ֻ18ज ֻ5௹ᇏݓܵ॓࿐, 2010୍ 10ᄅ ChineseJournalofManagementScienceOctober, 2010໓ᅣщݼ:1003-207(2010)05-0021-07需求随机时的存货质押贷款质押率决策研究张钦红1,赵泉午2(1.上海交通大学安泰经济与管理学院中美物流研究院,上海 200030;2.重庆大学贸易与行政学院,重庆 400044)ᅋ ေ:ླѯ֝ᇁ֥ڄག൞թࠊᇉವሧљႿႵࡎᆣಊᇉವሧ֥ᇶေٚ૫bЧ໓࣮ਔ֒թࠊ֥ླෛࠏѯൈ,ၿྛ֥ቋႪᇉੱथҦ໙ี,ѩབྷ༥ٳ༅ਔ҂֥ڄགொݺؓᇉੱ֥႕ཙ,ࢲંіૼڄགညذࠣാܿхൈ֥ᇉੱन֮Ⴟڄགᇏྟൈ֥ᇉੱbЧ໓ൈߎٳ༅ਔ֒ᇉੱ႕ཙվॻఒြ֥९թथҦൈ,ၿྛ֥ቋႪᇉੱथҦbቋު,๙ݖඔᆴෘ২ဒᆣਔ໓ᅣ֥ࢲંbܱՍ:թࠊᇉವሧ;ᇉੱ;नᆴ-ٚҵଆ;ാܿхᇏٳোݼ: ໓ངѓ്:A1 ႄ࣮Їও:BerlingބRosling(2005)࣮ਔࡎ۬ѯ֝ᇁ֥ҍༀڄགؓ९թथҦ֥႕ཙ[5];Xu&Birge୍ུ࣍ট,ݓଽຓ֥ᇙ؟ࣁವࠏܒ,ೂఋၿ(2006)ᄵٳ༅ਔ൧ӆླ҂ಒקൈቋႪ֥ളӁაҍྛaمݓϘၿྛaᅱഅၿྛ֩,षაҝԥࠣੀༀ৳ކथҦ[6];GuptaބWang(2009)࣮ਔॉ੮ఒြކቔԛਔթࠊᇉವሧڛༀbᄝھཛڛༀఒြࡗ֥അြྐႨൈ,ఒြ֥ቋႪ९թथҦ໙ี[7];ᇏ,ఒြࡼఃႚႵ֥թࠊቔູքЌ,ཟሧࣁิ܂ٚԛBabich(2010)ᄵٳ༅ਔ܂ႋഅթᄝҍༀڄགൈ,ᇅᇉ,ൈࡼᇉሇࢌ۳ऎႵކمЌܵӁሧ֥۬ᄯഅೂޅಒקቋႪ֥רܓބҍༀᆦӻҦ[8]bੀఒြ(ᇏࢺٚ)ࣉྛЌ,ܵၛࠆ֤վॻ(ၪ࿐֩,ݓଽ࿐ඌࢸؓթࠊᇉವሧြༀࣉྛਔࢠ؟֥2007[1])bթࠊᇉವሧᄝߏࢳఒြሧࣁ҂ቀ֥࣮,ၪ࿐(֩2007)ᄝӁࡎ۬ෛࠏѯິჿൈ,္ູၿྛaੀఒြิ܂ਔྍ֥০ᄹӉׄ,൞ڄགຓള่ࡱ༯,ٳ༅ਔ༯ҧڄགܿх֥ၿྛ֥ቋݓੀြაࣁವြ܋ܱᇿ֥ྍྖਵთbႪᇉੱथҦ[1];ၪ࿐֩(2007)ٳ༅ਔິჿڄགᄝթࠊᇉವሧြༀᇏ,၂۱ᇗေ֥ંބൌູᇗෛࠏٳ҃ൈ֥ᇉੱ໙ี[9];Ⴟ(2007)ॉ੮໙ี൞ೂޅಒקᇉ,ੱࠧվॻЧࣁაᇉթࠊַࡎ۬ڄགބੀྟڄག,ᄝິჿۀੱଽളࡌࡎᆴ֥бੱbଢభ࿐ඌࢸؓᆃ၂໙ี֥࣮؟