*ྐ༏٤ؓӫ༯ವሧ֥ჿඏྐݼѰᒮଆ ౕ࿐ ᆽđӵ๓đ້ ఼ čն৵۽ն࿐ܵ࿐ჽ ࣁವ۽ӱ࣮ა࣮ܵᇏྏđն৵ 116024 Ď ᅋေğ ࣮ਔྐ༏٤ؓӫ༯ఒြವሧथҦ໙ีđࡹ৫ਔჿඏྐݼѰᒮଆđབྷ༥ٳ༅ਔఒြࣜႏᆀބሧᆀࡗҐ౼؋൪ൔ֥čmyopicĎކቔٚൔބר৫Ӊ௹ކቔކჿ֥ਆᇕ౦ঃ. ᄝವሧݖӱᇏđࣜႏᆀ֥ሱԔሧࣁб২ࠣཛଢ֥൬ၭੱ֩ऎႵԮ־ྐݼ֥ቔႨ. ሧᆀॖ๙ݖܴҳࠇყ௹ᆃུྐݼหᆘ֥э߄ؓࣜႏᆀ֥֣֡ڄགࠣཟ࿊ᄴӱ؇ࣉྛҩ. ٳ༅іૼ: ࣜႏᆀࡼఃሱԔሧࣁб২ބ֣֡ڄག༢ඔЌӻᄝൡ֥֒ٓຶଽđॖၛః؋௹ሧࣜႏ֥ቋնིႨЌӻ҂э. ר৫Ӊ௹ކቔކჿđࣜႏᆀႵᄹնః֣֡ڄགӱ؇֥ࠗৣđࣜႏᆀЌӻࢠ֥ۚཟ࿊ᄴބ֣֡ڄགӱ؇đᄵࡼࠞ҂০Ⴟఃؓఒြ֥ࣜႏ. ܱՍğ ٤ؓӫྐ༏Ġ֣֡ڄགĠཟ࿊ᄴĠĠѰᒮ ᇏٳোݼğF830 ໓ངѓ്ğA Models of Constrained Signaling Game for Dynamic Investment –financing Strategy under Asymmetric Information Conditions QIN Xue-zhi, SUN Cheng-ting, WEI Qiang čResearch Center of Financial Engineering & Management, School of Management, Dalian University of Technology, Dalian, 116024,ChinaĎ Abstractğ In this paper, we study firm’s dynamic investment and financing problem and establish corresponding constrained signaling game models. Two cases are analyzed in details. One is the case in which the firm’s manager and the investor are both myopic in cooperation aspect, and the other is the case in which the firm’s manager and the investor are going to cooperate with each other for a longer time. The analysis shows that in the dynamic investment and financing process, the ratio of manager’s investment amount to the total investment amount and the investment profit ratio have the function of transferring the manager’s and the project’s signals of what and how they should be. The investor can infer the degree of the manager’s adverse selection