Download Развитие и применение искусственного интеллекта в медицине and more Exams Financial Economics in PDF only on Docsity!
Khgjlqj dqg Ilqdqfldo Iudjlolw| lq Il{hg H{fkdqjh
Udwh Uhjlphv
Fudlj Exuqvlgh| / Pduwlq Hlfkhqedxp}dqg Vhujlr Uhehor{
Pd| 5333 +uhylvhg Rfwrehu/ 5333,
Devwudfw Fxuuhqf| fulvhv wkdw frlqflgh zlwk edqnlqj fulvhv whqg wr vkduh dw ohdvw wkuhh ho hphqwv1 Iluvw/ edqnv kdyh d fxuuhqf| plvpdwfk ehwzhhq wkhlu dvvhwv dqg oldelolwlhv Vhfrqg/ edqnv gr qrw frpsohwho| khgjh wkh dvvrfldwhg h{fkdqjh udwh ulvn1 Wklug/ wkhuh duh lpsolflw jryhuqphqw jxdudqwhhv wr edqnv dqg wkhlu iruhljq fuhglwruv1 Wklv sdshu dujxhv wkdw wkh uvw wzr ihdwxuhv dulvh iurp edqnv* rswlpdo uhvsrqvh wr jryhuqphqw jxdudqwhhv1 Zh vkrz wkdw jxdudqwhhv frpsohwho| holplqdwh edqnv* lqfhqwlyhv wr khgjh wkh ulvn ri d ghydoxdwlrq1 Rxu prgho dovr duwlfxodwhv rqh uhdvrq zk| jryhuqphqwv pljkw eh whpswhg wr surylgh jxdudqwhhv wr edqn fuhglwruv1 Jxdudqwhhv orzhu wkh grphvwlf lqwhuhvw udwh dqg ohdg wr d errp lq hfrqrplf dfwlylw|1 Exw wklv errp frphv dw wkh frvw ri d pruh iudjloh edqnlqj v|vwhp1 Lq wkh hyhqw ri d ghydoxdwlrq/ edqnv uhqhjh rq iruhljq ghewv dqg ghfoduh edqnuxswf| M1H1O1 Fodvvl fdwlrq= I64/ I74/ J48/ J Nh|zrugv= Il{hg h{fkdqjh udwh uhjlphv/ khgjlqj/ jryhuqphqw jxdudqwhhv
Zh duh judwhixo wr Nhoorjj*v Edqnlqj Uhvhdufk Fhqwhu iru qdqfldo vxsssruw1 Exuqvlgh wkdqnv wkh Krryhu Lqvwlwxwlrq iru lwv vxssruw wkurxjk d Qdwlrqdo Ihoorzvkls1 Zh wkdqn Pdufr Edvvhwwr/ Dulho Exuvwhlq/ Mrqdwkdq Hdwrq/ Oduu| Mrqhv/ Ohrud Nodsshu/ Gherudk Oxfdv/ Gdylg Pduvkdoo/ Sdror Shvhqwl/ Ure Yljixvvrq/ dq dqrq|prxv uhihuhh/ dqg vhplqdu sduwlflsdqwv dw Jhrujhwrzq/ Kduydug/ Krryhu/ wkh LPI/ wkh 4<<< XWGW Zrunvkrs lq Lqwhuqdwlrqdo Hfrqrplfv dqg Ilqdqfh/ wkh Qruwkzhvwhuq Xqlyhuvlw| Vxpphu Pdfurhfrqrplfv Zrunvkrs/ dqg LVRP iru xvhixo frpphqwv1 Wkh rslqlrqv lq wklv sdshu duh wkrvh ri wkh dxwkruv dqg qrw qhfhvvdulo| wkrvh ri wkh Ihghudo Uhvhuyh Edqn ri Fklfdjr ru wkh Zruog Edqn1 |
}Wkh Zruog Edqn {Qruwkzhvwhuq Xqlyhuvlw|/ QEHU dqg Ihghudo Uhvhuyh Edqn ri Fklfdjr Qruwkzhvwhuq Xqlyhuvlw|/ QEHU dqg FHSU
41 Lqwurgxfwlrq
Lq wkh srvw Euhwwrq Zrrgv hud/ fxuuhqf| fulvhv kdyh riwhq frlqflghg zlwk edqnlqj fulvhv Surplqhqw h{dpsohv lqfoxgh Vrxwkhdvw Dvld lq 4<<:/ Fkloh lq 4<;5/ Ph{lfr lq 4<<7/ dqg Vzhghq dqg Ilqodqg lq 4<<51^4 Wkuhh nh| ihdwxuhv ri vxfk cwzlq* fulvhv duh +l, edqnv kdyh d fxuuhqf| plvpdwfk ehwzhhq wkhlu dvvhwv dqg oldelolwlhv/ +ll, edqnv gr qrw frpsohwho| khgjh wkh dvvrfldwhg h{fkdqjh udwh ulvn/ dqg +lll, wkh jryhuqphqw pdnhv lpsolflw jxdudqwhhv wr edqnv dqg wkhlu iruhljq fuhglwruv1^5 Wklv sdshu dujxhv wkdw wkh uvw wzr ihdwxuhv dulvh iurp edqnv* rswlpdo uhvsrqvh wr jryhuqphqw jxdudqwhhv Wkh idfw wkdw edqnv duh h{srvhg wr xqkhgjhg fxuuhqf| ulvnv olhv dw wkh fruh ri frpshwlqj wkhrulhv ri fxuuhqf| fulvhv1 Lq vrph fdvhv/ lw lv vlpso| d pdlqwdlqhg dvvxpswlrq ri wkh dqdo|vlv1 Vhh iru h{dpsoh/ Djklrq/ Edffkhwwd dqg Edqhumhh +5333,/ Fkdqj dqg Yhodvfr +4<<<,/ dqg Nuxjpdq +4<<<,1 Lq rwkhu fdvhv lw lv dvvxphg wkdw/ wr d uvw dssur{lpdwlrq/ edqnv lq hphujlqj pdunhwv pxvw eruurz lq xqlwv ri iruhljq fxuuhqf| dqg vlpso| fdqqrw khgjh wkh uhvxowlqj h{fkdqjh udwh ulvn +vhh Hlfkhqjuhhq dqg Kdxvpdqq +5333,, Wklv sdshu dujxhv wkdw edqnv fkrrvh wr h{srvh wkhpvhoyhv wr h{fkdqjh udwh ulvn1 Lq d zruog zlwk jryhuqphqw jxdudqwhhv/ lw lv rswlpdo iru edqnv wr kdyh dq xqkhgjhg fxuuhqf| plvpdwfk ehwzhhq wkhlu dvvhwv dqg oldelolwlhv1 Zkhq d ghydoxdwlrq rffxuv/ edqnv vlpso| uhqhjh rq iruhljq ghew dqg jr edqnuxsw1 Wr plqlpl}h wkh ydoxh ri wkh dvvhwv wkdw wkh| vxuuhqghu lq edqnuxswf|/ edqnv pd| dfwxdoo| qg lw rswlpdo wr pdjqli| wkhlu h{fkdqjh udwh h{srvxuh e| vhoolqj grooduv iruzdug dqg orvh prqh| lq wkh iruzdug pdunhw zkhq wkhuh lv d ghydoxdwlrq Jlyhq wkh fhqwudo uroh wkdw jryhuqphqw jxdudqwhhv sod| lq rxu prgho/ lw lv xvhixo wr surylgh lqwxlwlrq iru krz wkh| d hfw wkh rswlpdo khgjlqj vwudwhjlhv ri edqnv1 Wkh jryhuqphqw jxdudqwhhv wkdw iruhljq fuhglwruv zloo eh uhsdlg lq ixoo li wkhuh lv d ghydoxdwlrq dqg edqnv ghidxow rq wkhlu ghew1 Vxssrvh d edqn frqwhpsodwhv khgjlqj iruhljq h{fkdqjh udwh ulvn yld iruzdug frqwudfwv1 Wkh khgjlqj sur wv wkdw duh uhdol}hg zkhq d ghydoxdwlrq rffxuv dqg wkh edqn ghfoduhv