ၛקഡ༯,ൈࢳྐվದ௹ຬ০ੱቋն߄֥০ੱބྟٳ༅ູᇶᇉੱਆ۱эਈ[10];ఊؽെ(֩2008)ၛվॻఒြູ,ཌྷܱ֥קਈ࣮ࢠഒbఃᇏ,Joki vuo࣮ؓའ,ٳ༅ਔೂޅؓ၂վॻఒြᇉ֥෮ႵlleބPeura(2003)࿖Merton֥ࢲܒ߄ٚم࣮ਔվॻാაᇉੱᆭࡗ֥ܱ༢[2];Cossഅಒק၂ᇉੱ[11]bՎຓ,ᇫ໓֩(2007)ؓinބHuang(2003)ࡼఒြ֥ິჿۀੱഡູຓളэਈ,֤թࠊᇉವሧᇏ֥ڛༀקࡎ໙ีࣉྛਔٳ༅[12]b֞ਔაၿྛڄགӵ൳ି৯ཌྷ၂ᇁ֥ᇉੱ[3];Buza ഈඍ࣮ࡼթࠊ֥ࡎ۬ѯڄག൪ູᇉြༀ֥ᇶေڄག,ٳ༅Վൈ֥ቋႪᇉੱथҦ,طࢠഒॉcottބZhang(2004)Ֆఒြ֥࢘؇࣮ࠎႿሧӁ֥ವሧ,ࡼၿྛڄགܵބఒြ९թܵཌྷࢲކ੮թࠊ֥ླ҂ಒקྟ෮֝ᇁ֥ڄགbൌ࠽ഈ,֒,ٳ༅ਔ০ੱބᇉੱ֥࿊ᄴࠣఃؓၿྛބఒြ႔০ੱ֥ࣇࣇॉ੮ࡎ۬ѯ֝ᇁ֥ڄག໙ีൈ,թࠊᇉವ႕ཙ[4]bᄝ܂ႋ৽აࣁವ֥ࢌҭਵთ,սіྟ֥ሧაఃႵࡎᆣಊᇉವሧѩൌᇉ֥ҵљ,ః҂ׄ۷؟ุ֥གྷᄝᇉࡎ۬ѯ֥ٚൔބܿੰ൬۠ರ௹:2009-10-10;ྩרರ௹:2010-09-12ഈbطᄝթࠊᇉವሧြༀᇏ,ႨႿᇉ֥թࠊቋࠎࣁཛଢ:ݓࡅሱಖ॓࿐ࠎࣁ(71001063),(71002070)ቔᆀࡥࢺ:ᅦޣ(1981-),ଳ(ݱቂ),νߪದ,ഈݚࢌ๙ն࿐νᇔ൞ေ๙ݖ൧ӆཧ൲ԛಀ,൧ӆؓթࠊླ֥նཬࣜ࠶აܵ࿐ჽ,Ѱൖ,ᇹ࣮ჴ,࣮ٚཟ:ູࡼथקሢᆃུթࠊ֥ࡎᆴbੀࣁವa܂ႋ৽ڄགܵ ႿՎ,Ч໓࣮ླѯ֝ᇁ֥ڄགؓթࠊ
22 ᇏݓܵ॓࿐ 2010୍ᇉੱथҦ֥႕ཙ,ऎุ࣮֒ᇉթࠊᄝᇉ௹ଌ૫ਢෛࠏླൈ,ၿྛ֥ቋႪವሧᇉੱथҦbఃᇏm(1+Ir)T-vqm,M pq=bၞ֤ၿྛ֥p-vൈ௹ຬ০ູ:,ॉ੮֞ൌᇏվॻఒြ؟ࡼᇉ֥ሧࣁႨႿࣉ၂֥҄ሔࡆթࠊ,ࠧᇉੱ္႕ཙ֞վॻఒြ֥ME[ b( )]=ᄎႏथҦ,ၹՎЧ໓ࣉ၂࣮҄ਔ֒ၿྛ֥ᇉੱ!{(p-v)x+qm[v- p(10∀थҦ႕ཙվॻఒြ֥९թथҦൈ,ၿྛೂޅಒקቋ+Ic)T]}f(x)dx+! pqmT(Ir-Ic)f(x)dx(3)MႪ֥ᇉੱbؓഈඍݦඔቋႪ߄ॖ֤ၿྛ֥ቋႪᇉ,ੱೂଁี1෮ඍb2 ڄགᇏྟൈ֥թࠊᇉੱ࣮ଁี1:֒ᇅᄯഅ૫ਢ֥ླڛՖ၂Ϯٳ҃ൈ,Ч໓֥ᇶေژݼࠣఃݣၬೂі1෮ൕbڄགᇏྟ֥ၿྛఃቋႪթࠊᇉੱູMin{1, *#,ࡌഡᇅᄯഅࡼඔਈູqmaཧ൲ࡎູ۬p֥Ӂཟၿྛԛᇉ,ѩࠆ֤ࣁحູF-1Ir-Ic()(p-v)+vqm pqm֥ᇉվॻbᆃఃᇏ *1-Ir=bᇉੱऎࡌഡࡎ۬ܥק,ູყ௹֥ໃটཧ൲ࡎ۬bᇅᄯഅpqm(1+Ir)Tᆦڱ֥վॻ০ੱູႵೂ༯֥ྟᇉ:∃ᇉ௹ཋᄀӉ,ᇉੱᄀ;֮%ᇉIr,վॻൈࡗູT,ၿྛ֥ሧࣁӮЧູթॻ০ੱIc,ູٚьٳ༅,҂ٞഡ০ੱູֆ০bඔਈᄀ؟