and moral hazard by analyzing these signals. If the manager places the proportion of his investment amount to the total investment amount and his moral hazard degree within an appropriate scope, he can obtain his maximum operation utility within a short period and make it unchanged if the change of the proportion and the degree of his moral hazard were held in an appropriate range. However, if the investors wanted to cooperative with the manager for a longer period, there is an incentive for the manager to enhance his degree of moral hazard. Of course, the higher degree of adverse selection and moral hazard of the manager, the more disadvantage to the dynamic investment process in the long run. Key words: asymmetric information; moral hazard; adverse selection; dynamics; game 0 ႄ ఒြࣜႏᆀა၂Ϯሧᆀؓఒြཛଢࣜႏބؿᅚሑঃ֩ྐ༏֥ਔࢳӱ؇൞٤ؓӫ֥. ၂Ϯطđ *ݓࡅሱಖ॓࿐ࠎࣁሧᇹčĎ 1
__中__国__科__技__论__文__在__线_d_u_._c_n__၂ٚ૫đఒြࣜႏᆀбሧᆀؓཛଢ֥൧ӆమ৯aყ௹൬ၭੱࠣఃѯੱ֩ሑঃ۷ਔࢳĠਸ਼၂ٚ૫đ[1]ᄝಌكࡓ่֥ࡱ༯đఒြࣜႏᆀॖି߶٤مᅝႨࠇཨٮܢתಃၭ֩. భᆀॖି֝ᇁ෮໌֥ཟ࿊ᄴ[ 2 ]໙ีđбೂđູਔವሧथҦؓఃႵ০đܣၩॱնӁ֥൧ӆమ৯ࠇളӁඌඣđࠇܣၩॱնყ[1]௹൬ၭੱ֩Ġުᆀᆰࢤݝਔܢת֥ಃၭđ൞ׅ֥֣֡ڄག໙ี. ᄝ؟ࢨ؍ವሧݖӱᇏđሧᆀ[ 1, 3, 4]ॖၛՖၛສ֥ཛଢࣜႏሑঃ֩౦ঃᇏҩࣜႏᆀ֥ཟ࿊ᄴބ֣֡ڄགӱ؇. ఒြࣜႏᆀሱԔሧࣁᅝሹሧࣁ֥б২aཛଢ֥ሹሧحࠣཛଢ֥൬ၭੱ֩नॖቔູሧᆀ༯၂ࢨ؍ࣉྛሧथҦൈ؎ࣜႏᆀཟ࿊ᄴބ֣֡ڄགӱ؇֥ྐݼ. [1]Mukesh B.֩ದ(1998)ٳ༅ਔֆᇛ௹༯ఒြࣜႏᆀބሧᆀࡗ֥ྐݼѰᒮ౦ঃđѩؓᆃᇕ౦ঃ֥ཌྷܱ࣮໓ངࣉྛਔሸඍ. Ч໓ॉ੮؟ࢨ؍֥ྐݼѰᒮ໙ีđൈؓࣜႏᆀބሧᆀࡗҐ౼؋൪ൔ֥čmyopicĎކቔٚൔބሙСӉ௹ކቔ֥ਆᇕ౦ঃࣉྛਔษંđࡼMukesh B.֩ದ(1998)֥ཌྷܱࢲݔཟభࣉਔ၂ն҄. ᄝؓ؟ࢨ؍ವሧྐݼѰᒮଆ֥ࡌഡ่ࡱࣉྛབྷ༥ख़߂֥ࠎԤഈđЧ໓ҐႨਔᝀၳႿMusesh B.֩ದ෮Ⴈ֥࣮ٚمđ౼֤ਔ၂ུᆰܴႵ౿֥ࢲં. 