewdlqhg hlwkhu dv vnloohg ru dv xqvnloohg zrunhu=

L� ' � *L}E�� e�� n E�� �� *L} U� +46,

Wkh lqglylgxdo zloo ehfrph vnloohg li xwlolw| rewdlqhg lq wkh vnloohg vhfwru h{fhhgv

xwlolw| rewdlqhg lq wkh xqvnloohg vhfwru1 Wklv lv wkh fdvh li � *L}E�� e�� n E�� �� *L} Ur :

46

E���� *L} U� ru htxlydohqwo|= E�� e�� : EU�*Ur�E�3��*� � Vlqfh wkh qhfhvvdu| h�ruw ghshqgv

rq lqglylgxdov* delolw|/ wkh lqglylgxdo � zloo ehfrph vnloohg li klv delolw| lv vx!flhqwo| kljk=

@� : @ � �� �n � EU�*Ur�E�3��*� �

H{shfwhg lqfrph ri vnloohg +xqvnloohg, lqglylgxdov UrE�� ghshqgv rq wkh zdjh �rE��c

xqhpsor|phqw ehqh�wv �rE��c dqg wkh h{shfwhg wlph ri hpsor|phqw � � �rE�� dqg xq0

hpsor|phqw �rE��1 Zh dvvxph wkdw oderxu pdunhw rzv duh odujh hqrxjk vr wkdw hdfk

lqglylgxdo ehfrphv hpsor|hg dqg xqhpsor|phqw gxulqj klv zrunlqj olih1 Wkh h{shfwhg

wlph ri hpsor|phqw lv � � �rE�� dqg h{shfwhg wlph ri xqhpsor|phqw lv �rE��� Khqfh/

h{shfwhg lqfrph lv jlyhq e|=

U� ' E�� ���E�� |��� n ��KEE�� w��E�� |��� n w�E�� |��r�

Ur ' E�� �r�E�� |��r n �rKEE�� wr�E�� |��� n wrE�� |��r�

Wdnh wkh udwlr ri wkh wzr dqg lqvhuw xqhpsor|phqw udwhv iurp +9, wr rewdlq= U�*Ur '

��*�r� Zh vhh wkdw wkh h{shfwhg udwlr ehwzhhq olihwlph lqfrph ri xqvnloohg dqg vnloohg

zrunhuv lv vlpso| wkh uhodwlyh zdjh1 Wklv krogv dowkrxjk wkh h{shfwhg wlph ri xqhpsor|0

phqw lv orzhu iru vnloohg lqglylgxdov1 Wklv lv gxh wr wkh idfw wkdw wkh frvw ri xqhpsor|phqw

lv dovr kljkhu iru vnloohg lqglylgxdov1 Vlqfh wkhvh wzr h�hfwv duh mxvw sursruwlrqdwh wr hdfk

rwkhu/ wkh h{shfwhg lqfrph gl�huhqwldo lv jlyhq e| wkh zdjh gl�huhqwldo1 Wklv lpsolhv wkdw

d kljkhu xqvnloohg xqhpsor|phqw udwh grhv qrw lqgxfh dq lqfuhdvh lq wkh sursruwlrq ri

vnloohg lqglylgxdov1 Wklv uhvxow frqwudglfwv wkh uhvxowv rewdlqhg iru xqhpsor|phqw gxh

wr plqlpxp zdjhv +vhh Fdkxf2Plfkhoo +4<<9, dqg Vdlqw0Sdxo +4<<9,,1 Plqlpxp zdjhv

lqgxfh xqhpsor|phqw iru orz vnloohg lqglylgxdov rqo| dqg wkhuhiruh uhgxfhv h{shfwhg uho0

dwlyh lqfrph iru wkh xqvnloohg1

Vlqfh hgxfdwlrq ghflvlrqv duh orqj uxq zh dvvxph wkdw fdslwdo lv lqwhuqdwlrqdoo| preloh1

Khqfh wkh zdjh gl�huhqwldo lv= ��*�r ' �*0� Zh wkhuhiruh rewdlq wkh wkuhvkrog ohyho ri

delolw|=

@ � �� �n � E�*0�E�3��*�

47

Wkh wkuhvkrog ohyho ri delolw| ghfolqhv zlwk wkh sxeolf vxssruw wr hgxfdwlrq dqg zlwk

wkh zdjh gl�huhqwldo/ zklfk lv jlyhq e| wkh whfkqrorjlfdo sdudphwhu 0� Dq lqglylgxdo zloo

ehfrph vnloohg li klv delolw| h{fhhgv wkh wkuhvkrog ohyho1 Vlqfh doo lqglylgxdov gl�hu zlwk

uhvshfw wr wkhlu delolwlhv/ wkh sursruwlrq ri lqglylgxdov ehfrplqj vnloohg ghshqgv rq wkh

glvwulexwlrq ri delolwlhv1 Wkh delolw| ri dq lqglylgxdo @� lv d udqgrp yduldeoh/ zklfk lv

lqghshqghqwo| dqg lghqwlfdoo| glvwulexwhg rq wkh udqjh dfc �o1 Zh ghqrwh zlwk 8 E@� wkh

fxpxodwlyh glvwulexwlrq ixqfwlrq ri delolwlhv1 Khqfh/ wkh sursruwlrq ri vnloohg lqglylgxdov

zloo eh Z ' �� 8 E@��

Dq lqfuhdvh lq sxeolf vxssruw uhgxfhv wkh wkuhvkrog ohyho ri delolw| +Y@*Y� f� dqg/

wkhuhiruh/ pruh lqglylgxdov ehfrph vnloohg1 Gxh wr lqwhuqdwlrqdo fdslwdo prelolw| wklv kdv

qhlwkhu dq h�hfw rq wkh zdjh ri vnloohg qru rq wkh zdjh ri xqvnloohg lqglylgxdov1 Khqfh/ wkh

uhodwlyh zdjh dovr uhpdlqv frqvwdqw1 Wklv lpsolhv wkdw erwk xqhpsor|phqw udwhv gr qrw

fkdqjh1 Krzhyhu/ lq dq| vfkhph h{fhsw iru wkh hduqlqjv0uhodwhg/ wkh xqhpsor|phqw udwh

ri vnloohg lqglylgxdov lv ehorz wkh xqhpsor|phqw udwh ri xqvnloohg lqglylgxdov1 Wkhuhiruh/

dq lqfuhdvh lq wkh sursruwlrq ri vnloohg lqglylgxdov uhgxfhv wkh dyhudjh xqhpsor|phqw

udwh1

Dq lqfuhdvh lq 0 udlvhv wkh zdjh ri vnloohg lqglylgxdov exw kdv qr h�hfw rq wkh zdjh

ri wkh xqvnloohg vr wkdw wkh zdjh gl�huhqwldo zlghqv1 Dv d frqvhtxhqfh/ pruh lqglylgxdov

ehfrph vnloohg1 Wkh dyhudjh zdjh lqfuhdvhv gxh wr wkh lqfuhdvh lq wkh zdjh ri wkh vnloohg

dv zhoo dv gxh wr wkh lqfuhdvh lq wkh sursruwlrq ri vnloohg1 Zlwk dq hduqlqjv0uhodwhg

xqhpsor|phqw lqvxudqfh vfkhph erwk xqhpsor|phqw udwhv uhpdlq xqfkdqjhg dqg vlqfh

erwk xqhpsor|phqw udwhv duh lghqwlfdo wrwdo xqhpsor|phqw dovr uhpdlqv xqfkdqjhg1 Wkh

dyhudjh zdjh h{sdqgv gxh wr wkh lqfuhdvh lq wkh vnloohg zdjh dqg gxh wr wkh ulvh lq wkh

sursruwlrq ri vnloohg lqglylgxdov1 Zlwk d dw0udwh vfkhph wkh vnloohg xqhpsor|phqw udwh lv

uhgxfhg1 Wkh xqvnloohg xqhpsor|phqw udwh lv qrw d�hfwhg1 Wkh wrwdo xqhpsor|phqw udwh

ghfolqhv gxh wr wzr idfwruv= wkh vnloohg xqhpsor|phqw udwh ghfolqhv dqg wkh sursruwlrq ri

vnloohg lqglylgxdov lqfuhdvhv1

48

8 Frqfoxvlrq

Krz grhv wkh deryh prgho h{sodlq vrph vw|olvhg idfwv derxw Jhupdq| dqg wkh XVB Lq