ᇉੱᄀ֮bᄝᇉ௹ଌᆣૼ:(3)ൔॖࡥ߄ູ:,९թӁ૫ਢ֥ླູෛࠏэਈ,ః༵Mဒ֥ٳ҃ݦඔࠣۀੱૡ؇ູF(x),f(x).ᇉ௹E[ b( )]= pqm(Ir-Ic)T-!(p0ଌӁ֥ཧ൲൬ೆაໃཧ൲թࠊ֥җᆴᆭބ֮Ⴟႋ-v)F(x)dx(4)ᆦڱ֥Ч༏ބ,ᄵᇅᄯഅࠧິჿ,Վൈၿྛ൬֥߭ॻཛູᇅᄯഅ֥ཧ൲൬ೆࠣթࠊҗᆴ,ڎᄵၿྛࠆ֤ᄜႮ 2E( b)m(1+Irf(Mpq)T 2=-)<0p-vކჿܿק֥Ч༏bॖᆩE[ b( )]ູᇉੱ ֥χݦඔbᄜႮ၂ࢨ่ࡱ:і1 ژݼࠣఃݣၬ!E( b)ژݼݣၬ! =pqmT(Ir-Ic)-F(M)pqm=0(5)DӁᇔ؊ླcӁᇅᄯӮЧॖ֤ቋႪ֥ᇉੱ:ູpӁཧ൲ࡎ۬F-1Ir-Ic()(p-v)+vqm *1+IrvӁ௹ଌҗᆴ=(6)qmᇅᄯഅ֥թࠊᇉਈpqm(1+Ir)TIrᇉվॻ০ੱॉ੮֞ᇉੱсྶཬႿ1,ၹՎڄགᇏྟ֥ၿIcၿྛթॻ০ੱྛቋႪ֥ᇉੱູMin{1, *}. թࠊᇉੱTᇉൈࡗՖ(6)ॖၛुԛ,ෛሢᇉ௹ཋT֥ᄹࡆ,ቋႪF(x),f(x)ླ༵ဒٳ҃ࠣૡ؇ݦඔ֥ᇉੱ္ෛᆭࢆ֮bჰၹᄝႿ֒ֆ໊ൈࡗ֥ᇉ i( )০ݦඔi=b,rվॻ০༏ܥקൈ,ᇉ௹ཋᄀӉ,ᇅᄯഅႋ݂ߎ֥Ч༏ބᄀն,طᇅᄯഅ֥௹ຬ൬ೆ҂э,ၹՎິჿ֥ۀ ᄝഈඍࡌഡ༯,֒ቋᇔ֥ླડቀੱᄹࡆ,ູՎၿྛླေࢆ֮ᇉੱၛႋؓᆃ၂ڄགbpD+v(qm-D) pqm(1+Ir)TࠧՎຓ,ᇉੱॖࣉ၂҄іඍູF-1Ir-Ic(p-v)()+vD pqm(1+Ir)T-vqm (1)p- *1+Irqm=,ၹՎᇉੱაᇉvp(1+Ir)Tൈ,ᇅᄯഅࠆ֤֥ၘཧ൲൬ೆა࠱ଌഺჅӁ֥җඔਈӯڵཌྷܱܱ༢,ࠧᇉ֥թࠊᄀ؟,ᇉੱᄀᆴᆭބ֮Ⴟᇉ่ॻܿק֥Ч༏ބ,Վൈᇅᄯഅິ֮bჰၹᄝႿෛሢթࠊ֥ᄹࡆ,թࠊ҂ିཧ൲ԛಀჿ,ၿྛᆺିࠆ֤ཧ൲൬ೆބҗᆴb֥ۀੱ္ᄹࡆ,ၿྛ૫ਢ֥ڄགෛᆭᄹࡆ,ՎൈၿྛၹՎ,ၿྛ֥০ݦඔູ:္ླေࢆ֮ᇉੱၛַᇅᆃ၂ڄགbᆣиb b( )=3 ҂ڄགொݺ༯֥ᇉੱD(p-v)+qm[v- p(1+Ic)T],ifD M (2)pqm(Ir-Ic)T, otherwiseൌᇏ,ڄགᇏྟࠧ௹ຬ൬ၭቋն߄ສສѩ҂
ֻ5௹ ᅦޣ֩:ླෛࠏൈ֥թࠊᇉվॻᇉੱथҦ࣮ 23 ିࢳఒြ֥ྛູMM,Ⴍః൞ࡼڄག॥ᇅაܵቔູ2৫ྛᆭЧ֥ၿྛ,ఃؓڄགሹ൞ഡمܿх֥ѩ༐ຬ-2AB!F(x)dx-0!2AF(x)xdx(11)0ିܔಃޙ௹ຬ০ބڄགၛх૧ᄯӮն֥ാbၹMM22[E( 2)]=C+[!AF(x)dx]-2C0!A0Վ,༯໓ࣉ၂҄ٳ༅ၿྛᄝ҂ڄགொݺ༯֥ቋႪ F(x)dx(12)ᇉ,ੱѩაڄགᇏྟൈ֥ᇉੱࣉྛбࢠ,ૼಒڄགொݺၹؓᇉੱ֥႕ཙbᄵၿྛ০֥ٚҵॖࣉ၂҄ࡥ߄:ູMM3V( )=2A2M!F(x)dx-2A2F(x) ࠎႿनᆴٚҵଆ֥ቋႪᇉੱ0!0MMarkowitz(1952)ิԛ֥नᆴ-ٚҵٳ༅ٚم-[!2AF(x)dx](13)0(Mean-Variance)ູڄག-൬ၭ໙ีิ܂ਔປᆜ֥࠹ਈٳ༅ॿࡏ,ᄝࣁವሧਵთ֤֞ਔܼ֥ٗႋV( )ؓ ֝ॖ֤:MႨ[13]b୍࣍টᄝᄎႏܵਵთ֥࿐ᆀ္ष০Ⴈ!VT(1+Ir)नᆴ!F(x)dx! =2A[1-F(M)]pqm0-ٚҵٚمٳ༅Ԯ֥९թં,ChenބFe >0(14)degrouen(2000)ҐႨनᆴٚҵ֥ٚمٳ༅ਔБଆބ၂ུѓሙ֥ཋൈ؍֥९թଆ,ࢲંіૼՎൈ෮ၛၿྛ০֥ٚҵູᇉੱ ֥ᄹݦඔb֥९թרࠊਈေ֮Ⴟڄགᇏྟൈ֥רࠊਈູ֤௹ຬིႨቋն߄,ၿྛсྶൈॉ੮ః[14];০֥௹ຬބٚҵbקၬᇉੱ ൞ФᅝႪ(domi Mart nez-de-Alb nizބSimchi-Levi(2000)০Ⴈनᆴ-ٚҵଆٳ༅ਔ܂ႋഅ֥Ӊ௹Ґܓކ࿊ᄴ໙nated),֥֒ࣇ֒թᄝ ∋ડቀE[ ( ∋)](ีE[ ( )],V[ ( ∋)] V[ ( )],ਆ۱҂֩ൔсྶ[15]bࢹഈඍ໓ང,ࡌഡၿྛི֥Ⴈݦඔ:ູႵ၂۱ູ۬҂֩ൔ,ཁಖೂݔ ൞ФᅝႪ,֥ᄵఃU( )=E( )- V( )(7)ఃᇏ, >0іൕၿྛؓڄག֥ܿхӱ؇,ః౼҂ିൌགྷིႨ֥ቋն߄bᄝЧ໓ᇏ,֒ &[0, *]ൈE( ),V( )नᄹࡆ,ၹՎીႵ൞ФᅝႪ֥bطᄝᆴᄀնඪૼၿྛ֥ڄགညذӱ؇ᄀۚbV( )ູၿࡗ[ *,1]ଽ,E( )ູࡨཬ,طV( )ᄹࡆ,ၹՎ௹ྛ০֥ٚҵbଁี2۳ԛਔՎൈၿྛ֥ቋႪᇉੱbຬིႨ္ࡨཬ, नູՑႪࢳ,ᇉੱ҂߶ԩᄝھଁีࡗb෮ၛ,ቋႪ֥ᇉੱԩᄝࡗ[0, *]ଽb2:֒ၿྛູڄགܿх֥थҦᆀൈ,ః௹ຬིႨቋն߄֥ᇉੱၿྛི֥Ⴈݦඔູ::ູ *&argmaxU( ),ડቀM *U( )=C-(A+2 2AM!F(x)dx+2 2Amv *,ࠧڄགညذൈ֥ᇉੱ֮Ⴟڄགᇏྟൈ֥0ᇉੱbఃᇏMM, M!F2(x)xdx+ A2[!F(x)dx](15)00U( )=C-(A+2 A2M)!F(x)dx+2 A20ᆣиbMM !F2ഈඍ௹ຬིႨ֥іղྙൔࢠູگᄖ,ၛಒק(x)xdx+ A2[!F(x)dx]00ఃχྟbॉ੮֞ᇉੱ֥౼ᆴٓຶ[ູ0, *],ၹᆣૼ:ၿྛ০֥ٚҵູՎॖၛҐႨ၂ົෆ෬֥ٚم,֤Ч໓֥ඔᆴෘ২V( )=E[ -E2( )]=E( 2)-[E( 2)](8)҆ٳࠧҐႨ၂ົෆ෬֥ٚمԛਔऎุ౼ᆴbၞᆩ: ാܿхൈ֥ቋႪᇉੱ 2b( )=ᄝ૭ඍၿྛ֥ڄག؇ൈ,M-Vଆࡌഡၿ2{D(p-v)+qm[v- p(1+Ic)]T},ifD Mྛູڄགܿх֥ࣜ࠶ᇶุ,ಖطభࣟં(prospect2[ pqm(Ir-Ic)T], otherwisetheroy)іૼࣜ࠶ྛູᇶุສສؓ൬ၭ֥ᄹࡆ൞ڄ(9)གܿх,طؓ൬ၭ֥ാ൞ڄགொݺ֥[16],ࣜ࠶ದA=p-v,B=qm[v- p(1+Ic)T],C=֥ᆃᇕྛູФӫູ)ാܿх∗(lossaversion)b pqm(Ir-Ic)TbᄵႵ:SchweitzerބCachon(2000)ٳ༅ਔാܿхൈ֥ 2Бଆ,ࢲંіૼാܿх֥ఒြ,ఃቋႪҐܓਈb( A2D2+B2+2ABD,ifD M)=(10)C2, otherwise֮Ⴟڄགᇏྟൈ֥Ґܓਈ[17];WangބScottࣉطॖ:֤(2007)ࣉ၂҄ٳ༅ਔാܿхؓ܂ႋ৽ླྀט֥႕E( 2)=[(B+AM2)-C2]F(M)+C2ཙ[18];ഫިҌ֩(2004)ᄵٳ༅ਔാܿхൈ֥קᇅ
24 ᇏݓܵ॓࿐ 2010୍ࡱҐܓ໙ี[19]bࢹഈඍ໓ང,pqmT(Ir-Ic)-F(M( *))pqm(1+Ir)T=0W-W0, ifW(W0(23)U(w)=∀(W-W(16)0),otherwise৳৫(22)(23)ൔॖ:֤ఃᇏ∀(1іൕၿྛؓാܿх֥ӱ؇,֒∀=1pqmT(Ir-Ic)-F(M( *l))pqm(1+Ir)T>ൈၿྛູࠧڄགᇏྟbWіൕཧ൲࠱ࢫࢲඏൈၿpqmT(Ir-Ic)-F(M( *))pqm(1+Ir)T(24)ྛ֥০,طW0іൕၿྛ֥ҕॉ০,ᆃ҂ٞࡌࣉطॖ֤F(M( *l))<F(M( *)),ၹՎႵ *lഡູਬbଁี3۳ԛਔՎൈၿྛ֥ቋႪᇉੱb< *bଁี3:֒ၿྛູാܿх֥थҦᆀൈ,ఃቋႪᆣиb֥ᇉੱ *lડቀ၂ࢨ่ࡱ:4 ᇅᄯഅሔࡆളӁൈ֥ᇉੱpqmT(Ir-Ic)-F(M( *l))pqm(1+Ir)T-F(D0( *l))(∀-1)pqm(1+Ic)T=0ൌᇏ,ࢹॻఒြࠆ֤֥վॻສສေႨႿঔնՎൈ֥ᇉੱ֮Ⴟڄགᇏྟൈ֥ᇉ,ੱࠧളӁࠇሔࡆ९թ,Վൈ,ၿྛ֥ᇉ,ੱ္ࠧิ܂ሧႵ *ࣁ֥؟ഒࡼ႕ཙࢹॻఒြު࿃֥थҦ,ၹՎၿྛࣉl< *.