1 ࠎЧࡌഡ 1)ࡌഡఒြࣜႏᆀሙСᄝൈׄt=0,τ,...,(m−1)τ(m≥1)ؓଖཛଢࣉྛሧđτູᆞ֥ӈඔđԢሱԔሧࣁຓđೂႵсေđࣜႏᆀՖఃሧᆀ(ᄝ҂Ӂളఆၬ่֥ࡱ༯đ༯໓ࣇӫሧᆀ) ԩವሧđሧᆀ๙ݖॉҳཛଢ֥۲ཛᆷѓđೂളӁඌඣaყ௹൬ၭੱࠣఃѯੱaࣜႏᆀ֥ྐუ֩ၛުđಪູ۲ཛᆷѓડቀሱ֥࠭ሧေđᄵᄝt=0ൈೆ၂҆ٳሧࣁđڎᄵđ҂ሧđࡌഡၛު҂ᄜሧھཛଢĠࣜႏᆀބሧᆀ൙༵ჿקğt=0ൈሧᆀሧđૌॖၛᄝൈׄt = τ,...,(m−1)τԩࣉྛሧሧࣁטᆜđࠧචٚनॖሔࡆሧሧࣁđ္ॖԎԛ҆ٳࠇಆ҆ሧሧࣁđᆜ۱ሧݖӱᇀmτൈࢲඏ. ሧᆀ۴ऌܴҳ֥֞ཛଢభࠫ۱ࢨ؍֥ࣜႏሑঃࠣࣜႏᆀ֥ྐუ֩౦ঃުಒקᄝ۲ൈׄiτ(i=1,...m−1)֥ሧҦĠ 2) ࡌഡᄝൈࡗ؍[(i−1)τ,iτ)ଽࣜႏᆀሱԔሧሧࣁᅝሹሧሧࣁ֥б২ູβ(0≤β≤1)đھࢨii؍ሹሧحູ s(i=1,...,m)Ġβas(i=1,...,m)Ⴎࣜႏᆀაሧᆀ๙ݖѰᒮӁളĠ iii[1] 3) ࡌഡᄝൈࡗ؍[(i−1)τ,iτ)ଽࣜႏᆀ֥֣֡ڄག༢ඔູαđࠧ α(0≤α≤1đi=1,...,m)іൕiiiھࢨ؍ఒြࣜႏᆀ٤مᅝႨࠇཨٮܢתಃၭ֥б২đఃݣၬᄝ5)ᇏඪૼĠ 4)ᄝൈࡗ؍[(i−1)τ,iτ)ଽđཛଢ֥ളӁඌඣॖႨ႔০ح R=f(s)(u+ε)τ (i=1,...,m) (1) iiiii૭ඍđఃᇏf(s)іൕሧحູsൈ֥Ӂԛđf(0)=0đf(⋅)ູֆטᄹࡆχݦඔđu+εູֆ໊ൈࡗiiiiiii2֥႔০ੱč၂Ϯᆷ၂୍֥႔০ੱĎđఃᇏεູડቀनᆴູ0aٚҵູ σ֥ᆞٳ֥҃ෛࠏэਈĠ i0i 5) ᄝൈࡗ؍[(i−1)τ,iτ)ଽđࣜႏᆀՖఃϧ֣ྛູᇏ٤مᅝႨࠇཨٮ֥ܢתಃၭູ αR=αf(s)(u+ε)τ (i=1,...,m) (2) iiiiiii 6) ᄝൈࡗ؍[(i−1)τ,iτ)ଽđࣜႏᆀ֥ൌ࠽൬ၭູ Y=αR+β(1−α)R=[α+β(1−α)]R (i=1,...,m) (3) iiiiiiiiiiఃᇏđβ(1−α)Rູࣜႏᆀ֥ܢಃ൬ၭĠ iii 7) ᇀmτൈູᆸđࣜႏᆀ֤֥֞൬ၭ์གྷᆴູ(์གྷᇀt=0ൈ) m−irτ (4) T=Ye∑ii=1ఃᇏđrູ৵࿃گ০์གྷ০ੱ; 2 8) T֥नᆴEބٚҵσ ູTT 2
__中__国__科__技__论__文__在__线_d_u_._c_n__mmm2E=Eđ (5) σ=σσρT∑TiT∑∑TTijiji=1i=1j=1−irτ−irτ−irτఃᇏE=e[α+β(1−α)]f(s)uτđđσ=f(s)τσρіൕაe[α+β(1−α)]YeTiiiiiijTii0iiiiiiii−jrτᆭࡗ֥ཌྷܱ༢ඔ()Ġ i,j=1,...,mYej 9) ᄝൈࡗ؍[(i−1)τ,iτ)ଽđሧᆀؓࣜႏᆀ֣֡ڄགӱ؇֥ყ௹ູ α(0≤α≤1đi=1,...m)đؓiiཛଢ൬ၭੱࠣఃѯੱ֥ყ௹ٳљູuބ σ()đሧᆀ۴ऌᆃུყ௹ᆴथק൞ڎ࿃i=1,...,m0iiሧĠ 10) ሧᆀᄝൈࡗ؍[(i−1)τ,iτ)ଽሧđᄵఃყ௹֤֥֞ܢಃ൬ၭູ I=(1−β)(1−α)f(s)(u+ε)τ (i=1,...,m) (6) iiiiiii2ఃᇏε(i=1,...,m)ູनᆴູ0aٚҵູ σ֥ᆞٳ҃ෛࠏэਈĠሧᆀᄝھൈࡗ؍ଽ҂ሧđi0iᄵβ=1đI=0đՎൈሧᆀყ௹֤֥֞൬ၭಯॖႨ(6)ൔіൕĠ ii 