ֻ17ज ֻ5௹ᇏݓܵ॓࿐, 2009୍ 10ᄅ ChineseJournalofManagementScienceOct., 2009໓ᅣщݼ:1003-207(2009)05-0120-07基于风险项目价值的风险投资最优中止时机研究顾 婧1,周宗放2(11四川大学经济学院,四川成都 610065;21电子科技大学经济与管理学院,四川成都 610054)ᅋ ေ:ᇏᆸथҦି৯൞႕ཙڄགሧ܄ඳӉ௹ི֥ࠛᇗေᆷѓᆭ၂,ಖطགྷႵᇏᆸथҦٚمޭ൪ਔڄགཛଢؿᅚݖӱᇏྐ༏ؓཛଢࡎᆴ֥႕ཙ,Ֆط႕ཙਔᇏᆸथҦൈࠏbᆌؓھ໙ี,Ч໓൮༵ՖНွථުဒܙ࠹֥࢘؇ิԛਔڄགሧࡅުဒۀੱ֥ྐݼ࿐༝ݖӱ;ಖުᄎႨܿ߃ٚم,ᄝಒקؓڄགཛଢቋႪሧඣ֥ࠎԤഈ,۳ԛਔࠎႿڄགཛଢࡎᆴ֥ቋႪᇏᆸൈࠏଆ;ቋުؓቋႪᇏᆸൈࠏଆࣉྛਔෘ২ٳ༅bЧ໓ิԛ֥ቋႪᇏᆸଆॉ੮ਔڄགཛଢؿᅚݖӱᇏྍྐ༏٢ؓᇏᆸൈࠏ֥႕ཙ,ࢳथਔٳࢨ؍ሧ౦ྙ༯֥ቋႪᇏᆸथҦ໙ี,ູڄགሧࡅࠣൈቓԛᇏᆸथҦิ܂थҦ၇ऌbൈ,ھଆߎॖႨটٳ༅ڄགሧࡅؓڄགཛଢ֥ቋႪሧඣ໙ี,ູఃቓԛቋႪथҦิ܂ҕॉbՎຓ,ଆ֥ٳ༅္ູڄགཛଢԷದ๙ӈؿള֥ཟ࿊ᄴྛູิ܂ਔކ֥ࢳbܱՍ:ڄགሧ;ቋႪᇏᆸൈࠏ;ܿ߃;Ⴕིшࢸׄᇏٳোݼ:F27213 ໓ངѓ്:A1 ႄڄགሧ֥ᇏᆸथҦ҂ႿԛथҦ,൞ᆷؓᆞᄝሧ֥ڄགཛଢ۴ऌཛଢ֥ࣉᅚࠣଽຓ҆ྐ༏ႮႿڄགሧ܄ඳ෮ڄགཛଢ֥ࠞն҂ಒקэ߄Ґ౼၂ק֥ٚمؓཛଢభࣟࣉྛ؎,ၛथק,ྟӮۿ֥൬ၭބാϧ֥ӮЧ൞ऍն֥bၹՎ,ڄ൞ᄜሧaᇏᆸߎ൞௹֥၂ᇕथҦྛູbᇏᆸथགሧࡅᄝሧݖӱᇏ֥۲ᇕथҦཁ֤ႭູᇗေbҦ൞ڎࠣൈaथҦࢲݔ൞ڎሙಒᄝޓնӱ؇ഈथקᄝڄགሧࡅ֥۲ᇕथҦ࣮ᇏ,ܱႿڄགཛଢ֥ਔڄགሧ܄ඳ֥൬ၭ[4-6]bԚ࿊ᄴथҦ࣮ࢠ؟,ಏޓഒܱᇿఃᇏᆸथҦbଢభ,ݓຓႵܱᇏᆸथҦ࣮֥໓ངၛൌᆣंಖطٳࢨ؍ሧ൞ڄགሧ֥ࠎЧᄎቔٚൔ,ି؟,ؓᇏᆸथҦ֥ჰၹބགྷሑࣉྛਔٳ༅b২ೂܔႵֹིٳሧჷ[7],ط֤ڄགሧࡅႚႵᄝૄSahlman(1990)ᆷԛ၂Ϯڄགሧ܄ඳ҂჻ၩᇏ۱थҦׄ࿃ሧࠇᇏᆸሧ֥௹ಃ[1]bၹՎ࣮ᆸሧ֥ჰၹ:ෛሢؓڄགཛଢᇿሧࢨ؍֥ᄹࡆ,ෙٳࢨ؍ሧ౦ྙ༯֥ᇏᆸथҦ໙ีऎႵᇗေၩၬbಖڄགᄝ҂؎ᄹն,ࠆ֤Ӯۿ֥ॖିྟᄝࢆ,֮ಯ๙ӈ,ᄝڄགሧࡅٳࢨ؍ሧ֥భิ༯,ሧथҦಖॖିࠆ֤Ӯۿ,ၹطಯႵॖିࠆ֤٤ӈ֥ۚ߭Бѩ҂ၹູᆞಒ֥Ԛ࿊ᄴط҂گթᄝ,ّطෛሢྐ༏֥ࢣൕ,ླေڄགሧࡅ҂؎ܙڄགཛଢ,ቓԛੱbGuler(2003[1])֥ൌᆣ࣮ಪູ:ࠆ֤ڄགሧᄜሧࠇᆀᇏᆸ֥थҦbЧᇿሧࢨ؍ᄀ؟,न߭Бੱ߶ᄀ֮,ႋؓభࣟ҂ݺBergemennބHege֥ڄགཛଢࠣൈᇏᆸbP]owell(2002[8)ؿགྷ:ࠧ(1998)ิԛޅൈᄜሧၛࠣޅൈᇏᆸሧ൞ڄགሧࡅቋູ็ᅞྟ֥໙ีᆭ၂[2];ૌߎิԛᇏᆸथथҦᆀၩ്֞ڄགᄹࡆ,္ݔ؎Ґ౼ᇏᆸथҦbҦ൞ڄགሧࡅބԷြᆀ֥ᇶေԊᆭ၂[3]bଢᆃ൞ၹູथҦᆀᄝቓԛԚሧथҦު,ޭਔڄభགཛଢ֥ྍࣉᅚބߌ֥э߄,ીႵࠣൈ൬ࠢཌྷܱ,ᇏᆸथҦି৯൞႕ཙڄགሧ܄ඳӉ௹ི֥ࠛᇗေᆷѓᆭ၂,ᇏᆸथҦ္൞ڄགሧࡅӈႨ֥॥ྐ༏ؓཛଢᄜܙbPowell۴ऌؓնਈڄགሧᇅڄག൭؍ࡅ֥טҰ,ߎؿགྷ၂۱ޓႵ౿֥གྷའ:ᆺေႵ၂ׄӮ,ᆻᄝ՜ڄགሧ܄ඳ൬ၭ֥ቋն߄bۿ֥༐ຬ,ڄགሧࡅཟႿᄜሧ,ط҂൞ൡൈ֥ ൬۠ರ௹:2008-08-26;ྩרರ௹:2009-08-13ᇏᆸሧbൌ࠽ഈ,थҦᆀᆺႵ۴ऌ൬֥ࠢྐ༏҂ࠎࣁཛଢ:ݓࡅሱಖ॓࿐ࠎࣁሧᇹཛଢ(70671017)ቔᆀࡥࢺ:ܤប(1980-),୯(ݱቂ),ࡾ්ۚႯದ,ඹԫն࿐ࣜ࠶؎ֹؓڄགཛଢᄜܙ,ѩൡൈؓభࣟ҂ুܴ֥ཛ࿐ჽଢቓԛᇏᆸሧ,ҌିӉ௹Ќӻ֥ۚሧིࠛbਸ਼,Ѱൖ,ࢃഽ,࣮ٚཟ:ڄགሧथҦٳ༅.ຓ,۱ದ֥थҦொ္߶႕ཙᇏᆸथҦbRyan