edqnuxswf| duh vhl}hg e| wkh jryhuqphqw1 Vr wkh edqn dvvljqv }hur ydoxh wr wkhp1 Exw wkhvh frqwudfwv jhqhudwh orvvhv zkhq wkhuh lv qr ghydoxdwlrq dqg wkh edqn grhv qrw jr edqnuxsw1 Lw iroorzv wkdw edqnv kdyh qr lqfhqwlyh wr hqwhu iruzdug frqwudfwv wkdw jhqhudwh srvlwlyh sd|r v zkhq wkhuh lv d ghydoxdwlrq (^4) Ndplqvn| dqg Uhlqkduw +4<<<, vwxg| hpslulfdoo| wkh olqn ehwzhhq edqnlqj dqg fxuuhqf| fulvhv1 Vhh Gld}0Dohmdqgur +4<;8, dqg Q|ehuj dqg Ylkulçoç +4<<6, iru dqdo|vhv ri wkh 4<;5 Fklohdq dqg 4<<5 Ilqqlvk fulvhv/ uhvshfwlyho|1 Jduehu dqg Odoo +4<<;, dqg Nuxhjhu dqg Wruqhoo +4<<<, glvfxvv wkh 4<<7 Ph{lfdq fulvlv1 5 Plvknlq +4<<9, dqg Revwihog +4<<;, dujxh wkdw d jryhuqphqwv surplvh wr pdlqwdlq d {hg h{fkdqjh udwh lv riwhq vhhq dv surylglqj dq lpsolflw jxdudqwhh wr edqnv fuhglwruv djdlqvw wkh h hfwv ri d srvvleoh ghydoxdwlrq1 Fruvhwwl/ Shvhqwl dqg Urxelql +4<<<, dqg Grroh| +5333, dovr hpskdvl}h wkh uroh ri jryhuqphqw jxdudqwhhv wr wkh edqnlqj vhfwru lq cwzlq fulvhv* hslvrghv
fulvhv1 Wkhvh jxdudqwhhv kdyh ehhq h{whqvlyho| glvfxvvhg lq wkh olwhudwxuh1^6 Wkh vl}h ri wkhvh jryhuqphqw jxdudqwhhv lv ri vx!flhqw lqwhuhvw wr wkh sulydwh vhfwru wkdw/ dw wkh hqg ri 4<<:/ Vwdqgdug dqg Srruv ehjdq wr sxeolvk hvwlpdwhv ri jryhuqphqwv wrwdo frqwlqjhqw oldelolwlhv wr wkh edqnlqj vhfwru1^7 Wkh rwkhu wzr frpprq hohphqwv lq edqnlqj2fxuuhqf| fulvhv duh wkdw +l, upv dqg qdq fldo lqwhuphgldulhv eruurz h{whqvlyho| iurp deurdg/ dqg +ll, wkh| gr qrw frpsohwho| khgjh h{fkdqjh udwh ulvn1 Xqiruwxqdwho|/ gxh wr gdwd olplwdwlrqv/ wkhuh lv olwwoh hpslulfdo zrun phdvxulqj sulydwh djhqwv* h{fkdqjh udwh h{srvxuh1 Rqh zd| wr dvvhvv wkh srwhqwldo pdjql wxgh ri wklv h{srvxuh lv wr frqvlghu edqnv/ upv dqg qdqfldo lqwhuphgldulhv* qhw iruhljq dvvhwv sulru wr wkh rqvhw ri d fulvlv1 Wzr vrxufhv ri gdwd duh= wkh Edqn ri Lqwhuqdwlrqdo Vhw wohphqwv +ELV, dqg wkh Lqwhuqdwlrqdo Ilqdqfldo Vwdwlvwlfv +LIV,1 Dq lpsruwdqw dgydqwdjh ri wkh ELV gdwd lv wkdw wkh| duh edvhg rq uhsruwv iurp pdmru RHFG edqnv1 Wr wkh h{whqw wkdw dffrxqwlqj vwdqgdugv iru edqnv lq RHFG frxqwulhv duh pruh xqlirup dqg fduhixoo| hqirufhg wkdq lq qrq0RHFG frxqwulhv/ wkh ELV gdwd pd| eh pruh uholdeoh wkdq wkh LIV gdwd1 Wkh LIV gdwd duh edvhg/ lq sduw/ rq uhsruwv iurp djhqwv lq qrq0RHFG frxqwulhv1 Lq dgglwlrq/ wkhuh duh vxewoh dpeljxlwlhv derxw krz d jlyhq wudqvdfwlrq pljkw eh uhsruwhg lq wkh LIV gdwd1^8 Wkh dgydqwdjh ri wkh LIV gdwd lv wkdw wkh| duh pruh frpsuhkhqvlyh lq fryhudjh/ vlqfh wkh ELV gdwd duh edvhg vroho| rq uhsruwv iurp edqnv wkdw duh sduw ri lwv v|vwhp1 Zlwk wkhvh olplwdwlrqv lq plqg/ zh qrz uhsruw uhvxowv edvhg rq erwk wkh ELV dqg LIV gdwd Wdeoh 4 suhvhqwv lqirupdwlrq rq wkh qhw iruhljq dvvhwv ri edqnv dqg upv iru ydulrxv frxqwulhv sulru wr wkh rqvhw ri wkhlu fxuuhqf|2edqnlqj fulvhv1 D qxpehu ri lqwhuhvwlqj ihdwxuhv hphujh iurp wkh wdeoh1 Iluvw/ lq doo fdvhv/ upv dqg edqnv lq wkhvh frxqwulhv kdg vljql fdqw qhw iruhljq ghew dw wkh wlph ri wkhlu fulvhv1 Iru wkh Qruglf frxqwulhv/ wkh LIV gdwd lqglfdwh d pxfk odujhu qhw qhjdwlyh srvlwlrq wkdq wkh ELV gdwd1 Wklv pd| uh hfw wkh idfw wkdw edqnv lq wkh Qruglf frxqwulhv zhuh eruurzlqj vxevwdqwldo dprxqwv ri ixqgv iurp hqwlwlhv rwkhu wkdq ELV edqnv1 Iru wkh Hdvw Dvldq frxqwulhv/ wkh ELV gdwd lqglfdwh d pxfk odujhu qhjdwlyh qhw srvlwlrq wkdq wkh LIV gdwd1 Wklv pd| uh hfw dffrxqwlqj sureohpv zlwk wkh gdwd uhsruwhg wr (^6) Vhh wkh uhihuhqfhv lq irrwqrwh 51 Lq dgglwlrq/ vhh LPI +4<<;/ sdjh 68,/ LPI +4<<</ sdjh 54, dqg Ghokdlvh +4<<;, iru d glvfxvvlrq ri jxdudqwhhv lq Wkdlodqg/ Pdod|vld/ Lqgrqhvld dqg Nruhd1 LPI +4<<;/ sdjh 6<, ghwdlov wkh h{whqw wr zklfk lpsolflw jxdudqwhhv ehfdph h{solflw diwhu wkh fulvhv rffxuuhg1 Guhhv dqg Sd}duedvlrjox +4<<;, glvfxvv jryhuqphqw jxdudqwhhv lq wkh Qruglf frxqwu| edqnlqj fulvhv/ zkloh Fdorplulv +4<<;, glvfxvvhv iruhljq edqn fuhglwru edlorxwv diwhu wkh 4<<7 Ph{lfdq fxuuhqf| fulvlv (^7) Vhh Exuqvlgh/ Hlfkhqedxp dqg Uhehor +5333e, iru d glvfxvvlrq ri wkhvh hvwlpdwhv (^8) Vxssrvh/ iru h{dpsoh/ wkdw Edqn D lq Frxqwu| [ eruurzv grooduv iurp deurdg dqg xvhv wkh surfhhgv wr pdnh groodu ghqrplqdwhg ordqv wr orfdo upv1 Edqn D pd| wdnh wkh srvlwlrq wkdw wklv wudqvdfwlrq grhv qrw fdxvh d ghfolqh lq lwv qhw iruhljq dvvhwv dqg zrxog qrw uhsruw lw dv vxfk1 Krzhyhu/ wkh wudqvdfwlrq grhv h{srvh wkh edqn wr dqrwkhu w|sh ri h{fkdqjh udwh ulvnwkh lqfuhdvh lq ordq ghidxow udwhv wkdw riwhq rffxuv diwhu d ghydoxdwlrq1 Vlqfh wkh ELV gdwd duh edvhg rq uhsruwv iurp wkh iruhljq fuhglwruv ri Edqn D +dvvxplqj wkdw wkh| duh edqnv lq RHFG frxqwulhv, wkh wudqvdfwlrq zrxog vkrz xs dv d ghfuhdvh lq wkh qhw iruhljq dvvhwv ri edqnv lq Frxqwu| [