11) ᇀmτൈູᆸđሧᆀყ௹֤֞൬ၭ֥์གྷᆴູ(์གྷᇀt=0ൈ) m−irτ (7) T=IeI∑ii=12TE 12) ֥नᆴބٚҵσٳљູ IIImmm2đ (8) E=EIσ=σσρI∑iI∑∑IIijiji=1i=1j=1−irτ−−irτirτఃᇏEI=e(1−β)(1−α)f(s)uτđđρіൕაσ=e(1−β)(1−α)f(s)τσIeiiiiiiIiiii0ijiii−jrτᆭࡗ֥ཌྷܱ༢ඔ (). i,j=1,...,mIej 2 ჿඏྐݼѰᒮଆࠣٳ༅ࢲݔ < > ᄝ༯ඍٳ༅ᇏđଢѓݦඔनҐႨF. .FSDVSJPིႨݦඔ Ѱᒮݖӱ ࣜႏᆀބሧᆀҐ౼؋൪ൔކቔٚൔ֥౦ঃ ᆃ൞ࣜႏᆀބሧᆀᄝૄ۱ൈࡗ؍षൈनླᇗྍठᄴ൞ڎ࿃ކቔ֥౦ঃ. Ѱᒮݖӱູ ᄝt=(i−1)τൈׄԩğ 1) ሧᆀ๙ݖؓཛଢ֥భࠫ۱ሧࢨ؍֥ܴҳაਔࢳࠣՖࣜႏᆀ֥ሱԔሧࣁб২βބཛଢሹi−1ሧحs֩ྐ༏ᇏđҩЧሧࢨ؍ࣜႏᆀ֥֣֡ڄག༢ඔαđཛଢ൬ၭੱuࠣఃѯੱσ. ކi−1ii0iެሧေđᄵ࿃ሧđѩथק൞ሔࡆ҆ٳሧحߎ൞Ԏ߭҆ٳሧحđ҂ކެሧေđᄵԎ߭ಆ҆ሧحࠣཌྷႋ֥ಃၭđၛު҂ᄜ࿃ؓھཛଢሧ. ࿃ሧđሧᆀՖሱദሧ০ၭቋն߄ԛؿथקఃሧحđࠧᄝყ௹ࠇܴҳ֞ࣜႏᆀሱԔሧࣁб২βުđ๙ݖ i⎧bI−rτi−2rτ22222maxU=e(1−β)(1−α)f(s)uτ−e(1−β)(1−α)f(s)τσ⎪Iiiiiiiiii0ii (9) s⎨i2⎪irτ≥(1−β)sr⎩iiii֤֞s=s(β,α,u,σ)đՖطथקఃሧحູ(1−β)sđఃᇏb>0ູھࢨ؍ሧᆀ֥धؓڄགညiiiii0iiiIi 3
__中__国__科__技__论__文__在__线_d_u_._c_n__irτذ༢ඔđᆃၛeEI≥(1−βіൕሧᆀᄝt=(i−1)τൈሧحູ)sr(1−β)s֥Ќ൬ၭჿඏđrູiiiiiii−rτھࢨ؍ሧᆀ֥Ќ൬ၭੱđe(1−β)(1−α)f(s)uτູሧᆀᄝt=(i−1)τൈሧحູ (1−β)siiiiiii−2rτ22222֥ყ௹൬ၭ(ᅼགྷᇀt=(i−1)τൈ)đe(1−β)(1−α)f(s)τσູھყ௹൬ၭ֥ٚҵĠ iiii0i 2) ࣜႏᆀᆩ֡ሧᆀ֥ሧҦđѩᆩ֡ሧᆀؓཛଢ֥ყ௹൬ၭੱࠣఃѯੱބؓࣜႏᆀ֣֡ڄག༢ඔ֥ყ௹ᆴđᆩ֡ሧᆀ֥धؓڄགညذ༢ඔbđᄵࣜႏᆀՖሱദ০ၭቋն߄ԛؿಒקሱIiԔሧࣁб২βđࠧ๙ݖ i⎧bT−rτi−2rτ2222maxU=e[α+β(1−α)]f(s)uτ−e[α+β(1−α)]f(s)τσ⎪Tiiiiiiiiiii0ii (10) βi⎨2⎪≥0T⎩i֤֞β=β(s)đࣜႏᆀऌՎಒק α=α(s)ࠣఃሧحβs. ᆃࡌഡࣜႏᆀ֥ЌིႨູ0điiiiiiii−rτe[α+β(1−α)]f(s)uτູࣜႏᆀᄝt=(i−1)τൈሧحູ βs֥ყ௹൬ၭ(ᅼགྷᇀt=(i−1)τൈ)điiiiiiii−2rτ2222e[α+β(1−α)]f(s)τσູھყ௹൬ၭ֥ٚҵđb>0ູൈࡗ؍[(i−1)τ,iτ)ଽࣜႏᆀ֥धؓڄiiiii0iTiགညذ༢ඔ. ཁಖđഈඍଆ֥ൌᇉູࣜႏᆀބሧᆀࡗֆᇛ௹ವሧѰᒮଆ. ൞đഈඍٚمაMukesh B. ֩ದč1998Ďิԛ֥ٚم൞ᝀၳ֥ğMukesh B. ଆູჿඏྐݼѰᒮଆđطЧ໓൞ჿඏྐݼѰᒮଆ. ෙಖఃࢳ؇бMukesh B. ଆေն֤؟