ֻ5௹ ܤ ប֩:ࠎႿڄགཛଢࡎᆴ֥ڄགሧቋႪᇏᆸൈࠏ࣮#121#9](1995[)ᆷԛ:ࠧ෮ሧ֥ڄགཛଢཁൕԛ҂ݺڄགཛଢ(Ч໓҂ॉ੮ھڄགཛଢ֥ܙބೱ࿊ݖ֥൝,थҦᆀ္҂჻ၩᇏᆸሧ,ૌ۷ཟϜӱ)bູ॥ᇅڄག,VC࿊ᄴٳࢨ؍ሧ,ሧࢨ݂۴Ⴟᄠൈགྷའ,ࠇᆀ൞ຓ҆ჰၹbEdwards؍აڄགཛଢ֥ؿᅚࢨ؍၂ᇁb(1982[10])࣮ؿགྷ:थҦᆀࠧᆩ֡ᄜሧ҂ିࠆູܒࡹଆٚь,Ч໓ิԛၛ༯ࡌഡభ:ิ֤Ӯۿ,ૌ၂Ϯ္҂჻ၩᇏᆸሧ,ᇶေჰၹ൞མ1)ൌᆣіૼथҦᆀႵॖିொ௹ຬིႨંቓົૌ֥ԚथҦbطݓଽܱႿᇏᆸथҦ֥࣮ԛհ༂֥थҦ,ொ֥ჰၹᄝႿಪᆩࢲܒ֥अཋa҂ᇶေࠢᇏႿᇏᆸथҦٚمٚ૫,ᆃུ࣮ࡼთ႘ಒק่ࡱ༯ྐ༏֥ޭ൪,֩ၹՎ,Ч໓ࡌഡVC൞ഝaᆦӻཟਈࠏaՙҡࠢaଆൔ്љ֩ᄎႨ֞ᇏᆸथྟ֥थҦᇶุ[1]bҦ࣮ഈট[11-14]b2)҂ॉ੮VCሧࣁ҂ቀބሧொݺ֩໙,ีቔଢభݓଽຓ֥ᇏᆸथҦٚمᇶေ݂ବູোbູᇏᆸथҦᇶุ֥VC൞ྟದ,ఃࡼ၇ऌ௹ຬི၂൞൬ၭބӮЧбࢠم[15]bᄝགྷൌᇏ,ؓ൬ၭބႨંࣉྛު࿃ሧथҦbӮЧ֥ܙෘ૫ਢሢޓն֥҂ಒקྟ,ၹՎھٚمᄎ3)ڄགཛଢᄝఃؿᅚݖӱᇏ҂Ӂളᇏࡗ൬ၭbႨఏটႵޓն֥؇[16];ؽ൞ၛB[17]uellູսі֥ᄝሧࢨ؍ಆ҆ࢲඏު,ೂݔڄགཛଢӮۿ,ᄵӁളཛଢᇏᆸଆbھٚم๙ݖؓཛଢ֥טҰ֤ԛ႕ཙಒק֥൬ၭR;ೂݔڄགཛଢാϧ,ᄵીႵޅ൬ཛଢࣉᅚ֥؟ᇕၹ,๙ݖၹ֥э߄ಒקᇏᆸथၭbҦ,ᆃোᇏᆸथҦٚمીႵ၂֥ѓሙ္ીႵ๙Ⴈ4)ڄགཛଢӮۿ෮ླ֥ൈࡗބሧඣ൞൙༵֥ଆ,ൌ࠽ᄎႨᇏࢠູ;൞ࢹR&Dཛଢ҂ಒק֥bᇏᆸथҦٚم֥۲ᇕקਈљٚم[5,6,11-14]bᆃུ5)VCᄝޅ၂۱ᇏᆸथҦׄႵնਈሧఃٚمᄝൌ࠽ႋႨᇏթᄝሢࢠն֥ބअཋྟ,২ڄགཛଢ֥ࠏ߶bೂ໓ང[6,7]֥ಌׄᄝႿေ࿊ᄴбࢠဢЧ,थҦׄ6)VCބEN൞ڄགᇏྟ,֥ႚႵ܋֥ᅼࢠູ၇ঠႿلᆴ;໓ང[11]֥ಌׄᄝႿޭ൪ਔ२ੱDI(0,1)bR&Dཛଢ֥;ྟ໓ང[12]֥ಌׄᄝႿၛ࿊7)ڄགཛଢᄝാϧ౦ঃ༯ԛགྷݺྐݼ֥ۀੱູᄴᆦӻཟਈࠏ֥SVMނݦඔ;໓ང[13,14]֥ಌׄ0bᄝႿथҦ֥ࣚ؇ࢠູ၇ঠဢЧඔਈބᇉਈbЧ໓ࡼڄགཛଢቋᇔ֥ሱಖሑ(ख़߂ູؽሸഈ෮ඍ,གྷႵ֥ᇏᆸथҦٚمޭ൪ਔڄགཛཛࢲܒ:ӮۿSބാϧF,ࠧ(={S,F},ఃᇏӮۿଢ֥,ྟޭ൪ਔྐ༏֥ؿᅚؓު࿃ሧथ൞ᆷڄགሧЧӮۿֹՖڄགཛଢԛ,ӮۿԛЇҦ֥႕ཙ,ીႵಪ്֞ྍྐ༏֥٢ؓᇏᆸथҦൈওڄགཛଢൌགྷIPOࠇᆀၛކൡ֥ࡎ۬છԛڄགࠏ࿊ᄴ֥႕ཙ,ط္ીႵܱᇿྐ༏ࠆ౼ބሧथཛଢbൌᆣࢲݔіૼVC൞ڎቓԛᇏᆸथҦაڄགҦᆭࡗ֥ଽᄝܱ༢bࠎႿՎ,Ч໓൮༵ՖНွථުཛଢ֥Ӯۿۀੱཌྷܱ[1]bູࣉ၂҄ख़߂ڄགཛଢ֥ဒܙ࠹֥࢘؇,ิԛਔڄགሧࡅުဒۀੱ֥ྐݼ҂ಒק,ྟૌႄೆڄགཛଢ֥Ӯۿۀੱ[2]b࿐༝ݖӱ;ಖުᄎႨܿ߃ٚم,ᄝಒקؓڄགཛVCᄝԚሧൈಪູھڄགཛଢ൞Ӯۿ֥ᆃ၂൙ଢ֥ቋႪሧඣ֥ࠎԤഈ,ิԛਔࠎႿڄགཛଢࡱۀੱູA0,ࠧA0=P(S),A0ॖुቔVCಪູھڄࡎᆴ֥ቋႪᇏᆸൈࠏଆ;ቋުؓቋႪᇏᆸൈࠏଆགཛଢӮۿ֥Ԛۀੱ(ၛ༯ࡥӫVC֥Ԛۀࣉྛਔෘ২ٳ༅bЧ໓ิԛ֥ቋႪᇏᆸൈࠏଆੱ),ପહVCಪູھڄགཛଢാϧ֥ԚۀੱູҀਔགྷႵ໓ངޭ൪ڄགཛଢྟ֥ಌ,ׄ൫-A0,ࠧ1-A0=P(F),ఃᇏ0<A0<1bࢳथٳࢨ؍ሧᇏྐ༏٢౦ྙ༯֥ቋႪᇏᆸथҦՖྟٳ༅֥࢘؇ট,ुު࿃ሧ֥थҦࠎԤ໙ี,ູڄགሧࡅࠣൈaᆞಒቓԛᇏᆸथҦิ܂ҕᄝႿྐ༏֥ࠆ౼bЧ໓ࡼᄝૄ۱ሧࢨ؍(थҦ)ׄॉbࠆ౼֥ྐ༏ٳູݺྐݼބߊྐݼਆো,ၹՎഡVCᄝૄ۱ሧࢨ؍ܴҳ֞ؽჭྐݼgbst={st,st},ః2 ଆ֥ิԛᇏt൞ሧࢨ؍,൞֥,t=0,1,,,Tbၛݺྐ211 ࡌഡࠣэਈࢳݼູ২,ݺྐݼԛགྷ֥ۀੱᇶေ൳ଽളၹބຓളଖڄགཛଢ֥Էದ(ၛ༯ࡥӫEN)ႚႵଖཛၹ႕ཙbଽളၹЇওVC֥ሧඣaڄགཛህ০,ಌك࣮ބؿᅚ(R&D)෮ླေ֥ሧࣁ,ࣜଢ֥ದ৯ሧЧބႵྙሧӁ֩;ຓളၹЇওݓࡅޡܙೱ࿊ުڄགሧࡅ(ၛ༯ࡥӫVC)थקሧھܴߌބӁြᆟҦ֩၂ུ҂ಒקၹbູࡹଆٚ
#122#ᇏݓܵ॓࿐ 2009୍ь,Ч໓࿊౼VC֥ሧඣቔູ႕ཙݺྐݼԛགྷۀੱ֥ଽളၹbptֻູtࢨ؍ᄝڄགཛଢӮۿ่ࡱ༯ܴҳ֞ݺྐݼ֥ۀ,ੱࠧpt=Pg(st|S),ཁಖݺྐݼԛགྷ֥ۀੱptླေႮֻtࢨ؍VC֥ሧඣc(pt)थק,pt൞VCሧඣc(pt)֥ᄹݦඔbࡌקc(pt)აpt֥ཌྟܱ༢ູc(pt)=cpt,c>0(1)ఃᇏcູӁളݺྐݼ֥ш࠽ӮЧbૄ၂ࢨ؍ܴҳ֞ݺྐݼ֥ቋնۀੱູp(0<p<1),ֻ֒tࢨ؍ܴҳ֞ݺྐݼ֥ۀੱptI(0,p]ൈ,ᄹࡆVC֥ሧඣ൞ॖྛ֥bߐᆭ,֒VC1 ҂ሧඣ༯ުဒۀੱ֥ྐݼ࿐༝ݖӱ֥ሧඣӑݖc(p)ൈ,ݺྐݼԛགྷ֥ۀੱ҂߶ᄹࡆbՎॖᆩVC֥ުဒۀੱᄝܴҳ֞ߊྐ༏ުෛൈࡗෛሢڄགཛଢ֥ؿᅚ၍ط༯ࢆ,VCؓڄགཛଢ֥భࣟۋ֞ИܴbՖ1,VCࡼᇯ҄۷ྍؓڄགཛଢభ֥ࣟყ௹bೂݔॖुԛVC֥ުဒۀੱ༯ࢆ֥ږ؇ෛሧඣ֥ᄹVCᄝֻtࢨ؍ܴҳ֞ߊྐݼ,ᄵVC۷ྍఃؓڄགཛଢభ֥ࣟಪ്bࡆطᄹնbᆣиAt+1ູՎຓ,Ֆ1ᇏߎॖुԛ:֒VCؓڄགཛଢ֥VC۴ऌֻtࢨ؍ܴҳ֞ߊྐݼಪູھڄགཛଢӮۿ֥ᆃ၂൙ࡱ֥ުဒۀੱభࣟಪ്ࢠູಒקൈ(ࠧAt+1࣍Ⴟ0ࠇ1ൈ),ః(ၛ༯ࡥӫVC֥ުဒۀੱ)bުဒۀੱ༯ࢆ֤ࢠતbఃᆰܴၩၬᄝႿ֒At+1࣍1ൈ൞VCېېሧڄགཛଢൈ,Վൈ,VCಪູھ212 VCުဒۀੱ֥ྐݼ࿐༝ݖӱ۴ऌНွථ܄ൔ֤VCܴҳ֞ߊྐݼ֥ުဒۀڄགཛଢ߶Ӯۿ,ၹՎ,VCؓཛଢېېԛགྷ֥ߊྐੱݼ҂߶ᄝၩbܴҳ֞ߊྐݼൈࡗࢠӉ,VCAt+1൞VC༵ဒۀੱAtބVCሧඣcpt֥ݦඔ֥ުဒۀੱᄵ߶ࡆ༯ࢆ,หљ൞֒VCؓڄགཛଢ֥భࣟಪ്ࢠູଆൈ(ࠧAt+1࣍Ⴟ1/2ൈ),AAt(1-pt)t+1=At(1-pt)+1-A(2)ఃުဒۀੱ༯ࢆ֤ࢠॹ,ՎൈVCؓھཛଢ֥భࣟtཁಖࢠູИܴbطVCؓఃೞാྐྏ,ުުဒۀੱAt+1,ෛሢൈࡗ֥၍,ڄགཛଢಯીႵӮۿൈ,ުဒۀੱAt+1ӯ༯ࢆ൝bਸ਼ຓ,VCܴҳ֞ߊႿ0,༯ࢆږ؇ᄜՑࡨߏ,ުဒۀੱAt+1၂Ϯ҂ྐݼ֥ުဒۀੱAt+1ߎॖၛіൕູԚۀੱA0ބభ߶༯ࢆ֞ᆃ၂ࢨ؍,ၹՎՎభھཛଢၘФVCᇏᆸb213 