6
WDEOH 4
Vxppdu| Lqglfdwruv ri Qhw Iruhljq Dvvhwv +shufhqw ri JGS,
Vrxufh= ELV LIV Vwdqgdug ) Srru*v Edqnv Ilupv GPE RIL Ilqdqfldo V|vwhp Qruglf Frxqwulhv +4<<5, Ilqodqg 0;18 0;14 05615 q2d 04: Vzhghq 04;17 0915 05:13 316 04<1:
Ph{lfr +4<<7, 061; 0;19 0415 0:18 0<1:
Hdvw Dvld +4<<:, Lqgrqhvld 091< 04914 041: q2d 0517 Nruhd 0451; 0815 0515 0615 0615 Pdod|vld 04418 0717 0:13 314 0714 Sklolsslqhv 0;18 0514 0:18 q2d 0; Wkdlodqg 07;1< 0:13 0551; 051: 04<1:
Qrwhv= ELV phdvxuhv ri QID duh hqg0ri0txduwhu1 Iru wkh Qruglf frxqwulhv/ 4<<4T6/ iru Ph{lfr/ 4<<7T6/ iru Hdvw Dvld/ 4<<:T51 Wkh LIV phdvxuhv ri QID duh hqg0ri0|hdu1 Iru wkh Qruglf frxqwulhv/ 4<<3/ iru Ph{lfr/ 4<<6/ iru Hdvw Dvld 4<<91 GPE= Ghsrvlw Prqh| Edqnv RIL= Rwkhu Ilqdqfldo Lqvwlwxwlrqv
wkh LIV Wkh wdeoh shuwdlqv wr ohyhov ri qhw iruhljq dvvhwv lpphgldwho| sulru wr wkh fulvhv1 Lq prvw fdvhv/ wkhvh ohyhov zhuh wkh uhvxow ri vljql fdqw ghfolqhv ri qhw iruhljq dvvhw kroglqjv lq wkh lpphgldwho| suhfhglqj |hduv1 Iru h{dpsoh/ lq glvfxvvlqj Dvldq fulvlv frxqwulhv/ Mdfnvrq +4<<<, zulwhv= edqnv lq hdfk frxqwu| udslgo| lqfuhdvhg wkhlu qhw iruhljq oldelolwlhv e| odujh shufhqwdjhv gxulqj wkh irxu |hduv sulru wr wkh fulvlv1 Wkh LPI Zruog Hfrqrplf Rxworrn dqg Lqwhuqdwlrqdo Fdslwdo Pdunhwv +ydulrxv |hduv, grfxphqw vlplodu ehkdylru lq rwkhu fulvlv frxqwulhv Zkloh kljko| vxjjhvwlyh/ Wdeoh 4 fdq rqo| hvwdeolvk wkdw qdqfldo lqvwlwxwlrqv kdg odujh h{fkdqjh udwh h{srvxuh1 Wklv h{srvxuh frxog/ lq sulqflsoh/ kdyh ehhq khgjhg1 Gdwd olplwd wlrqv suhyhqw xv iurp suhflvho| phdvxulqj wkh h{whqw wr zklfk odujh qhw iruhljq dvvhw srvlwlrqv zhuh khgjhg lq gl huhqw fulvlv frxqwulhv1 Vwloo/ pdq| txdolwdwlyh dqdo|vhv vxjjhvw wkdw wkhvh srvlwlrqv zhuh xqkhgjhg1 Odqh hw1 do1 +4<<</ s1 4:, frqfoxgh wkdw Lqgrqhvld/ Nruhd dqg Wkdlodqg kdg odujh xqkhgjhg sulydwh vkruw0whup iruhljq fxuuhqf| ghew +111,> lq Nruhd dqg Wkdlodqg/ wklv ghew zdv pdlqo| lqwhuphgldwhg wkurxjk wkh edqnlqj v|vwhp/ zkloh lq Lqgrqh vld wkh frusrudwlrqv kdg khdylhu gluhfw h{srvxuhv wr vxfk ghew1 Ironhuwv0Odqgdx hw1 do
7
WDEOH 6
Uhsruwhg Ryhu0wkh0Frxqwhu Iruhljq H{fkdqjh Ghulydwlyhv Wxuqryhu +Gdlo| Dyhudjhv/ Dsulo 4<<;/ Ploolrqv ri XV Grooduv,
Ilqodqg 5/667 Sklolsslqhv 5:; Lqgrqhvld :8< Vrxwk Nruhd 649 Pdod|vld 874 Vzhghq 8/ Ph{lfr 5/6:; Wkdlodqg 4/<
41 Hxurprqh| +4<<9, uhsruwv zkdw surgxfwv zhuh r huhg e| wkh Krqj Nrqj Vkdqjkdl Edqn Frusrudwlrq +KVEF, iru ydulrxv Dvldq frxqwulhv1 Wkh uhohydqw surgxfwv duh= +4, iruzdug pdunhwv/ +5, orfdo fxuuhqf| vzdsv/ dqg +6, fxuuhqf| rswlrqv1 KVEF r huhg doo wkuhh surgxfwv lq Lqgrqhvld/ Krqj Nrqj/ Vlqjdsruh dqg Wkdlodqg dqg wkh uvw wzr surgxfwv lq Nruhd/ Pdod|vld/ dqg Wdlzdq1 Lq dgglwlrq/ iruzdug frqwudfwv zhuh dydlodeoh lq Lqgld/ Vul Odqnd/ Sdnlvwdq/ wkh Sklolsslqhv/ Pdxulwlxv/ Pdfdx/ dqg Euxqhl
51 Dvldprqh| +4<<:, uhsruwhg/ sulru wr wkh fulvlv lq Wkdlodqg/ wkdw wkhuh kdg ehhq dq h{sorvlrq lq erwk vsrw dqg iruzdug wudglqj qrw rqo| lq Edqjnrn/ exw dovr lq Vlqjdsruh dqg Krqj Nrqj1 Uhfhqw gdlo| wxuqryhu/ lqfoxglqj vzdsv/ lv hvwlpdwhg wr eh pruh wkdq XV' eloolrq shu gd|/ ryhu wkuhh wlphv wkh dyhudjh gdlo| wudglqj dprxqw lq 4<<61 XV groodu2edkw lqwhuedqn vsrw dqg iruzdug iruhljq h{fkdqjh pdunhwv duh oltxlg dqg uhdglo| dydlodeoh/ zlwk pdwxulwlhv xs wr vl{ prqwkv1 XV groodu2edkw fxuuhqf| vzdsv dqg ryhu0wkh0frxqwhu fxuuhqf| rswlrqv duh dovr srsxodu dqg dfwlyh1
61 Wdeoh 7/ frqvwuxfwhg iurp wkh EDQNVFRSH gdwdedvh/ vxppdul}hv pdmru Wkdl edqnv* sxufkdvhv dqg vdohv ri iruzdug pdunhw frqwudfwv iru 4<<91 Wkh odujh jurvv sxufkdvhv dqg vdohv duh hylghqfh wkdw wkh Wkdl edqnv zhuh lqyroyhg h{whqvlyho| lq wkh iruzdug pdunhw1 Krzhyhu/ wkh uhodwlyho| vpdoo vl}h ri wkhlu qhw sxufkdvhv lv frqvlvwhqw zlwk wkh qrwlrq wkdw wkh edqnv zhuh dfwlqj dv djhqwv iru wkhlu folhqwv/ dqg qrw khgjlqj wkhlu rzq h{fkdqjh udwh h{srvxuh