đః۷ژކൌ࠽౦ঃ. Ч໓ࡼᄝࢫ۳ԛཌྷႋ֥࠹ෘٚم. ࣜႏᆀބሧᆀӉ௹ކቔކჿ֥౦ঃ ᆃ൞ࣜႏᆀބሧᆀՖm۱ࢨ؍֥ᆜุ০ၭԛؿቓԛሧაڎथҦ֥౦ঃ. ᄝt=0ൈׄԩđࣜႏᆀބሧᆀनᆩཫؓٚ߶ᄝॉ੮ᆜ۱m۱ࢨ؍০ၭ֥ࠎԤഈࣉྛሧथҦ. ၹՎđՖᆜ۱ሧ௹ིႨቋն߄ԛؿđྙӮ༯ਙѰᒮଆğ [6]࠺{s,i=1,...,m},{β,i=1,...,m}ູNashनޙׄđᄝሧᆀؓࣜႏᆀ֣֡ڄག༢ඔყ௹ᆴაࣜႏiiᆀൌ࠽֣֡ڄག༢ඔ၂ᇁࣜႏᆀაሧᆀؓؓٚሧҦ֥؎აൌ࠽၂ᇁൈđNashनޙׄડቀ ⎧bI2maxU=E−σIII⎪{s,i=1,...,m}i2⎪ (11) ⎨m−(i−1)rτ⎪≥e(1−β)srI∑iii⎪⎩i=1b⎧T2maxU=E−σ⎪TTT{β,i=1,...,m}i2 (12) ⎨⎪≥0⎩T ఃᇏđb>0ބb>0ٳљູሧᆀބࣜႏᆀ֥धؓڄགညذ༢ඔ. ᆃၛITm−(i−1)rτіൕሧᆀ֥Ќ൬ၭჿඏđಯࡌഡࣜႏᆀ֥ЌིႨູ0. E≥e(1−β)srI∑iiii=1 2ē2 ٳ༅ࢲݔ ᄝf(⋅)֥ݦඔྙൔࢠگᄖൈđഈඍଆ၂ϮླҐႨඔᆴࢳمট࠹ෘ. ູਔٚьđЧ໓ࣇࣼf(x)Ģ2[1]cccx(x≥0,c>0)֥౦ঃࣉྛษં. ॖᆩđ. ′f(x)f(x)=′f(x)= ࣜႏᆀބሧᆀҐ౼؋൪ൔކቔٚൔ֥౦ঃ 4
__中__国__科__技__论__文__在__线_d_u_._c_n__irτࣇؓ(9)a(10)ਆൔࣉྛษં. ႮႿeEI≥(1−β)srॖڿཿູ (1−α)f(s)uτ≥srđ෮ၛ(9)ൔiiiiiiiiii[ 7]֥Lagrangeݦඔॖܒᄯູ L(s,λ)=U+λ[(1−α)f(s)uτ− (13) sr]1iiIiiiiiiii[7]෮ၛđ໙ี(9)֥ቋႪࢳડቀ༯ਙ၂ࢨсေ่ࡱ(Kuhn-Tucker่ࡱ)ğ ∂L1−rτ−2rτ2222′′ =e(1−β)(1−α)f(s)uτ−be(1−β)(1−α)f(s)f(s)τσ iiiiiIiiiiii0ii∂si+λ[(1−α′)f(s)uτ−r]Ģ0 (14) iiiiiiބ λλ≥0[(1−α)f(s)uτ−sr]=0đ (15) iiiiiiiiႮ(14)ൔॖ֤ A (16) s=iB−rτ22−2rτ222222ఃᇏđA=[e(1−β)+λ][(1−α)ucτđ]B=[be(1−β)(1−α )cτσ+2λr. ]iiiiIiioiiii−rτ2222ק1 1) be(1−β)(1−α)cτσ<rđᄵ໙ี(9)֥Kuhn-Tucker่ࡱડቀ Iii0iiiA2−rτ−2rτ22222s==[(1−αđ)ucτ/r]λ=e(1−β)−be(1−β)(1−α)cτσ/r>0Ġ iiiiiiIii0iiiB−rτ22222) be(1−β)(1−α)cτσ≥rđᄵ໙ี(9)֥Kuhn-Tucker่ࡱડቀ Iii0iiirτuei2đλ=0. s=[]ii2b(1−β)(1−α)cτσIii0ii−rτ2222ᆣૼ be(1−β)(1−α)cτσ<rđᄵႮ(16)ൔބ(1−α)f(s)uτ=srॖ֤Iii0iiiiiiiii2−rτ−2rτ22222s=[(1−α)ucτ/r]ބλ=. ّᆭđe(1−β)−be(1−β)(1−αđ1)֤ᆣ)cτσ/r>0iiiiiiIii0iii−rτ2222be(1−β)(1−α)cτσ≥rđॖᆩ҂թᄝ(16)ൔބ(1−α)f(s)uτ=srൈӮ৫֥ᆞλđၹՎđIii0iiiiiiiiiiႮ(15)ބ(16)ൔॖ֤λ=0đՖطॖᆩ2)֥ࢲંӮ৫. i