ࠎႿڄགཛଢࡎᆴ֥ቋႪᇏᆸൈࠏଆtࢨ؍ܺሧඣ{cp0,cp1,,,cpt}֥ݦඔtؓႿڄགཛଢط,ႚႵԚۀੱA0֥ཛଢࡎA0F(1-ps)ᆴ֥ቋնᆴ൞ႮቋႪሧඣބቋႪᇏᆸൈࠏथקAs=0t+1=t(3)A֥bᄝVC֥ᇏᆸथҦቓԛު,҂߶ᄜႵሧඣ0F(1-ps)+(1-A0)s=0֥࿃bᇏᆸथҦׄॖၛ૭ඍູᇏᆸथҦൈ֥ൈࡗೂݔVCૄࢨ؍ؓڄགཛଢ֥ሧඣЌӻ҂ׄT,္ॖၛ૭ඍູᇏᆸथҦൈVC֥ުဒۀੱэ,ࠧpt=p,ᄵުဒۀੱAt+1൞ሧඣ֥ࡨݦඔATbؓႿ۳ק֥ሧඣ{cp0,cp1,,,cpT},Ⴎ(3)AA10(1-t+p)t+1=ൔ۴ऌНွථمᄵॖၛಒקᇏᆸथҦׄTཌྷؓႋAt+1(4)0(1-p)+1-A0ᄝ҂֥ሧඣ༯,VCܴҳ֞ߊྐݼ֥ު֥ުဒۀੱATbဒۀੱV(At)ֻູtࢨ؍ᄝVCቋႪሧඣ༯֥At+1֥࿐༝ݖӱೂ1෮ൕbקཛଢࡎᆴ,ቋႪ֥ሧඣॖၛ๙ݖܿ߃ં1:VC֥ުဒۀੱᄝܴҳ֞ߊྐݼުෛൈࡗ၍ط༯ࢆ,VCؓڄགཛଢ֥భࣟۋ֞И,ܴطࠆ౼,൮༵ॉ੮ቋႪᇏᆸथҦ֥ׄުဒۀੱATbཁVC֥ުဒۀੱ༯ࢆ֥ږ؇ෛሧඣ֥ᄹࡆطಖ,ཛଢࡎᆴсྶ҂ཬႿ0,ࠧVCՖሧᇏࠆ֤֥ᄹնb௹ຬ൬ၭ҂ཬႿሧӮЧ[1],ࠧᆣૼATpTR-cpT\0,pTI[0,p](5):Ⴎ(2)ൔ֤At+1ෛൈࡗt֥၍طࢆ,֮ၹّݖটඪ,ೂݔVCՖሧᇏࠆ֤֥௹ຬ൬ၭ
ֻ5௹ ܤ ប֩:ࠎႿڄགཛଢࡎᆴ֥ڄགሧቋႪᇏᆸൈࠏ࣮#123#ཬႿሧӮЧ,ࠧק2:(1)VC֥ቋႪሧඣ൞ቋն߄ሧATpTR-cpT<0(6)ඣcp,ᆰ֞ቋႪᇏᆸൈࡗT*ູᆸb(2)ڄགཛପહVC֥ቋႪथҦ൞ᇏᆸሧ,҂ᇏᆸ,ڄଢࡎᆴॖႮ༯ൔ۳ԛVT*(A0)=A0p(R-c)གཛଢໃট֥൬ၭᄵࡼࣉ၂҄༯ࢆbՖ(5)ൔބ(6)1-DT*(1-T*p)1-DT*ൔॖ֤ᇏᆸथҦ֥Ⴕིшࢸׄ-(1-A0)cp1-D(1-p)1-Db(3)ڄགATpTR-cpT=0ZA*=c/R(7)ཛଢ֥ቋႪᇏᆸൈࡗູႮT(7)ൔॖᆩ:ေࢆ֮ႵིшࢸׄA*,ॖᄹ*p) T={T|max(A1-DT(1-0p(R-c)ࡆܥק൬ၭRࠇᆀࢆ֮Ӂളݺྐݼ֥ш࠽ӮЧb1-D(1-p)ႮႿڄགཛଢࡎᆴބܴҳ֞ݺྐݼ֥ۀੱऎႵ-(1-A1-DT0)cp1-D)}ཌྟܱ༢,ೂݔቋު၂ՑሧؿളᄝT,ପહ,VC֥ቋႪ࿊ᄴ൞࿊ᄴᆣૼ:ࡌഡVCؓڄགཛଢ֥ሧඣषႿpT=pbၹՎ,ቋު၂ࢨ؍֥ڄགཛଢࡎᆴ֥ቋնᆴൈࡗࢫׄtࢲඏႿൈࡗࢫׄT,ٳљ࠺ູ{cpt,cpt+1,:ູ,,cpT},۴ऌ(9)ൔڄགཛଢࡎᆴॖၛ๙ݖᅼ२֥V(AT)=ATpR-cp(8)ڄགཛଢࡎᆴॖၛ๙ݖ༯૫֥ܿ߃ٚӱ־ٚൔіൕູTs-1֤:֞EDs-t((AspsR-cps)F(1-Arpr))(11)s=tr=tV(At)=max{AtptR-cpt+(1-Atpt)DV(At+1)}t-1ptF(1-Arpr)=1,۴ऌНွථمᄵ,Ⴎ(2)(9)r=t(9)ൔᇏVC֥ުဒۀੱAt+1ႮAtބֻtࢨ؍֥ൔॖ֤ሧඣs-1s-1cptथק,ॖႮ(2)ൔ۴ऌНွථمᄵ࠹ෘ֤֞b(9)ൔіૼਔҐ౼ሧඣcpt֥֒భࡎᆴFt(1-AArpr)=r)(12)r=tAF(1-psr=tބໃটࡎᆴbᄹնሧඣcpt,ෙಖᆰࢤ֝ᇁਔAt1-AtA=At+s-1(13)ሧӮЧ֥ᄹࡆ,൞