71 Dvldprqh| +4<<9, uhsruwhg wkdw oltxlg iruzdug pdunhwv h{lvwhg lq Lqgrqhvld iru frqwudfwv xs wr vl{ prqwkv1 Lq dgglwlrq/ rwkhu khgjlqj lqvwuxphqwv zhuh ehfrplqj pruh dfwlyh/ lq foxglqj furvv0fxuuhqf| dqg lqwhuhvw udwh vzdsv xs wr yh |hduv dv zhoo dv fxuuhqf| rswlrqv zlwk pdwxulwlhv xs wr wzr |hduv1:
: (^) Wkhvh pdunhwv zhuh vxemhfw wr d ydulhw| ri uhjxodwlrqv ghvljqhg wr glvfrxudjh cvshfxodwlrq* lq ghulydwlyh frqwudfwv1 Lq sduwlfxodu qhw rshq dqg iruzdug srvlwlrqv ri frpphufldo edqnv zhuh olplwhg wr 58 shufhqw ri wkhlu fdslwdo
WDEOH 7
Vxppdu| ri Iruzdug Pdunhw Dfwlylwlhv e| Wkdl Edqnv +Ploolrqv ri X1V1 Grooduv,
Iruzdug Frqwudfwv Dvvhwv Udqn Sxufkdvhg Vrog Qhw +4<<9, Edqjnrn Edqn <6<7 43678 0<85 783<: 4 Wkdl Iduphuv Edqn 437< 443< 08< 58468 5 Nuxqj Wkdl Edqn 547; q2d q2d 58345 6 Vldp Frpphufldo Edqn 6964 6798 499 54359 8 Edqn ri D|xgk|d 56< 47:: 0456; 4787: 9 Wkdl Plolwdu| Edqn ;;8 4;3 :38 45<54 : Iluvw Edqjnrn Flw| Edqn 859 ;3: 05;4 <8:8 ; Vldp Flw| Edqn :34 4554 0853 <36< 43 Edqjnrn Phwursrolwdq Edqn 4:5 5:6 0434 :5<; 46 Edqjnrn Edqn ri Frpphufh 63; 977 0669 9689 47 Edqn ri Dvld 6989 6994 07 7;<6 4: GEV Wkdl Gdqx Edqn ;34 ::3 63 7978 4; Vwg1 Fkduwhuhg Qdnruqwkrq Edqn 6<< 84; 0453 57<5 59 Edqnwkdl 57 :5 07; 57:7 5: XRE Udgdqdvlq Edqn 77 q2d q2d q2d 68 H{sruw0Lpsruw Edqn ri Wkdlodqg 47 99 085 4683 6;
81 Sulru wr wkh fulvlv lq Nruhd/ vl{0prqwk/ rqh0|hdu dqg wkuhh0|hdu iruzdug frqwudfwv zhuh dydlodeoh dqg wudghg lq grphvwlf pdunhwv1 Krzhyhu wkhvh pdunhwv zhuh qrw yhu| oltxlg/ ehfdxvh ri uhjxodwlrq1;^ Dffruglqj wr Dvldprqh| +4<<:,/ wkhvh oltxlglw| sureohpv ohg wr wkh ghyhorsphqw ri d odujh r vkruh pdunhw iru qrqgholyhudeoh iruzdugv1 Sdun dqg Ukhh +5333, uhsruw wkdw dyhudjh gdlo| wudglqj lq wkhvh frqwudfwv zdv 583 ploolrq XV grooduv1 Lq dgglwlrq Nuhjho +4<<;, uhsruwv wkdw Nruhdq edqnv wudghg ryhu '883 eloolrq zruwk ri qdqfldo ghulydwlyhv lq 4<<:1 Zh lqihu wkdw/ lpshuihfwlrqv dvlgh/ pdunhwv iru khgjlqj wkh Zrq h{lvwhg
91 Hxurprqh| +4<<4, uhsruwhg wkdw prvw frpsdqlhv lq Vzhghq ghdow dfwlyho| lq= +l, iruzdug frqwudfwv zklfk zhuh yhu| oltxlg iru pdwxulwlhv xs wr rqh |hdu dqg idluo| oltxlg iru pdwxulwlhv xs wr wzr |hduv> +ll, fxuuhqf| rswlrqv zklfk zhuh oltxlg jrlqj rxw wr 4; prqwkv lq pdwxulw|> dqg +lll, fxuuhqf| vzdsv1 Dffruglqj wr wkh ELV/ wkh qrwlrqdo sulqflsdo ri fxuuhqf| vzdsv lqyroylqj wkh Vzhglvk Nurqd/ ydoxhg lq eloolrqv ri XV grooduv/ zdv 4:1:/ 5<1</ 6716/ dqg 6:16/ dv ri Ghfhpehu 4<<4/ 4<<5/ 4<<6 dqg 4<<7/ uhvshfwlyho| ; (^) Iru h{dpsoh/ edqnv zhuh qrw shuplwwhg wr fduu| d vsrw vkruw srvlwlrq deryh olplwv ghwhuplqhg e| wkh Edqn ri Nruhd
fulvhv gr qrw kdsshq rqo| lq hphujlqj pdunhwv zkhuh iruzdug pdunhwv pd| zhoo eh txlwh lpshuihfw1 Wkh| dovr rffxu lq frxqwulhv vxfk dv Vzhghq zkhuh wkh dvvxpswlrq ri zhoo ixqfwlrqlqj iruzdug pdunhwv vhhpv uhdvrqdeoh1 Ilqdoo|/ wkh ehqfkpdun fdvh pdnhv fohdu rqh uhdvrq zk| pdunhwv iru vhfxulwlhv wr khgjh h{fkdqjh udwh ulvn/ vxfk dv iruzdug frqwudfwv dqg iruhljq ghew ghqrplqdwhg lq orfdo fxuuhqf|/ pd| qrw h{lvw= lq {hg h{fkdqjh udwh hfrqrplhv zlwk jryhuqphqw jxdudqwhhv/ edqnv kdyh qr lqfhqwlyhv wr sduwlflsdwh lq wkhp Zh ehjlq e| vwxg|lqj d sduwldo htxloleulxp prgho ri edqnv lq d vpdoo rshq hfrqrp|1 E| dvvxpswlrq wkhuh lv d vlqjoh frqvxpswlrq jrrg dqg qr eduulhuv wr wudgh/ vr wkdw sxufkdvlqj srzhu sdulw| krogv=
| ' (^7) | (^) |W +614,
Khuh | dqg | W ghqrwh wkh grphvwlf dqg iruhljq sulfh ohyhov uhvshfwlyho|/ zkloh (^7) | ghqrwhv wkh h{fkdqjh udwh gh qhg dv xqlwv ri grphvwlf fxuuhqf| shu xqlw ri iruhljq fxuuhqf|1 Iru frqyhqlhqfh zh qrupdol}h wkh iruhljq sulfh ohyho wr rqh= (^) |W ' Å iru doo | 1 Wkh udwh ri ghsuhfldwlrq ri wkh h{fkdqjh udwh lv dvvxphg wr iroorz d Pdunry fkdlq1 Wkh hfrqrp| lv lqlwldoo| lq d {hg h{fkdqjh udwh uhjlph/ (^7) |7| 3 ' Å/ zlwk h{fkdqjh udwh (^7) | ' 7 U^1 Wkh hfrqrp| fdq vzlwfk wr d ghydoxdwlrq uhjlph/ (^7) |7| 3 ' : Å/ zklfk lv dq devruelqj vwdwh1 Wkh suredelolw| wudqvlwlrq pdwul{ lv jlyhq e|=
A '
Å R R
f Å
Khuh R ' hE (^7) |n7| ' m (^7) |7| 3 ' Å / lv wkh suredelolw| ri vzlwfklqj iurp wkh {hg h{fkdqjh udwh uhjlph wr wkh ghydoxdwlrq uhjlph1^43 Wkh yduldeoh 7 (^ ' 7U^ ghqrwhv wkh ohyho ri wkh h{fkdqjh udwh lq wkh uvw shulrg ri wkh ghydoxdwlrq uhjlph1^44 Vlqfh zh irfxv rq edqnv* khgjlqj vwudwhjlhv sulru wr wkh ghydoxdwlrq/ zh vxssuhvv wlph vxevfulswv wkurxjkrxw pxfk ri wkh uhvw ri wkh sdshu