Ⴎ༯ඍٳ༅ᆩđቋႪ֥ವሧҦؓႋ֥U၂ק҂ཬႿ0đ෮ၛđᄝ༯ਙٳ༅ݖӱᇏ҂ॉ੮໙Ti(ี10)ᇏ֥ჿඏ่ࡱ. Ⴎ ∂UTi−rτ−2rτ222 (17) =e(1−α)f(s)uτ−be[α+β(1−α)](1−α)f(s)τσ=0iiiiTiiiii0ii∂βi෮ၛđ rτuei−αi2bf(s)τσTii0iiβ= (18) i1−αi ק2 ࣜႏᆀ֥ቋႪིႨູ 5
__中__国__科__技__论__文__在__线_d_u_._c_n__2uiU=> 0 (19) Ti222bσT0ii ᆣૼ ᆺླࡼ(18)սೆ(10)ൔᇏьॖ֤֞ࢲં. ሸކ(9)a(10)ࠣഈඍ֝đॖ֤ԛ ં1 ᄝࣜႏᆀބሧᆀҐ౼؋൪ކቔٚൔ֥౦ঃ༯đႮഈඍჿඏྐݼѰᒮଆॖ֤ −rτ2222 1) be(1−β)(1−α)cτσ<rđᄵ۲ࢨ؍֥ሹሧح֥э߄აളӁඌඣaყ௹൬ၭੱIii0iii֥э߄ᆞཌྷܱđაࣜႏᆀ֣֡ڄག༢ඔ֥э߄ڵཌྷܱđაሧᆀधؓڄགညذӱ؇ބࣜႏᆀሱԔሧࣁ−rτ2222б২֥э߄ܱ(ᆺေᆃ҆ٳ֥э߄Ќᆣbe−)(1−)c<r (1βατσ)Ġ Iii0iii−rτ2222 2) be(1−β)(1−α)cτσ≥rđᄵ۲ࢨ؍ሹሧح֥э߄აყ௹൬ၭੱaࣜႏᆀሱԔሧࣁIii0iiiб২aࣜႏᆀ֣֡ڄག༢ඔ֥э߄ᆞཌྷܱđაሧᆀधؓڄགညذӱ؇aളӁඌඣ֥э߄ڵཌྷܱ(ᆺ−rτ2222ေᆃ҆ٳ֥э߄Ќᆣbe(1−β)(1−α)cτσ≥r)Ġ Iii0iii 3) ᄝѰᒮݖӱᇏđࣜႏᆀॖၛ๙ݖטᆜః֣֡ڄག༢ඔބሱԔሧࣁб২ఃቋႪི֥ႨЌӻ҂э. ༯૫ษંβაαࡗ֥ܱ༢ބࣜႏᆀ֥ཟ࿊ᄴӱ؇ؓሧ֥႕ཙ. iiં2 β֥э߄აα֥э߄ڵཌྷܱ. iirτueiᆣૼ ࡼ(18)ൔڿཿູ[α+β(1−α)]=đᄜႮק1ॖ֤ğiii2bf(s)τσTii0iirτuer∂ββ−1−rτ2222iiiibe(1−β)(1−α)cτσ<rđᄵ [α+β(1−α)]= đ ֤<0Ġ=Iii0iiiii222ib(1−α)ucτσ∂α1−αTii0iiii2u(1−β)(1−α)σ−rτ2222iii0ibe(1−β)(1−α)cτσ≥rđᄵ [α+β(1−α)]=đ ֤Iii0iiiiii2uσi0i2∂βu(β−1)σiii0i=<0Ġ֤ᆣ. 22∂αuσ(1−α)+u(1−α)σii0iiii0iႮ(19)ൔބં2ॖᆩđࣜႏᆀऎႵᆃဢ֥ࠗৣğЌӻαൡ֒ն֥ൈሧᆀؓα֥ყ௹҂ӑiiݖః٢ఙሧ֥ӱ؇. ሧᇀmτൈࢲඏđᄵᄝֻmࢨ؍ࣜႏᆀႵᄹնα֥ॖି. ࢨ؍ඔmູi౫նđᄵູਔႥ࿃ࣜႏđࣜႏᆀऎႵ֣֡ڄག༢ඔᇔЌӻ҂ն֥ࠗৣ. ં3 ࣜႏᆀႵᇗ֥ཟ࿊ᄴౠཟđᄵؓఃࣜႏ൞҂০֥. ∂s∂siiᆣૼ Ⴎק1ᆩ>0ađ෮ၛđࣜႏᆀ֥ཟ࿊ᄴҦॖି၂ൈ߶ሧᆀؓཛଢ≤02∂u∂σi0iሹሧح֥ყ௹ᄹն. ሧᆀܴҳ֞ਔࣜႏᆀ֥ཟ࿊ᄴౠཟđᄵॖି۳ԛࢠཬ֥ყ௹ᆴuބࢠi2ն֥ყ௹ᆴσđՖطሧحࡨഒđമᇀԎ߭ಆ҆ሧሧࣁđၹՎđᄝ؟