္ᄹࡆ֒భݺྐݼԛགྷ֥ۀsF(1-pr)ੱބЧࢨ؍֥௹ຬ൬ၭAtptRbൈ,1-Atpt္ཌྷႋr=tֹࡨഒਔbೂݔڄགཛଢᄝֻtࢨ؍ᄝሧඣࡼ(12)ൔބ(13)ൔսೆ(11)ൔ,ॖ֤Ts-1EDs-tcp((AtpsR-Atcps)F(1-pr)-cps(1-t༯ಯໃӮۿ,ᄵުဒۀੱAt+1ࡼ࿃༯ࢆ,ཌྷႋs=tr=tֹӁളڄགཛଢ֥ӻ࿃ᆴV(At+1)bAt))(14)(9)ൔൈ္іૼᄝቋު၂ࢨ؍թᄝ֥ཛଢࡎVCᄝֻtࢨ؍Ґ౼ቋႪሧඣcpt,ᄵᆴაݺྐݼԛགྷۀੱpT֥ཌྟܱ༢bၹՎ,ᆺေ(14)ൔэູVC֥ުဒۀੱնႿႵིшࢸׄA*,VC֥ቋႪ࿊Tᄴ൞Ґ౼ቋն߄ሧඣcp,ൌགྷpt=ppt(AtR-c)+EDs-t((AtpsR-Atcps)(1-,ڎᄵ֒s=t+1VC֥ުဒۀੱ൮ՑཬႿႵིшࢸׄA*ൈVCࣼᇏs-1ᆸሧbቋႪᇏᆸൈࡗࣼ൞ᄝVCҐ౼ቋն߄ሧpt)F(1-pr)-cps(1-At))(15)r=t+1ඣcp֥౦ঃ༯,ުဒۀੱ҂ཬႿႵིшࢸׄA*ཁಖ(15)ൔބptӯཌྟܱ༢,ေ(15)ൔ౼֤֥ӻ࿃ൈࡗbၹՎ,ቋႪᇏᆸൈࡗT*ॖၛႮ༯ൔቋնᆴ,ᄵpt=p,ࠧVCႋҐ౼ቋն߄֥ሧඣ۳ԛcp,ᆃ൞VC֥ቋႪ࿊ᄴbࣉطॖᆩᄝૄ၂۱ࢨT*p)؍VCႋҐ౼ቋն߄֥ሧඣᆰᇀᇏᆸሧbT=maxTA0(1-|A0(1-Tp)+1-A\A*0ೂ(10)ൔପဢקၬቋႪᇏᆸൈࡗູT*,ps=p,(10)s=t,t+1,,,T*,ᄵॖၛ֤֞(10)ൔᇏTູᇏᆸथҦ֥ൈࡗׄbཁಖ,ڄགT*ཛଢ֥ቋႪᇏᆸൈࡗT*౼थႿVC֥ԚۀੱVT*(At)=EDs-t(As-ttp(R-c)(1-p)-cp(1s=tA0,ࠧT*=T*(A0)bቋႪᇏᆸൈࡗT*ູՖҕა-At))(16)ሧൈVC֥ԚۀੱA0֞ުဒۀੱ൮ՑཬႿႵི֒t=0ൈ,ॖ֤шࢸׄA*֥ൈࡗࡗۯbॖ۴ऌ(9)ൔ֥־໙ี֤1-DT*(1-T*p)֞Ⴕི֥ሧඣބڄགཛଢࡎᆴ֥ቋնᆴbVT*(A0)=A0p(R-c)-(11-D(1-p)
#124#ᇏݓܵ॓࿐ 2009୍1-DT*ಪູھڄག-AVCᆭ෮ၛሧھڄགཛଢ,൞ၹູ0)cp1-D(17)ཛଢ֥Ӯۿۀੱࢠն,ܣՎԩVC֥ԚۀੱࢠնbVC൞ሔӑح൬ၭ֥,ࠧڄགཛଢࡎᆴсྶࡌഡ၇ऌ311ᇏ֥ٚم,۲ၘᆩҕඔಒקࢲݔіնႿਬ,ᇏᆸൈࠏູཛଢࡎᆴൌགྷቋն߄֥ൈࠏb1,ఃᇏі1ᇏ֥A0іൕVCಪູھڄགཛଢӮۿࡼ(17)ൔᇏ֥T*ႨTูߐ,ॖࡼఃཿӮ၂Ϯྙൔ,֥Ԛۀੱ;pіൕૄ၂ࢨ؍ܴҳ֞ݺྐݼ֥ቋնࠧۀ;ੱcіൕӁളݺྐݼ֥ш࠽ӮЧ;Rіൕᅼ२;ੱV-DT(1-Tp)T(A0)=A0p(R-1c)(1-RіൕڄགཛଢӮۿӁള֥໗ק൬ၭb1-D-(1-p)A1-DT1 ҂ሧඣ༯ުဒۀੱ֥ྐݼ࿐༝ݖӱ0)cp1-D(18)ApcRRቋႪᇏᆸൈࠏູ01950172@1090198@109T*={T|max(A0p(R-1-DT(1-Tp)c)1-D(1-p) ࡼі1ᇏ֥۲ҕඔս(ೆ7)ൔބק2,൮༵Ⴎ(7)ൔᆩ:A*=c/R,ܣA*=0125b-(1-A1-DT0)cp1-D)},ᆣиbႮק2ᆩ:TT3* ෘ২ٳ༅ T=WB{T|max(A0p(R-1-D(1-p)c)1-D(1-p)311 