ᆣૼ:ྛᇉੱथҦൈсྶॉ੮ࢹॻఒြ֥ު࿃ᄎႏथ b(D, )=D(p-v)+qm[v- p(1+Ic)T]=0ҦbЧ҆ٳࣉ၂҄ٳ༅֒վॻఒြࠆ֤֥ሧࣁႨႿሔࡆ९թൈ,ၿྛ֥ቋႪᇉੱb(17)ഈඍٚӱ֥ࢳູࠧD[ p(1+Ic)T-vႄႨഈ໓֥ჰႵࡌഡ,֒҂թᄝሧࣁჿඏൈ,ᇅ]qm0=bp-vᄯഅ֥০ݦඔູ:ఃݣၬູ:֒ቋᇔൌགྷ֥ླູD0ൈ,ၿྛൌགྷ႔ m(q)=pmin(D,q)+vmax(0,q-D)-cޙ,ط֒ླཬႿD0ൈၿྛ֥০ཬႿਬ,ڎ(25)ᄵնႿਬbၹՎ,ാܿх֥ၿྛ֥௹ຬིႨ:ູၞ֤ఒြቋႪ֥ളӁࠇҐܓਈ:ູDE*p-c[U( b( ))]=(∀-1)!0{(p-v)x+qm[vq=F-1()(26)0p-v- p(1+Ic]T}f(x)dx+E[ b( )](18)ࡌഡᇅᄯഅॖႨটളӁ֥ሱႵሧࣁູB,ѩડࣉ၂҄ࡥ߄:ູቀ҂֩ൔ*cq>B.ࠧᇅᄯഅીႵቀܔ֥ሧࣁളӁDEԛቋႪ֥ਈ,ՎൈᇅᄯഅԚ֥९թרܓਈࠇള[U( b( ))]=E[ b( )]-(∀-1)!0(p0Ӂਈູ:M-v)F(x)dx= pqmT(Ir-Ic)-!(p-v)F(x)dxB0q0=(27)cD0-(∀-1)!(p-v)F(x)dx(19)ູߏࢳሧࣁჿඏ,ᇅᄯഅॖࡼᆃུթࠊႨႿᇉ0ႮՎॖ֤ؽࢨ่ࡱ,ၛࠆ֤վॻ pq0,ᇅᄯഅࡼࠆ౼֥վॻႨႿሔ:!2E(U2ࡆሧ,ሔࡆު֥ሹ९թࠇളӁਈ:ູ)qm(1+Irf(M[p)T])-(∀-1)! 2=-**p-vq, if pq0(cq-Bq=(1+ (28))q0, otherwise [pqm(1+2Ir)T]f(D0)<0(20)p-vᄝ(28)ൔᇏ,ֻ၂ᇕ౦ঃіૼᇅᄯഅ๙ݖವሧࠧၿྛ௹ຬིႨູ ֥χݦඔ,ࣉطႮ၂ࢨ่طࠆ֤֥ሧࣁਈॖၛЌᆣఒြࡼ९թᄹࡆ֞ቋႪࡱ!E(U):! =0,ॖ֤ቋႪ֥ᇉੱડቀਈ*qbطᄝֻؽᇕ౦ঃ༯,ᇅᄯഅࠆ֤ವሧުಯࣸ:҂ିЌᆣఒြࡼ९թิശ֞*qbpqmT(Ir-Ic)-F(M( *l))pqm(1+Ir)TؓႿၿྛط,ႮႿླ֥ෛࠏ,ྟ֒ᇔ؊ླ-F(D0( *l))(∀-1)pqm(1+Ic)T=0(21)ડቀೂ༯่ࡱൈ,վॻఒြ֥ཧ൲൬ೆა௹ଌ९թࣉ၂҄ॖ֤:֥ࡎᆴᆭބࡼཬႿႋᆦڱ֥Ч༏ބbpqmT(Ir-Ic)-F(M( *l))pqm(1+Ir)T=pD+v(q-D) pq0(1+Ir)T(29)F(D0( *l))(∀-1)pqm(1+Ic)T>0(22)ࠧ:ఃᇏ *lіൕാܿхൈ֥ቋႪᇉੱb pq0(1+Ir)T-vqႮࠎЧଆ֥ٳ༅ॖᆩD :p-(30)v