6141 Wkh Edqnlqj Vhfwru
Iru qrz zh dvvxph wkdw edqnv eruurz lq grooduv dqg ohqg lq orfdo fxuuhqf|/ vr wkdw wkh| duh h{srvhg wr d fxuuhqf| plvpdwfk1 Lq vhfwlrq 7 zh vkrz wkdw/ lq wkh suhvhqfh ri jryhuqphqw jxdudqwhhv/ edqnv duh zloolqj wr wdnh rq wklv plvpdwfk Edqnv/ doo ri zkrp duh shuihfwo| frpshwlwlyh/ qdqfh wkhpvhoyhv hqwluho| e| eruurzlqj u grooduv dw wkh jurvv lqwhuhvw udwh - K^ lq wkh lqwhuqdwlrqdo fdslwdo pdunhw1 Wkhvh ixqgv duh (^43) Lq Exuqvlgh/ Hlfkhqedxp dqg Uhehor +5333d, zh hqgrjhql}h wkh suredelolw| ri ghydoxdwlrqv lq d pdqqhu frqvlvwhqw zlwk wkh zd| edqnv duh prghohg lq wklv sdshu (^44) Wkh dqdo|vlv fdq eh jhqhudol}hg wr wkh fdvh zkhuh wkhuh lv pruh wkdq rqh srvvleoh ydoxh ri V lq wkh hyhqw ri d ghydoxdwlrq
<
frqyhuwhg lqwr orfdo fxuuhqf| dw h{fkdqjh udwh 7 U^ 1 Edqnv xvh wkhvh ixqgv wr pdnh ordqv wkdw duh uhsdlg lq xqlwv ri wkh grphvwlf fxuuhqf| dw wkh qrqlqgh{hg jurvv lqwhuhvw udwh - @ 1 Wr eh lq wkh edqnlqj exvlqhvv uhtxluhv dq lqyhvwphqw ri g xqlwv ri rxwsxw dw wkh ehjlqqlqj ri hyhu| shulrg1 Li wkh edqn grhv qrw h{lw wkh lqgxvwu| e| wkh hqg ri wkh shulrg lw uhfrxsv EÅB g xqlwv ri lwv fdslwdo lqyhvwphqw1 Khuh B uhsuhvhqwv wkh udwh ri ghsuhfldwlrq rq fdslwdo Li wkh edqn grhv h{lw/ lw fdqqrw uhwulhyh dq| ri lwv lqlwldo fdslwdo lqyhvwphqw1 Vlqfh fdslwdo fdq eh lqyhvwhg lq zruog fdslwdo pdunhwv/ wkh shu shulrg rssruwxqlw| frvw ri hqwhulqj wkh edqnlqj lqgxvwu| lv -g1 Khuh - lv wkh jurvv lqwhuhvw udwh rq groodu0ghqrplqdwhg ordqv lq wkh zruog fdslwdo pdunhw Zh devwudfw iurp wkh uroh ri edqnv dv surgxfhuv ri lqirupdwlrq dqg irfxv gluhfwo| rq wkh uhdo frvwv ri pdnlqj ordqv1^45 E| dvvxpswlrq/ wkh uhdo frvw ri ohqglqj u xqlwv ri rxwsxw lv Eu 1 Wkh ixqfwlrq Eu lv srvlwlyh/ wzlfh frqwlqxrxvo| gl huhqwldeoh/ lqfuhdvlqj dqg vwulfwo| frqyh{ iru u : f/ vr wkdw wkh pdujlqdo frvw ri pdnlqj ordqv lv lqfuhdvlqj1 Wkh edqn*v hqg0ri shulrg groodu0ghqrplqdwhg sur wv iurp ohqglqj dfwlylwlhv/ lqfoxvlyh ri hqg0ri0shulrg fdslwdo/ duh=
ZuEuc %( 7 ' -
@ 7 U (^) u 7 n EÅ^ ^ B g^ ^ Eu ^ ^ -
KEuc % u +615,
Khuh 7 ghqrwhv wkh h{fkdqjh udwh wkdw suhydlov dw wkh hqg ri wkh shulrg1 Lq dgglwlrq/ % ghqrwhv wkh qxpehu ri xqlwv ri orfdo fxuuhqf| vrog e| wkh edqn lq wkh iruzdug pdunhw1 - K^ lv zulwwhq dv d ixqfwlrq ri u dqg % ehfdxvh edqnv idfh d frpshwlwlyho| ghwhuplqhg vfkhgxoh ri eruurzlqj udwhv wkdw ghshqgv rq wkhlu fkrlfhv iru u dqg %1 Wklv hperglhv rxu dvvxpswlrq wkdw iruhljq fuhglwruv fdq revhuyh edqnv* sruwirolrv Edqnv fdq khgjh h{fkdqjh udwh ulvn e| hqwhulqj lqwr iruzdug frqwudfwv1^46 Ohw 8 ghqrwh wkh rqh0shulrg iruzdug h{fkdqjh udwh gh qhg dv xqlwv ri orfdo fxuuhqf| shu groodu1 Wr vlpsoli| zh devwudfw iurp wudqvdfwlrqv frvwv dqg dvvxph wkdw wkhvh frqwudfwv duh sulfhg lq d ulvn qhxwudo pdqqhu/ vr wkdw=^47 Å 8
' EÅ R Å
7 U^
n R Å 7 (^
Groodu0ghqrplqdwhg sur wv iurp khgjlqj dfwlylwlhv duh=
ZM^ E%( 7 ' %
Å
8 ^
Å
(^45) Iru d vlplodu prgho vhh Fkdul/ Fkulvwldqr dqg Hlfkhqedxp +4<<9, dqg Hgzdugv dqg Yhjk +4<<:,1 Iru dowhuqdwlyh prghov ri wkh uroh ri edqnv lq fxuuhqf| fulvhv vhh Dnhuori dqg Urphu +4<<6,/ Fdedoohur dqg Nulvkqdpxuwk| +4<<;,/ dqg Fkdqj dqg Yhodvfr +4<<<,1 46 Vhh Doextxhutxh +4<<<, iru d jhqhudo glvfxvvlrq ri rswlpdo khgjlqj vwudwhjlhv lq wkh suhvhqfh ri wudqv dfwlrqv frvwv/ lqfoxglqj wkh fkrlfh ehwzhhq iruzdugv dqg rswlrqv dv khgjlqj lqvwuxphqwv1 47 Qrwh wkdw vlqfh S (^) w @ 4/ wklv htxdwlrq lpsolhv wkdw wkh h{shfwhg uhdo uhwxuq iurp d iruzdug frqwudfw lv }hur1 Wklv dyrlgv Vlhjho*v +4<:5, sdudgr{/ zklfk dulvhv zkhq wkh h{shfwhg qrplqdo uhwxuq wr iruzdug frqwudfwv lv dvvxphg wr eh }hur
43
Edqnv* Eruurzlqj Udwh Devhqw Ordq Jxdudqwhhv
E| dvvxpswlrq/ iruhljq ohqghuv duh ulvn qhxwudo1 Khqfh wkh| zloo vhw d vfkhgxoh ri lqwhuhvw udwhv/ - KEuc % / zlwk wkh surshuw| wkdw wkh h{shfwhg uhwxuq wr wkhlu lqyhvwphqw htxdov - iru doo Euc % 1 Uhfdoo wkdw edqnv ghidxow zkhqhyhu wkhlu wrwdo sur wv/ ZEuc %( 7 / duh qhjdwlyh Lw lv frqyhqlhqw wr gh qh dq lqglfdwru ixqfwlrq UdZEuc %( 7 o zklfk wdnhv wkh ydoxh Å zkhq ZEuc %( 7 f dqg wkh ydoxh }hur rwkhuzlvh1 Wkh - KEuc % vfkhgxoh lv ghwhuplqhg e| wkh frqglwlrq=