ࢨ؍ವሧݖӱᇏđ0i∂βiᇗ֥ཟ࿊ᄴӱ؇ؓࣜႏᆀ൞҂০֥. Ⴎᆩđ֒ࣜႏᆀሱԔሧሧࣁб২ࢠཬൈđॖିႅݣ<0∂αiሢࢠն֥֣֡ڄགđ൝с֝ᇁሧᆀधؓڄགညذ༢ඔ֥ᄹնđႮקᆩđࡼॖି֝ᇁሹሧح֥ࡨഒ. ࣜႏᆀބሧᆀר৫Ӊ௹ކቔކჿ֥౦ঃ 6
__中__国__科__技__论__文__在__线_d_u_._c_n__༯૫ؓ(11)ބ(12)ൔࣉྛษં. ܒᄯ(11)ൔؓႋ֥Lagrange ݦඔğ mm−(i−1)rτb2−(i−1)rτIL (20) (s,λ)=U+λ[E−e(1−β)sr]II∑iii=(1+λ)E−σ−λe(1−β)srII∑iiii=12i=1ᄵ໙ี(11)֥ቋႪࢳડቀ֥၂ࢨсေ่ࡱ(Kuhn-Tucker่ࡱ) ູm−(i−1)rτ∂L∂E−irτI−λe(1−β)rĢ0, (21) i=1,...,m=(1+λ−b′)e(1−β)(1−α)f(s)τσσρiiI∑iiii0iIijj∂s∂sj=1iim−(i−1)rτđλ≥0 (22) λ[E−e(1−β)sr]=0I∑iiii=1 ၹՎđႵ ק3 ໙ี(11)֥ቋႪࢳs=(s,s,...,s)ડቀ 12mm1) đi=1,...,m (23) ρσ=u/(bσ)∑ijIiI0ijj=1m−(i−1)rτE>e(1−β (24) )srI∑iiii=1mࠇrτ2 2) đ i=1,...,m (25) ρσ={2re/[bσ(1−α)cτ]}f(s)∑ijIiI0iiiijj=1m−(i−1)rτ (26) E=e(1−β)srI∑iiii=1m−(i−1)rτᆣૼ 1) ֒E>e(1−βൈđႮ(22)ൔᆩđ)srλ=0đၹՎđႮ(21)ൔॖᆩ(23)ൔӮ৫. 2)I∑iiii=1m֒−(i−1)rτൈđႮ(21)ൔॖ֤ E=e(1−β)srI∑iiii=1m−(i−1)rτ−irτ e(1−β)r−be(1−β)(1−α′)f(s)τσσρ=0iiI∑iiii0iIijjj=12ᄝഈൔਆшൈӰၛđѩ০Ⴈ′đॖ֤(25)ൔ. f(s)f(s)f(s)=c/2iiiiiiཁಖđ(23)ൔބ(25)ൔູ֥ཌྟٚӱቆđط(24)ބ(26)ൔॖቔູဒ่ࡱ. ၹՎđᄝf(x)Ģf(s)iicx֥ࡌഡ༯đ(23)~(26)֥ࢳ൞ࢠಸၞ֥. ༯૫ٳ༅໙ี(12). Ⴎ༯૫֥ٳ༅ॖᆩđࣜႏᆀ֥ቋႪིႨնႿ0đၹՎᄝ༯ਙٳ༅ݖӱᇏ҂ॉ੮ჿඏ่ࡱ. m∂UT−irτ−irτႮĢ0đ֤ =e(1−α)f(s)uτ−be(1−α)f(s)τσρσiiiiT∑iii0iijTj∂βj=1imui đ i=1,...,m (27) ρσ=∑ijTjbσj=1T0i mmmmσuETiT2iiႻႮ(5)ൔᆩđđၹՎđႮ(12)ൔॖ֤ σ=σσρ==T∑∑TTij∑∑ijbσbi=1j=1i=1i=1T0iTק4 ࣜႏᆀ֥ቋႪིႨູ m1 (28) U=E=∑TTi2i=1ࠧࣜႏᆀ֥ቋႪིႨູః௹ຬሧ൬ၭ֥၂϶. 7
__中__国__科__技__论__文__在__线_d_u_._c_n__∂E∂U1TႮTiॖᆩ =>0∂α2∂αiiં4 ᄝЌᆣ؟