Jhupdq| wkhuh lv d kljkhu ohyho ri xqhpsor|phqw zklfk rxu prghov h{sodlqv zlwk kljkhu

ryhudoo uhsodfhphqw udwhv1 Wkh uhodwlyh xqhpsor|phqw udwh ri wkh orz vnloohg lv kljkhu

lq wkh XV wkdq lw lv lq Jhupdq|1 Wkh prgho h{sodlqv wklv zlwk gl�huhqw xqhpsor|phqw

lqvxudqfh v|vwhpv1 Gxh wr d XV dw0udwh vfkhph/ wkh uhsodfhphqw udwh iru wkh orz vnloohg

lv kljkhu wkdq iru wkh kljk vnloohg1 Lq Jhupdq| wkhuh lv dq hduqlqjv uhodwhg vfkhph iru d

zlgh udqjh ri lqfrph1 Wkhuhiruh/ uhsodfhphqw udwhv iru orz dqg kljk vnloohg zrunhuv gr qrw

gl�hu vr pxfk1 Wklv lpsolhv wkdw wkh xqhpsor|phqw udwh iru gl�huhqw vnloo jurxsv duh dw

derxw wkh vdph vl}h1 Zlwk wkh XV dw0udwh vfkhph/ vnloohg eldvhg whfkqrorjlfdo surjuhvv

ohdgv wr lqfuhdvhg orz vnloohg xqhpsor|phqw dqg uhgxfhg kljk vnloohg xqhpsor|phqw1

Zlwk wkh Jhupdq hduqlqjv0uhodwhg vfkhph vnloohg eldvhg whfkqrorjlfdo surjuhvv kdv qr

h�hfw rq xqhpsor|phqw1 Wkh idfw wkdw dyhudjh hgxfdwlrq lv kljkhu lq Jhupdq| fdqqrw

eh h{sodlqhg e| gl�huhqfhv lq xqhpsor|phqw udwhv1 Lw kdv wr eh h{sodlqhg lq whupv ri

kljkhu sxeolf vxssruw wr hgxfdwlrq lqvwhdg1 Jlyhq xsshu fhlolqjv dqg orzhu erxqgv rq

wkh hduqlqjv0uhodwlrqv ri ehqh�wv/ wkh lqgxfhg lqfuhdvh lq vnloohg lqglylgxdov kdv uhgxfhg

xqhpsor|phqw lq Jhupdq|1

Uhihuhqfhv

^4` Dwnlqvrq/ D1 E1 dqgPlfnhozuljwk/ M1 +4<<4, Xqhpsor|phqw Frpshqvdwlrq dqg Oderu

Pdunhw Wudqvlwlrqv= D Fulwlfdo Uhylhz1 Mrxuqdo ri Hfrqrplf Olwhudwxuh/ [[L[/ 49:<

0 4:5:1

^5` Eodqfkdug/ R1 M1 dqg Zroihuv/ M1 +4<<<, Wkh Uroh ri Vkrfnv dqg Lqvwlwxwlrqv lq wkh

Ulvh ri Hxurshdq Xqhpsor|phqw= Wkh Djjuhjdwh Hylghqfh1 QEHU Zrunlqj Sdshu/

Z:5;51

^6` Errwk/ D1 O1 +4<<8, Wkh Hfrqrplfv ri wkh Wudgh Xqlrq1 Fdpeulgjh Xqlyhuvlw| Suhvv/

Fdpeulgjh1

49

^7` Exlwhu/ Z1 K1 dqg Nohw}hu/ N1 P1 +4<<6,1 Shupdqhqw Lqwhuqdwlrqdo Surgxfwlylw|

Jurzwk Gl�huhqwldov lq dq Lqwhjudwhg Joredo Hfrqrp|1 Lq= P1 Dqghuvrq dqg N1 R1

Prhqh +hgv1,/ Hqgrjhqrxv Jurzwk1 Eodfnzhoo/ R{irug/ :: 0 4361

^8` Fdkxf/ S1 dqg Plfkho/ S1 +4<<9, Plqlpxp Zdjh Xqhpsor|phqw dqg Jurzwk1 Hxur0

shdq Hfrqrplf Uhylhz/ 73/ 4796 0 47;51

^9` Guh}h/ M1 K1 dqg Vqhhvvhqv/ K1 +4<<:, Whfkqrorjlfdo Ghyhorsphqw/ Frpshwlwlrq iurp