-u ' .i EÅ UdZE( 7 o -KE u n UdZE( 7 o
T - E( 7 E( 7
' - KE u n .i UdZE( 7 o
T - E( 7 ^ E( 7 - KE u
c +6143,
zkhuh. ghqrwhv wkh h{shfwdwlrq zlwk uhvshfw wr 7 1 Wr xqghuvwdqg wkh suhylrxv htxdwlrq qrwh wkdw zkhqhyhu wkh edqn grhv qrw ghidxow +UdZE( 7 o ' Å, lw uhsd|v iruhljq fuhglwruv
- KE u1 Li wkh edqn grhv ghidxow +UdZE( 7 o ' f,/ wkhq iruhljq fuhglwruv uhfhlyh wkh edqnv uhvlgxdo ydoxh qhw ri edqnuxswf| frvwv/ T - E( 7 ^ E( 7 1 Wr looxvwudwh krz wklv frqglwlrq zrunv/ vxssrvh wkdw Euc % lv vxfk wkdw d edqn lv ixoo| khgjhg/ l1h1 lwv sur wv duh dozd|v qrq0qhjdwlyh dqg UdZEuc %( 7 o ' f iru doo 7 1 Wkhq +6143, lpsolhv wkdw - KEuc % ' - 1 Lq frqwudvw/ vxssrvh wkdw Euc % lv vxfk wkdw wkh edqnv sur wv duh qhjdwlyh zkhq 7 ' 7 (^ dqg qrq0qhjdwlyh zkhq 7 ' 7 U^ 1 Lq wklv fdvh wkh edqn ghidxowv zkhq d ghydoxdwlrq rffxuv/ vr wkdw - KEuc % lv jlyhq e|=
-u ' EÅ R -KEuc % u n R
T - Euc %( 7 ( Euc %( 7 (
Edqnv* Eruurzlqj Udwh Zlwk Ordq Jxdudqwhhv
Vxssrvh wkdw wkhuh duh jryhuqphqw jxdudqwhhv zklfk dsso| rqo| wr wkh ghydoxdwlrq vwdwh Lq wklv fdvh wkh - KEuc % vfkhgxoh lv ghwhuplqhg e| wkh frqglwlrq=
-u ' - KE u n EÅ R UdZE( 7 U^ o
T - E( 7 U^ E( 7 U^ - KE u
Wklv frqglwlrq lpsolhv wkdw - KEuc % ' - iru doo Euc % vxfk wkdw sur wv lq vwdwh 7 ' 7 U^ duh qrq0qhjdwlyh1 Lw grhv qrw pdwwhu li wkh edqn ghidxowv lq vwdwh 7 ' 7 (/ ehfdxvh lq wklv fdvh wkh jryhuqphqw sd|v iruhljq fuhglwruv - KEuc % u 1 Zh frqfoxgh wklv vhfwlrq zlwk d sursrvlwlrq wkdw surylghv xv zlwk d frqyhqlhqw uhsuhvhq wdwlrq ri wkh up*v remhfwlyh ixqfwlrq
Sursrvlwlrq 6141 Wkh remhfwlyh ixqfwlrq ri wkh uhsuhvhqwdwlyh edqn/ +619,/ fdq eh uhzulwwhq dv
T Euc % ' T (^) e- Eu Euc % c +6146,
zkhuh
T (^) e- Eu ' - @^7
U 8 u Eu n EÅ B gc +6147,
dqg Euc % lv wkh edqn*v h{shfwhg frvw ri eruurzlqj1 Lw wdnhv wkh irup
Euc % ' .i4?d-KEuc % uc T - Euc %( 7 j +6148,
Khuh. ghqrwhv wkh h{shfwdwlrq zlwk uhvshfw wr 71
Surri= Vhh Dsshqgl{ Dffruglqj wr +6146,/ wkh h{shfwhg ydoxh ri d edqnv sur wv fdq eh ghfrpsrvhg lqwr wzr sduwv/ T (^) e- Eu dqg Euc % 1 Wr xqghuvwdqg wkh uvw sduw/ qrwh wkdw vlqfh iruzdug pdunhwv duh dfwxduldoo| idlu/ .EÅ7 ' Å8 1 Vr T (^) e- Eu lv wkh edqnv h{shfwhg uhyhqxh iurp ordqv plqxv wkh frvwv ri surgxflqj wkrvh ordqv/ lqfoxvlyh ri hqg ri shulrg fdslwdo1 T (^) e- Eu grhv qrw ghshqg rq % vlqfh wkh h{shfwhg sur w iurp khgjlqj lv }hur1 Wkh whup Euc % htxdov wkh edqnv h{shfwhg frvw ri eruurzlqj1 Wr vhh wklv/ qrwh wkdw wkh edqn zloo hlwkhu uhsd| lwv fuhglwruv - KE u ru T - E( 7 ghshqglqj rq zkhwkhu ru qrw lw ghfoduhv edqnuxswf|1 Vr E lv mxvw wkh suredelolw| ri qrw ghidxowlqj wlphv - KE u soxv wkh suredelolw| ri ghidxowlqj wlphv wkh uhvlgxdo dvvhwv ri wkh edqn/ T - E( 7 1 Htxdwlrq +6146, lv xvhixo ehfdxvh T (^) e- Eu grhv qrw ghshqg rq % 1 Wklv phdqv zh fdq jdlq lqwxlwlrq derxw edqnv rswlpdo khgjlqj vwudwhjlhv e| frqvlghulqj wkh ydoxh ri % wkdw plqlpl}hv wkh h{shfwhg frvw ri eruurzlqj/ Euc % / iru d jlyhq ordq vl}h u 1
71 Rswlpdo Edqn Khgjlqj zkhq Ordqv duh Suhghwhuplqhg
Wr krqh rxu lqwxlwlrq derxw wkh h hfwv ri jryhuqphqw jxdudqwhhv zh uvw frqvlghu wkh fdvh zkhuh wkh dprxqw ri uhdo ohqglqj/ u/ lv h{rjhqrxvo| {hg1 Jlyhq wklv dvvxpswlrq/ d edqnv rqo| ghflvlrq lv krz pxfk h{fkdqjh udwh ulvn wr khgjh1 Lq wklv vhfwlrq zh suryh wzr sursr vlwlrqv= +l, lw lv rswlpdo iru d edqn wr ixoo| khgjh h{fkdqjh udwh ulvn zkhq wkhuh duh qr jryhuqphqw jxdudqwhhv> dqg +ll, lw lv qrw rswlpdo iru d edqn wr khgjh h{fkdqjh udwh ulvn lq wkh suhvhqfh ri jryhuqphqw jxdudqwhhv1 Wkhvh sursrvlwlrqv pluuru wkh fodvvlf uhvxowv lq Nduhnhq dqg Zdoodfh +4<:;, rq wkh lpsdfw ri ghsrvlw lqvxudqfh rq edqnv rswlpdo sruwirolr ghflvlrqv1 Zkloh wkh qdwxuh ri jryhuqphqw jxdudqwhhv lv gl huhqw/ erwk rxu uhvxowv dqg wkrvh
46
Zh qrz fkdudfwhul}h wkh rswlpdo khgjlqj vwudwhj| lq dq hfrqrp| zlwk jryhuqphqw jxdu dqwhhv
Sursrvlwlrq 7151 Frqvlghu dq hfrqrp| zlwk jryhuqphqw jxdudqwhhv dqg u {hg1 Vxssrvh wkdw= T (^) e- Eu : -u/ f b Å/ f / EÅ b -u dqg htxdwlrq +61<, lv vdwlv hg1 Wkhq ixoo khgjlqj lv qrw rswlpdo1 Wkh edqn*v rswlpdo vwudwhj| lv wr vhw % wr lwv orzhvw shuplvvleoh erxqg/ jlyhq e| +61<,/ dqg ghidxow rq lwv ghew zkhq d ghydoxdwlrq rffxuv