ҕඔ֥ಒק-(1-A1-DT0)cp1-D)}(19)ᄝଆᇏ,Ⴈ֥֞ҕඔᇶေႵA0,p,c,D,Rbҕඔ֥ಒקॖҐႨ֥ٚمᇶေႵ:ࡥֆ࠹مބህࡅ-DT*(1-T*p)VT*(A0)=A0p(R1-c)ၩم1-D(1-p)(֣غ٣م[18])b(1)A0֥ಒקbࡥֆ࠹م-(1-A1-DT*0)cp1-D(20):ᄝؓھڄགཛଢሧభ,VCॖᄝھཛଢ෮උྛြ࿊౼აھཛଢࡼ۲ҕඔսೆ(19)ൔ֤:ཌྷܱ؇ࢠ֥ۚཛଢቔູဢЧ,ഡဢЧಸਈູm,ࣜݖTT࠹ؿགྷ,ဢЧᇏ֥Ӯۿཛଢ܋n۱,ᄵॖၛႨဢЧ T|max(0195@017@6@109@1-019@0131-019@013ᇏԛགྷӮۿཛଢ֥ੱ(n/m)࣍රֹіൕھཛଢ-0105@017@2@109@1-019T)(21)Ӯۿ֥Ԛۀੱ,ࠧA0Un/m,֒ಖ,ဢЧಸਈᄀ011նѩ(ؓ21)ൔܱႿT,֝ѩھൔ֩Ⴟ0,Ֆط,A0֥ሙಒ؇ཌྷؓᄀۚb֣غ٣م:οᅶ֣غ٣م֥ӱ,ؓህࡅၩࣉྛሸކ,ࠧॖࠆ֤֤T*=318bA0֥ყҩᆴbՎຓࣉ၂҄ࡼ*T=318ս(ೆ20)ൔ:֤,္ॖၛࡼഈඍٚمࠁކႨ,Ґ౼ቆކT*T*ყҩඌ,ၛิۚყҩࣚ؇bV(1-p)T*(A0)=A0p(R-1-Dc)1-D-(1(1-p)*(2)p֥ಒקbॖၛҐႨ֣غ٣مყҩ֤֞,္ॖၛ๙ݖؓڄགሧ܄ඳۄህြದൖބຓ҆ህ-A1-DT0)cp1-D=512@109ࡅטҰ࠹ࠆ౼b۴ऌഈ໓֥࠹ෘࢲݔ,֤A*aT*ބVT*(A0),(3)c֥ಒקbႮڄགሧ܄ඳህြದൖࢲކਙႿі2bі2ᇏ֥ᇏᆸथҦ֥Ⴕིшࢸ;ׄT*іൕሧࣜဒބཌྷܱඔऌ,ุࠢษંथקbቋႪᇏᆸൈࡗ;VT*(A0)іൕቋႪᇏᆸൈࡗ෮ؓႋ(4)R֥ಒקbႮڄགሧ܄ඳህြದൖ۴ऌ֥ڄགཛଢࡎᆴb൧ӆ߭Б,ѩࢲކሧࣜဒބཌྷܱඔऌࠆ֤b(5)D֥ಒקbᇶေ۴ऌі2 ໃᆩҕඔ࠹ෘࢲݔVC֥ڄགሧЧӮЧটಒקbA*VT*(A0)T*0125512@109318312 ෘ২ࡌഡVCؓ؟۱ڄགཛଢೱ࿊ުಒקሧଖڄ313 ૹۋྟٳ༅གཛଢ,ѩVCႨٳࢨ؍ٚൔሧ,ၹՎթᄝᇏ(1)҂ሧඣؓᇏᆸൈࠏ֥႕ཙᆸሧ֥ॖିbႋႨЧ໓ิԛ֥ቋႪᇏᆸൈࠏଆႮק1ބ1ॖᆩ:VCؓڄགཛଢ֥ሧࣉྛᇏᆸथҦٳ༅,ླၘᆩҕඔAapacaRaRbਸ਼ຓ,ඣ҂,ᄵVC֥ުဒۀੱAt+1֥э߄ӱ؇൞҂
ֻ5௹ ܤ ប֩:ࠎႿڄགཛଢࡎᆴ֥ڄགሧቋႪᇏᆸൈࠏ࣮#125#၂ဢ֥bࣉ၂҄Ֆ1ၧॖुԛ,ሧඣp1>གཛଢቋႪሧඣ֥ࠎԤഈ,۳ԛࠎႿڄགཛଢp2,ᄝႵིшࢸׄA*ഈ,ቋႪᇏᆸൈࡗTp<Tpbࡎᆴ֥ቋႪᇏᆸൈࠏଆ,ູڄགሧࡅࠣൈaކ12ཁಖ,VCؓڄགཛଢ֥ሧඣᄀۚ,ᄝڄགཛଢቓԛᇏᆸथҦิ܂ં၇ऌ,္ູڄགሧࡅቓԛԛགྷߊྐݼ֥౦ྙ༯,VC֥ުဒۀੱ༯ࢆ֥ᄀॹ,ቋႪሧथҦิ܂ંҕॉbՎຓ,ଆ֥ٳ༅ູڄགཛଢᄀಸၞᇏᆸbھࢲં္ॖႮ(7)ൔބ(10)EN๙ӈؿള֥ཟ࿊ᄴྛູิ܂ਔކ֥ࢳbൔԛbЧ໓ิԛ֥ᇏᆸथҦଆԉٳॉ੮ਔڄགཛଢ(2)ڄགሧॖ॥