ࢨ؍ሧିܔӻ࿃༯ಀ่֥ࡱ༯đࣜႏᆀႵᄹն֣֡ڄག༢ඔ֥ౠཟ. ᇿၩđࢫაࢫ֥ܱႿࣜႏᆀ֣֡ڄག֥ٳ༅ࢲݔႵ҂đॖ؋൪ൔކቔٚൔႵᇹႿჿඏࣜႏᆀ֥֣֡ڄགౠཟ. 3 ࢲඏე Ⴎഈඍٳ༅ॖᆩđᄝವሧݖӱᇏđఒြࣜႏᆀ֥ሱԔሧሧࣁб২aሧحࠣൌ࠽൬ၭੱ֩ऎႵԮ־ྐݼ֥ቔႨđሧᆀॖၛ๙ݖܴҳࠇყ௹ᆃུหᆘᆷѓҩఒြࣜႏᆀ֥֣֡ڄགࠣཟ࿊ᄴӱ؇. ٳ༅ࢲݔіૼđ۲ࢨ؍ሹሧح֥э߄(ࠇཛଢ֥ࣜႏܿଆ֥э߄)აളӁඌඣaყ௹֥൬ၭੱaࣜႏᆀ֥֣֡ڄག༢ඔaሧᆀधؓڄགညذӱ؇ࠣࣜႏᆀ֥ሱԔሧࣁб২э߄ࡗ֥ཌྷܱܱ༢ᇶေႮၛ༯ࠫ۱ၹಒקğሧᆀ֥धؓڄགညذӱ؇aࣜႏᆀ֥ሱԔሧࣁб২ބ֣֡ڄག༢ඔaളӁඌඣࠣཛଢყ௹൬ၭੱ֥ѯੱ֩. ᄝഈඍٳ༅ᇏđၛห൹ྙൔ֥ളӁݦඔބིႨݦඔູษંؓའđᆃЧ໓֥ࢲંթᄝଖུअཋྟđႮႿఃႋႨࢠٚьaཌྷܱ֥ࢲં္ऎႵ၂ק֥սіྟ֩ჰၹđᆃᇕྙൔ֥ളӁݦඔᄝཌྷܱ֥໓ངᇏ֤֞ਔࢠ؟֥ႋႨ. ਸ਼ຓđᆴ֤ᆷԛ֥൞đЧ໓ࡌഡگ০m−irτ์གྷ০ੱᄝ۲۱ࢨ؍Ќӻ҂эđᆃՂե൞ູਔіղഈ֥ٚьđൌ࠽ഈđॖၛࡼ(4)ൔקၬ֥T=Ye∑ii=1iimm−τrm−τr∑j∑j−irτj=1j=1ބ (7)ൔקၬ֥ٳљڿཿູބđࡼაᆃਆ۱ൔሰႵܱT=IeT=YeT=IeI∑i∑iI∑ii=1i=1i=1֥іղൔቓཌྷႋֹྩڿࠧॖđఃᇏrіൕൈࡗ؍[(i−1)τ,iτ)ଽؓႋ୍֥৵࿃گ০ੱ. ႮႿᆃဢቓ߶ᄹjࡆіղ֥گᄖྟđؓࢲݔ҂߶Ӂളൌᇉ֥႕ཙđၹՎđᆃ҂ᄜབྷ༥ษં. ᇁ྆ğᆇӴۋ़྆щ߶ഽބਆ໊ബህࡅ֥Џၩ. ҕ ॉ ໓ ང [1] Mukesh Bajaj, Yuk-shee Chan and Supipto Dasgupta. The relationship between ownership financing decisions and firm performance: a signaling model [J]. International Economic Review, 1998 , 39(3)ğ723-744 [2]Neil A. Dohery and Lisa L. Posey. On the value of a checkup: adverse selection, moral hazard and the value of information [J]. The Journal of Risk and Insurance, 1998, 65: 189-211 [3]ౕ࿐ᆽ, Ԋڃ. ກದაսದ֥ሧིႨ[J], ༢۽ӱ࿐Бđ2002đ17(2)ğ150– 154 [4]ౕ࿐ᆽ, Ԋڃ. ྐ༏٤ؓӫӱ؇აఒြࡅིႨaሧЧࢲܒaఒြ൧ӆࡎᆴ[J], ᇏݓܵ॓࿐, 2001, 9(4):1-6 [5]Fabio Mercurio. Claim pricing and hedging under market incompleteness and “mean-variance” preferences[J]. European J. of Operational Research, 2001, 133ğ635 – 652 [6]ᅦົ႒. Ѱᒮંაྐ༏ࣜ࠶࿐[M]. ഈݚ: ഈݚ৳, 1997 [7]นߕ໓, ౕ࿐ᆽ. ൌႨቋႪ߄ٚم[M]. ն৵ğն৵۽ն࿐ԛϱഠ, 2000 ቔᆀࡥࢺğ ౕ࿐ᆽ(1965Ē)đଳđୡն৵ದđڬ࢝൱đѰൖ. ᇶေ࣮ٚཟ: ࣁವ۽ӱა༢۽ӱ. ᄝݓଽຓᇗေ࿐ඌ௹़ބ߶ၰഈؿіં໓50Ⴥđఃᇏ10ჅФEIaMRaISTP֩෬. ӵ๓(1962Ē)đଳđն৵۽ն࿐ܵ࿐ჽѰൖളđ࣮ٚཟğඥ൬ંაఒြವሧथҦ. ້ ఼(1970Ē)đଳđն৵۽ն࿐ܵ࿐ჽѰൖളđ࣮ٚཟğၿྛሧંა༢۽ӱ. 8