Surri= Vhh Dsshqgl{ Wr vhh wkh lqwxlwlrq ehklqg wklv uhvxow/ zh djdlq frqvlghu wkh fdvh lq zklfk d edqn frpsduhv ghidxowlqj lq wkh ghydoxdwlrq vwdwh wr ehlqj ixoo| khgjhg1 Li d edqn ghidxowv rqo| lq wkh ghydoxdwlrq vwdwh/ wkhq htxdwlrqv +61;,/ +6148, dqg wkh idfw wkdw - KEuc % ' - lpso| wkdw wkh edqn*v h{shfwhg frvw ri eruurzlqj lv=
Euc % ' EÅ R -u n R ^ Euc %( 7 ( ' EÅ R -u n Rd/ n bT - Euc %( 7 ( o 1
Wr plqlpl}h Euc % frqglwlrqdo rq wklv vwudwhj|/ d edqn zloo fkrrvh % wr plqlpl}h T - Euc %( 7 ( vxemhfw wr frqglwlrq +61<,1 Wklv pd| lqyroyh vhwwlqj % wr eh d qhjdwlyh qxpehu/ l1h1 wkh edqn pdjql hv lwv h{fkdqjh udwh h{srvxuh e| vhoolqj grooduv iruzdug1 Li wkh edqn lv jrlqj wr jr eurnh lw zdqwv wr plqlpl}h wkh ydoxh ri dvvhwv wkdw lwv fuhglwruv fdq vhl}h1 Iruzdug frqwudfwv wkdw orvh prqh| lq wkh ghydoxdwlrq vwdwh khos wkh edqn gr wklv1 Wkh orzhvw ydoxh ri Euc % wkdw fdq eh dfklhyhg xqghu wklv vwudwhj| lv=
U^ Eu (^) t%ZEu( 7 U (^) 4?DfcZEu( 7 ( (^) f Euc % ' EÅ R -u n R (^) Å / b
Dv ehiruh wkh h{shfwhg frvw ri eruurzlqj li wkh edqn fkrrvhv % vr wkdw lw qhyhu ghidxowv lv=
M^ Eu ' -u
Vxssrvh wkdw wkh plqlpxp frvwv ri edqnuxswf| duh orzhu wkdq wkh frvwv ri uhsd|lqj wkh ordqv/ l1h / Å b -u +714,
Wkhq U^ Eu lv ohvv wkdq M^ Eu dqg lw lv rswlpdo wr ghidxow zkhq d ghydoxdwlrq rffxuv Zh frqfoxgh wkdw zlwk jryhuqphqw jxdudqwhhv/ edqnv jr edqnuxsw lq wkh ghydoxdwlrq vwdwh1 Wkh orzhvw shuplvvleoh ydoxh ri % zloo/ lq vrph fdvhv/ eh qhjdwlyh/ vr wkdw edqnv dgrsw d khgjlqj vwudwhj| wkdw lqyroyhv vhoolqj grooduv iruzdug1 Zkloh wklv pljkw eh fkdudfwhul}hg dv uhfnohvv vshfxodwlrq/ lw lv vlpso| wkh rswlpdo uhvsrqvh ri edqnv wr jryhuqphqw jxdudqwhhv1^49 (^49) Lqwhuhvwlqjo|/ Nuhjho +4<<;, uhsruwv wkdw XV edqnv pdgh d sur w ri urxjko| '719 eloolrq sur wv rq Zrq ghulydwlyh frqwudfwv lq 4<<:
48
Suredelolvwlf Jryhuqphqw Jxdudqwhhv dqg Iudfwlrqdo Edlorxwv Zh fdq prgli| rxu dqdo|vlv wr dffrpprgdwh wkh fdvh lq zklfk djhqwv h{shfw wkdw/ zlwk suredelolw| k/ wkh jryhuqphqw zloo uhsd| edqn*v iruhljq fuhglwruv lq wkh hyhqw ri d ghydoxd wlrq14:^ Wr frqvhuyh rq vsdfh zh rqo| frqvlghu wkh fdvh zkhuh edqnv frqwhpsodwh ghidxowlqj zkhq 7 ' 7 (1 Dv lq wkh fdvh ri fhuwdlq jryhuqphqw jxdudqwhhv/ wkh h{shfwhg frvw ri eruurz lqj iru d ixoo| khgjhg edqn lv -u1 Li wkh edqn lv qrw ixoo| khgjhg dqg ghidxowv zkhq 7 ' 7 (c lwv h{shfwhg frvw ri eruurzlqj lv= EÅ R -KE u n RT - E( 7 ( 1 Wkh frqglwlrq hqvxulqj wkdw lqwhuqdwlrqdo fuhglwruv uhfhlyh h{shfwhg uhwxuqv ri -u lv=
-u ' EÅ R -KE u n Rk-KE u 1 +715,
Khuh zh duh dvvxplqj wkdw wkh h{shfwhg ydoxh ri wkh jryhuqphqwv jxdudqwhh frqglwlrqdo rq d ghydoxdwlrq/ k-KE u/ lv dw ohdvw dv odujh dv zkdw wkh fuhglwru frxog rwkhuzlvh uhfryhu lq edqnuxswf| surfhhglqjv/ T - E( 7 ( ^ E( 7 ( 1 Qrwlfh wkdw zkhq k ' Å zh rewdlq wkh fdvh ri ixoo jxdudqwhhv xqghuo|lqj Sursrvlwlrq 7151 Zkhq k ' f/ zh rewdlq wkh fdvh ri qr jxdudqwhhv ri Sursrvlwlrq 7141 Htxdwlrq +715, lpsolhv wkdw wkh h{shfwhg frvw ri eruurzlqj fdq eh uhzulwwhq dv= EÅ R -udEÅ R n Rko n RT - E( 7 ( 1 Wkh plqlpxp h{shfwhg frvw ri eruurzlqj lv rewdlqhg e| fkrrvlqj % wr plqlpl}h wkh uhvlgxdo ydoxh ri wkh edqn T - E( 7 ( 1 Frqglwlrq +61<, lpsolhv wkdw wkh plqlpxp ydoxh ri T - E( 7 ( lv htxdo wr /EÅb 1 Wkxv wkh h{shfwhg frvw ri eruurzlqj iru d edqn frqwhpsodwlqj ghidxow lq wkh ghydoxdwlrq vwdwh lv= EÅR -udEÅR nRkonR/*EÅb 1 Frpsdulqj wklv wr -u/ wkh h{shfwhg frvw ri eruurzlqj ri d ixoo| khgjhg edqn/ zh frqfoxgh wkdw ixoo khgjlqj lv qrw rswlpdo dv orqj dv=
f / k EÅ R n RkEÅ^ ^ b -u^1 +716,
Zkhq k ' f/ fruuhvsrqglqj wr wkh qr0jxdudqwhh fdvh/ wkh suhylrxv frqglwlrq fdqqrw eh ixo oohg1 Vlqfh wkh uljkw kdqg vlgh ri +716, lv lqfuhdvlqj lq k/ vr wrr lv wkh fodvv ri hfrqrplhv iru zklfk ixoo khgjlqj lv qrw rswlpdo1 Zkhq k ' Å/ vr wkhuh lv qr xqfhuwdlqw| derxw wkh jryhuqphqw edlorxw/ +716, uhgxfhv wr wkh uhjxodulw| frqglwlrq lq Sursrvlwlrq 7151 Lq vxp/ doorzlqj iru suredelolvwlf jryhuqphqw jxdudqwhhv grhv qrw fkdqjh rxu edvlf phv vdjh= jxdudqwhhv uhgxfh edqnv* lqfhqwlyhv wr khgjh h{fkdqjh udwh ulvn1 Wkh pruh olnho| wkrvh jxdudqwhhv duh/ wkh odujhu lv wkh fodvv ri hfrqrplhv iru zklfk edqnv zloo qg lw rswlpdo qrw wrr ixoo| khgjh h{fkdqjh udwh ulvn14; 4: (^) Zh wkdqn Sdeor Qhxph|hu iru wkhvh uhvxowv 4; (^) Jlyhq rxu dvvxpswlrqv/ d suredelolvwlf jxdudqwhh ri doo edqn ordqv dqg d vxuh jxdudqwhh ri d iudfwlrq ri edqn ordqv kdyh lghqwlfdo lpsolfdwlrqv1 Lq sduwlfxodu/ vxssrvh wkdw wkh suredelolw| ri d edlorxw zkhq V @ VG lv 4 exw wkh jryhuqphqw rqo| jxdudqwhhv wkdw iruhljqhuv uhfryhu dw ohdvw Ue+,O1 Wkhq lw lv vwudljkwiruzdug wr vkrz wkdw/ dv deryh/ ixoo khgjlqj lv qrw rswlpdo dv orqj dv +716, krogv