ҕඔ֥ૹۋྟ֥ྍࣉᅚބߌ֥э߄ؓު࿃ሧथҦ֥႕ཙ,ࠣᄝڄགཛଢቋႪᇏᆸൈࠏଆᇏ,ؓENط,ൈ۴ऌཌྷܱ֥ྐ༏ؓڄགཛଢᄜܙ,ᄝ၂קӱ؇Ⴕུҕඔ൞҂ॖथק,֥ೂA0apaD;֩Ⴕུҕඔ൞ഈࡨཬਔVCᇶܴၣҩ֥ڄག,ิۚਔVC֥ሧॖ႕ཙ֥,ೂRac֩,༯૫Ч໓ࡼؓENॖ႕ཙ֥ҕथҦᇉਈbၹՎ,๙ݖྐݼ࿐༝ުቓԛ֥ᇏᆸथҦඔࣉྛૹۋྟٳ༅,Ֆطษંᆃུҕඔؓڄགཛଢԉٳॉ੮ਔྐ༏ؓᇏᆸथҦ֥႕ཙ,۷ژކሧൌᇏᆸൈࠏ֥႕ཙ,ೂ2a3෮ൕbbЧ໓ᄝ໓ང[19]֥ࠎԤഈ,࿊౼ਔڄགሧЧሧඣቔູଽളэਈॉ੮ڄགཛଢ֥ᇏᆸथҦ໙ี,ՖطՖଽള֥࢘؇ࢳथਔڄགཛଢ֥ᇏᆸथҦbၹՎ,Ч໓ิԛ֥थҦٚمࢠ໓ང[19]֥ࣚಒྟۚbھଆ֥ႋႨ౼थႿଆҕඔ֥ࠆ౼,ᄝڄགཛଢဢЧಸਈࢠն֥౦ྙ༯,ၞႿࠆ֤ଆᇏཌྷܱҕඔbطଢభ௴ђթᄝڄགཛଢဢЧಸਈࢠཬ֥໙ีbၹՎ,ླေڄགሧ܄ඳӉ௹֥ࠒބႵིЌթ,Ҍି۷ݺֹႋႨބܼھଆbਸ਼ຓ,Ч໓ູิ໙ีބܒࡹଆ,ؓ໙ีቔਔࡥ߄ԩ,ᆺॉ੮ଽ2 R֥ૹۋྟളэਈ(ڄགሧЧሧඣ)ؓݺྐݼԛགྷۀੱ֥႕ཙ,ીႵॉ੮ຓളэਈ֥႕ཙbၹՎ,ᄝ٢ॺࡌഡ֥ࠎԤഈປaܼଆ൞ૌࣉ၂֥҄۽ቔ!ҕॉ໓ང:[1]Guler,I..AstudyofDecisionMakingCapabilitiesandPerformanceintheVentureCapitalIndustry[M].2003:38-54.[2]Bergemann,D.,Hege,U..Venturecapitalfinancing,moralhazard,andlearning[J].JournalofBanking&Finance,1998,22:703-735.3[3]Bergemann,D.,Hege,U..Thefinancingofinnovation: c֥ૹۋྟLearningandstopping[J].TheRANDJournalofEco-Ⴎ2a3ॖᆩ,ڄགཛଢ֥ቋႪᇏᆸൈࠏაnomics,2005,36(4):Ӯّཟܱ༢,طაRӮᆞཟܱ༢bENބVC֥ଢ[4]߰ਞ.ڄགሧཛଢ֥ᇏᆸथҦ[J].ܵൗࢸ,2004,ѓ҂,EN֥ଢѓ൞ࠆ౼༯၂ࢨ؍ڄགሧЧॖି(12):131-132.ྟ֥ቋն߄[5]ဇ༩,ূ.ڄགሧཛଢᇏᆸथҦଆ࣮[J].॓,طVC֥ଢѓ൞෮ڄགཛଢ൬ၭ֥ቋն߄bམӉVC֥ሧᇛ௹ॖ๙ݖਆᇕࣥࣉ҄აؓҦ,2005,(12):100-103.ൌགྷ[6]ਾӑ.ڄགሧ֥ᇏᆸथҦሸඍ[J].۽ြඌࣜ࠶,:ᄹࡆܥק൬ၭR;ࢆ֮Ӂളݺྐݼ֥ш࠽ӮЧ,ᆃა(7)ൔ֤ԛ֥ࢲં൞၂ᇁ֥bھࢲં္ູ2006,25(3):152-154.[7]Sahlman,..Thestructureandgovernanceofven-EN๙ӈؿളཟ࿊ᄴྛູิ܂ਔކ֥ࢳbturecapitalorganizations[J].JournalofFinancialEco-nomics,1990,27: ࢲე[8]Powell,.,Puranam,P.,Singh,H..DecisionЧ໓ᄎႨۀੱંބܿ߃ં,ᄝಒקؓڄMakingPerspectivesonDueDiligenceFailure[M].
#126#ᇏݓܵ॓࿐ 2009୍2002:35-67.[14]ࣟ.R&DཛଢᇏᆸथҦ֥ཬѯຩଆൔ്љ[J].[9]Ryan,..WhySomeVentureCapitalistsEscalateܵ॓࿐࿐Б,2001,4(2):[J].[15]Dixit,.,Pindyck,..TheOptionsApproachAcademyofManagementJournal(BestPapersProceed-toCapitalInvestment[J].HarvardBusinessReview,ings),1995:,(May-June):105-115.