Orz0Zdjh Hfrqrplhv dqg Orz0Vnloohg Xqhpsor|phqw1 Lq= G1 M1 Vqrzhu dqg J1 gh od

Ghkhvd +hgv1,/ Xqhpsor|phqw Srolf|1 Jryhuqphqw Rswlrqv iru wkh Oderxu Pdunhw1

Fdpeulgjh Xqlyhuvlw| Suhvv/ Fdpeulgjh/ 583 0 5::1

^:` Iuhhpdq/ U1 E1 dqg Vfkhwwndw/ U1 +5333, Wkh Uroh ri Zdjh dqg Vnloo Gl�huhqfhv lq

XV0Jhupdq Hpsor|phqw Gl�huhqfhv1 QEHU Zrunlqj Sdshu/ :7:71

^;` Jrhunh/ O1 +4<<;, Elvpdun yhuvxv Ehyhulgjh= Iodw0 dqg Hduqlqjv0Uhodwhg Xqhpsor|0

phqw Lqvxudqfh lq d Jhqhudo H!flhqf| Zdjh Iudphzrun1 Ilqdq}dufkly +iruwkfrp0

lqj,1

^<` Jrhunh/ O1 dqg Pdgvhq/ M1 E1 +5333, Hduqlqjv0Uhodwhg Xqhpsor|phqw Ehqh�wv dqg

Xqhpsor|phqw lq Xqlrqlvhg Hfrqrplhv1 Glvfxvvlrq Sdshu1

^43` Od|dug/ U1 dqg Qlfnhoo/ V1 +4<<3, Lv Xqhpsor|phqw Orzhu li Xqlrqv Edujdlq ryhu

Hpsor|phqwB Txduwhuo| Mrxuqdo ri Hfrqrplfv/ 438/ ::6 0 :;:1

^44` Pduwlq/ M1 S1 +4<<9, Phdvxuhv ri Uhsodfhphqw Udwhv iru wkh Sxusrvh ri Lqwhuqdwlrqdo

Frpsdulvrq= D Qrwh1 RHFG Hfrqrplf Vwxglhv/ 59/ << 0 4471

^45` Qlfnhoo/ V1 M1 dqg Ehoo/ E1 +4<<9, Fkdqjhv lq wkh Glvwulexwlrq ri Zdjhv dqg Xqhp0

sor|phqw lq RHFG Frxqwulhv1 Dphulfdq Hfrqrplf Uhylhz= Sdshuv dqg Surfhhglqjv/

;9/ 635 0 63;1

^46` Qlfnhoo/ V1 M1 dqg Ehoo/ E1 +4<<:, Zrxog Fxwwlqj Sd|uroo Wd{hv rq wkh Xqvnloohg Kdyh

d Vljql�fdqw Lpsdfw rq Xqhpsor|phqw1 Lq= G1 M1 Vqrzhu dqg J1 gh od Ghkhvd +hgv1,/

Xqhpsor|phqw Srolf|1 Jryhuqphqw Rswlrqv iru wkh Oderxu Pdunhw1 Fdpeulgjh Xql0

yhuvlw| Suhvv/ Fdpeulgjh/ 5<9 0 65;1

4:

^47` S jhu/ P1 S1 +4<<:, Rq wkh Hpsor|phqw H�hfwv ri Uhyhqxh Qhxwudo Wd{ Uhirupv1

Ilqdq}dufkly/ 87/ 763 0 7791

^48` Vdlqw0Sdxo/ J1 +4<<9, Gxdo Oderu Pdunhwv= D Pdfurhfrqrplf Shuvshfwlyh1 Wkh PLW

Suhvv/ Fdpeulgjh Pdvvdfkxvhwwv1

^49` Vlhehuw/ K1 +4<<:, Oderu Pdunhw Uljlglwlhv= Dw wkh Urrw ri Xqhpsor|phqw lq Hxursh1

Mrxuqdo ri Hfrqrplf Shuvshfwlyhv/ 44/ 88 0 :71

^4:` Wrsho/ U1 K1 +4<<:, Idfwru Sursruwlrqv dqg Uhodwlyh Zdjhv= Wkh Vxsso|0Vlgh Gh0

whuplqdqwv ri Zdjh Lqhtxdolw|1 Mrxuqdo ri Hfrqrplf Shuvshfwlyhv/ 44/ 88 0 :71

^4;` Ylmoeulhi/ K1 dqg ydq gh Zlmqjdhuw/ U1 +4<<8, Xqhpsor|phqw Lqvxudqfh Srolf| dqg

Xqlrq Zdjh Irupdwlrq1 Oderu/ </ 566 0 5841

4;