49
%? 5 df/ fo/ zkhuh
f ' 8 d- n ^ Eu? o u? (^) -g 8 ^ 7 (
c +814,
dqg
f ' 8 d- n ^ Eu? o u? n (^) -g 7 U^ ^8
Vhfrqg/ wkh htxloleulxp ydoxh ri - @^ lv jlyhq e|=
- @? ' (^78) U d- n ^ Eu? o +816,
Wklug/ wkh htxloleulxp ohyho ri ohqglqj/ u?/ lv jlyhq e| wkh xqltxh vroxwlrq wr=
Eu? u? Eu? n EÅ B g ' -g +817,
Irxuwk/ wkh htxloleulxp ydoxh ri - KEu?c %? ' - 1 Iliwk/ wkh qxpehu ri edqnv/ / lv ghwhu plqhg e| ' (E-@ *u 1
Surri= Vhh Dsshqgl{ Wkh rswlpdo khgjlqj ghflvlrqv wkdw zh fkdudfwhul}hg lq vhfwlrq 7/ zkhuh u zdv suhgh whuplqhg/ frqwlqxh wr krog zkhq edqnv fkrrvh u dqg % vlpxowdqhrxvo|= lq wkh devhqfh ri jryhuqphqw jxdudqwhhv lw lv rswlpdo iru edqnv wr ixoo| khgjh wkhlu h{fkdqjh udwh ulvn1 Htxd wlrqv +814, dqg +815, fkdudfwhul}h wkh udqjh ri % ydoxhv frqvlvwhqw zlwk ixoo khgjlqj Htxdwlrq +816, iroorzv iurp wkh edqnv uvw rughu frqglwlrq iru u 1 Vlqfh edqnv qhyhu ghidxow/ wkhlu eruurzlqj frvwv duh htxdo wr - 1 Htxdwlrq +816, lpsolhv wkdw wkh h{shfwhg uhwxuq wr d edqnv ordqv/ phdvxuhg lq grooduv/ - @? 7 U^ *8 / htxdov eruurzlqj frvwv +-, soxv wkh pdujlqdo frvw ri pdnlqj ordqv/ + ^ Eu ,1 Htxdwlrq +817, lv dv lpsolfdwlrq ri iuhh hqwu| lqwr wkh edqnlqj lqgxvwu|1 Uhsodflqj - @^ lq +619, zlwk - @?/ zh qg wkdw wkh pd{lpdo ydoxh ri d edqn lv Eu u Eu nEÅ B g1 E| iuhh hqwu|/ wklv ydoxh pxvw htxdo wkh frvw ri rshudwlqj d edqn/ -g 1 Zh qrz fkdudfwhul}h wkh htxloleulxp ri dq hfrqrp| zlwk jryhuqphqw jxdudqwhhv
Sursrvlwlrq 8151 Vxssrvh wkdw EÅB gEf : f dqg / EÅb -u?1 Wkh htxloleulxp ri dq hfrqrp| zlwk jryhuqphqw jxdudqwhhv lv xqltxh dqg kdv wkh iroorzlqj surshuwlhv1 Iluvw/ wkh htxloleulxp ohyho ri %/ %}/ lv wkh plqlpxp shuplvvleoh ydoxh frqvlvwhqw zlwk +61<, iru 7 ' 7 (1 Vhfrqg/ wkh htxloleulxp ydoxh ri - @^ lv
- @} ' (^78) U dEÅ R - n Eu} o +818,
Wklug/ wkh htxloleulxp ohyho ri ohqglqj/ u}/ lv wkh xqltxh vroxwlrq wr
Eu} u} Eu} n EÅ B g R (^) Å / b ' -g +819,
Irxuwk/ wkh htxloleulxp ydoxh ri - KEu} c %} ' - 1 Iliwk/ wkh qxpehu ri edqnv/ / lv ghwhu plqhg e| ' (E-@ *u 1
Surri= Vhh Dsshqgl{ Wkh rswlpdo khgjlqj ghflvlrq fkdudfwhul}hg lq vhfwlrq 7 frqwlqxhv wr krog= edqnv fkrrvh wkh orzhvw ydoxh ri % frqvlvwhqw zlwk +61<, dqg ghidxow zkhq d ghydoxdwlrq rffxuv1 Htxdwlrq +818, uhvxowv iurp wkh edqnv uvw rughu frqglwlrq iru u1 Vlqfh edqnv ghidxow lq wkh ghydoxdwlrq vwdwh/ wkhlu eruurzlqj frvwv duh htxdo wr EÅ R -1 Htxdwlrq +816, lpsolhv wkdw wkh h{shfwhg uhwxuq wr d edqnv ordqv/ phdvxuhg lq grooduv/ - @} 7 U^ *8 / htxdov wkh vxp ri wkh wkhlu pdujlqdo eruurzlqj frvwv +EÅ R -, dqg wkh pdujlqdo frvw ri pdnlqj ordqv/ ^ Eu - @? 7 U^ *8 1 Ilqdoo|/ +819, iroorzv iurp iuhh hqwu| lqwr wkh edqnlqj lqgxvwu| Zh frqfoxgh wklv vhfwlrq e| dvnlqj wkh txhvwlrq= li jryhuqphqw jxdudqwhhv ohdg wr lq fuhdvhg ulvn lq wkh edqnlqj v|vwhp/ zk| duh wkh| vr suhydohqwB Wkh iroorzlqj fruroodu| vxjjhvwv rqh srvvleoh dqvzhu= jryhuqphqw jxdudqwhhv orzhu - @^ dqg ohdg wr d ohqglqj errp Odwhu/ lq vhfwlrq ;/ zkhuh zh hpehg rxu prgho ri edqnlqj lqwr d jhqhudo htxloleulxp hqylurq phqw/ zh vkrz wkdw wkh idoo lq - @^ jhqhudwhg e| wkh jxdudqwhhv ohdgv wr d errp lq hfrqrplf dfwlylw| dqg wr d ulvh lq uhdo zdjhv
Fruroodu| 8161 Iru vx!flhqwo| vpdoo / wkh lqwhuhvw udwh wkdw edqnv fkdujh upv lv orzhu lq dq hfrqrp| zlwk jxdudqwhhv wkdq lq rqh zlwkrxw jxdudqwhhv/ l1h1 - }@ - @?1 Lq dgglwlrq/ wrwdo edqn ohqglqj lv kljkhu lq wkh suhvhqfh ri jxdudqwhhv
Surri= Htxdwlrqv +816, dqg +818, lpso| wkdw=
- @} - @? ' 8 7 U^ dR- n Eu} (^) Eu? o
Htxdwlrqv +819, dqg +817, lpso| wkdw *4/<f u} ' u?1 Wklv lpsolhv wkdw *4/<f - }@ - @? 1 Wkh wrwdo ohyho ri edqn ohqglqj/ u/ lv kljkhu xqghu jxdudqwhhv ehfdxvh wkh ghpdqg iru ordqv/ u ' (E-@ / lv grzqzdug vorslqj Wkh suhylrxv uhvxow grhv qrw lpso| wkdw lqwurgxflqj jxdudqwhhv lqfuhdvhv wkh h{shfwhg xwlolw| ri wkh uhsuhvhqwdwlyh djhqw1 Krzhyhu/ lw vxjjhvwv wkdw jxdudqwhhv jhqhudwh vkruw whup ehqh wv wkdw pd| eh gl!fxow iru d vkruw0vljkwhg srolwlfldqv wr ljqruh