[10]Edwards,W..ConversationinHumanInformation[16]Adner,R.,Levinthal,..:Heuristicstion:ConsideringboundariesfortheapplicationofrealandBiases[M].CambridgeUniversityPress,1982:optionstobusinessstrategy[J].,2004,29(1):74-85.[11]ڈႇर,Ϧౢ,࿒ڂ,࿐ಆ.R&DཛଢᇏᆸथҦ[17]Buell,..Whentoterminatearesearchanddeve-l֥თ႘ഝଆ[J].ܵ۽ӱ࿐Б,2004,18(3):69-opmentproject[J].ResearchManagement,1967,473.(x):275-283.[12]ࣟ,ဗྮ.ࠎႿᆦӻཟਈࠏބ၌Ԯෘم֥R&D[18]ޱুࡾ,ۚभभ,֣߲.ڄགఒြ֥ࣜቋႪࢳௗൈཛଢᇏᆸथҦᆐ؎[J].ᇏݓܵ॓࿐,2007,15(ህࠏଆ[J].༢۽ӱ࿐Б,2005,20:55-61.ࠠ):41-44.[19]ܤប,ᇛሷ٢.ࠎႿྍྖඌఒြྐݼ࿐༝֥ᇏᆸथҦ[13]ᇆ,ӧਪ,ᇒѯ.၂ᇕࠎႿڿࣉՙҡ֥ࠢR&Dᇏᆸٳ༅[J].॓ܵ,2009,30(2):157-165.थҦٚم[J].ᇏݓܵ॓࿐,2005,13(6):,ZHOUZong-fang2(11SchoolofEconomics,SichuanUniversity,Chengdu610065,China;21SchoolofManagementandEconomics,UniversityofElectronicScience&TechnologyofChina,Chengdu610054,China)Abstract:,,thusinfluencetheterminationdecisiontime1Aimingatthisproblem,fromtheviewofBayesianposteriorestimate,thispaperproposestheposteriorprobabilitysignallearningprocessofventurecapitalistfirstly;basedondeterminingtheopt-imalinvestmentamounttoventureproject,;andanumericalexam-plewhichanalysestheoptimalterminationtimemodelisgivenlastly1Theoptimalterminationmodelputforwardinthispaperconsiderstheinfluenceoftheincominginformationreleasingontheterminationtime,-turecapitalisttomaketerminationdecision1Atthesametime,,,:venturecapital;optimalterminationtime;dynamicprogramming;theefficientboundarypoint