ֻ5௹ ᅦޣ֩:ླෛࠏൈ֥թࠊᇉվॻᇉੱथҦ࣮ 25 ∀ pq0(1+Ir)T-vqN=,ᄵၿྛ֥০ູ:+Ic)T]f(x)dx+! pq0(Ir-Ic)Tf(x)dx(32)p-vN b( )=ᄝഈൔᇏ,ႮႿ *pq0(Iq, r-Ic)T, ifD(N if pq0(*cq-B(31)q=pD+v(q-D)- pq0(1+Ic)T,otherwise(1+ ,ၹՎႻॖၛ)q0,otherwiseၹՎ,ၿྛ֥௹ຬ০ູ:ࡼၿྛ֥௹ຬ০іղ(ູ33)ൔ:NE[ b( )]=![px+v(q-x)- pq0(10 E[ b( )]=N∀*!1*cq-B[px+v(q-x)- pq0(1+Ic)T]f(x)dx+! pq0(Ir-Ic)Tf(x)dx, if (0N1pq0(33)N∀!2{px+v[(1+ )q0-x]- pq0(1+Ic)T}f(x)dx+! pq0(Ir-Ic)Tf(x)dx, otherwise0N2 pq0(1+Ir)T-*vq ఃᇏ,NIc)T1=,(p-v)F-1p(Ir-()+vq0p-vp(1+Ir)T-v,ᄵቋႪ֥ᇉ pq0(1+Ir)T-vq0pq0(1+Ir)T-v(1+ )q0N2=bp-vੱॖಒקೂ༯:ཁಖၿྛ֥௹ຬ০൞ٳ؍ݦඔ,ᄝקၬთ(1)ಒקਆ۱קၬთଽ֥ቋႪᇉੱ: *1, *2;**cq-B*[,+∀)ބקၬთcq-B[0,]ഈऎႵ҂Ⴎχݦඔ֥ྟᇉॖ֤ *cq-B1=max( 1,), *2=pq0pq0pq0֥іղൔb*m-Bin( cq2,)ಸၞ֤௹ຬ০֥၂ࢨ֝ඔpq0:(2)ؓбE[ b( *1)],E[ b( *2)],ಒקቋႪᇉdE( b)d =,ੱࠧ: *pq&argmax{E[ b( *1)],E[ b( *2)]}(37)0(Ir-Ic)T-pq0(1+Ir)TF(N1)(34)pq0(Ir-Ic)T-[p(1+Ir)T-v]q0F(N2)ؽࢨ֝ඔ5 ඔᆴෘ২:2dE( b)Чࢫ๙ݖඔᆴෘ২ဒᆣ໓ᅣ֥ࢲ,ંѩٳ༅҂d 2=֥ҕඔ౼ᆴؓቋᇔᇉੱ֥႕ཙbpq0(1+Ir)T҂ٞഡܤग़ླູ[0,1]ഈ֥नᄋٳ,҃ᄵఃٳ-pq0(1+Ir)TF(N1)<0p-v҃ݦඔބૡ؇ݦඔٳљູ:F(x)=x,f(x)=1bѩpq0(1+Ir)T-vq0-[p(1+Ir)T-v]q0F(N2)<0p-vഡՎൈᇅᄯഅႨটᇉ֥ඔਈູ:qm=p-c,ఃݣp-v(35)ၬᄝႿᇅᄯഅ۴ऌෛࠏླ֥ٳ҃ݦඔ౼௹ຬ০ࠧၿྛ֥௹ຬ০ݦඔᄝਆ۱קၬთഈनູχݦඔ,ၹՎ,ၿྛ֥ቋႪᇉੱႋડቀ၂ࢨ่ࡱቋն߄֥Ґܓਈp-cp-cqm=F-1()=bࣉ၂҄:p-vp-v =۳۲ҕඔڮᆴೂ༯:p=100;c=80;v=40;T=2;Ic*=; =;∀=ᄝഈඍҕඔᇏ,T=2іൕ(p-v)F-1Ir-Ic()+vq1+*Irᇉ௹ཋູ2۱ᄅ,Ic=ູၿྛ֥ሧࣁӮЧ,ᄵ,if (cq-Bpq0(1+Ir)Tpq0(36)Ic)TႵ1qm=b(p-v)F-1p(Ir-()+vq30p(1+Ir)T-v,otherwise1۳ԛਔᇉੱෛվॻ০ੱބڄགொݺ҂pq0(1+Ir)T-vq0ൈ֥౼ᆴbՖ1ॖၛुԛ:(1)֒ၿྛູڄགܿх*(p-v)F-1Ir-Ic()+vqᄜࠇᆀാܿхൈ,ఃᇉੱ֮Ⴟڄགᇏྟൈ֥ᇉ 1+Ir1=; 2=pq0(1+Ir)Tੱ,ᆃაభඍࢲંཌྷژ;(2)ෛሢվॻ০༏֥ᄹࡆ,ቋ
26 ᇏݓܵ॓࿐ 2010୍Ⴊ֥ᇉੱ္ᇯࡶᄹࡆ,ᆃ၂གྷའ֥ჰၹᄝႿ০༏ٮႨᄀۚ,ၿྛՖᇉವሧြༀᇏࠆ֤֥ш࠽൬ၭ္ᄀ,ۚၹՎၿྛ჻ၩิ܂۷؟֥վॻ,ࠧഡᇂ۷֥ۚವሧᇉ,ੱՎൈၿྛ૫ਢ֥ڄག္۷,ۚဒᆣਔ൬ၭაڄགࡗ֥ؓႋܱ༢b3 ҂ᇉඔਈൈ֥ᇉੱ1 ҂ᇉ০༏ൈ֥ᇉੱ,E(ȴb( *2))=ၹՎ,ቋᇔ֥ᇉੱႋູ =2۳ԛਔ҂ᇉ௹ཋ༯ڄགᇏྟ֥ၿྛ֥ቋႪᇉੱ(ఃᇏIc=,Ir=)bࢲંіૼ6 ࢲე,ᇉੱෛᇉ௹ཋ֥ᄹࡆطࢆ֮,ᆃაଁี1֥ࢲЧ໓࣮ਔླෛࠏѯൈթࠊᇉವሧြༀંཌྷژbᇏᇉੱ֥थҦ໙ี,ᄝթࠊླڛՖ၂Ϯٳ֥҃ࡌഡ༯,ٳ༅ਔऎႵ҂ڄགொݺ֥ၿྛ֥ቋႪթࠊᇉੱb໓ᅣൈߎٳ༅ਔ֒վॻఒြࡼᇉࠆ֤֥ሧࣁႨႿളӁࠇሔࡆթࠊൈ,ၿྛೂޅಒקቋႪ֥ᇉੱbЧ໓֥ࢲંіૼ,ᄝڄགᇏྟ֥ࡌഡ่ࡱ༯,ၿྛ֥ቋႪᇉੱაᇉ௹ཋބᇉඔਈૡ్ཌྷ,ܱఃᇏᇉ௹ཋᄀӉ,ᇉੱᄀ֮;ᇉඔਈᄀ؟ᇉੱ္ᄀ֮b֒ၿྛູڄགܿхބാܿхൈ,ቋႪ֥ᇉੱ֮Ⴟڄགᇏྟൈ֥ᇉੱb֒վॻఒြࡼᇉ෮֤ሧࣁႨႿሔࡆթࠊൈ,ᇉੱ֮Ⴟ҂ॉ੮2ᆃ၂थҦൈ֥ᆴbླေᆷԛ֥൞ഈඍࢲંनࠎႿᆃ ҂ᇉ௹ཋൈ֥ᇉੱဢ֥ࡌഡ:֒ᇅᄯഅ֥௹ଌཧ൲෮֤ބഺჅ९թࡎ3ᄵཁൕਔڄགᇏྟൈᇉੱෛᇉඔਈ֥ᆴᆭބ֮Ⴟႋڱ֥Ч༏ބൈվॻఒြࠧິჿbᆃ၂э߄౦ঃ(ఃᇏIc=,Ir=,T=3)bࢲંࡌഡࢠູژކൌ࠽,ൌᇏ๙ݖᇉವሧڛༀࠆ֤ဢဒᆣਔ໓ᅣ֥ࢲ,ંࠧᇉੱෛሢᇉඔਈ֥վॻ֥ఒြສສ૫ਢሢࢠູࣅᅦ֥ሧࣁሑঃ,ၹՎᄹࡆطࢆ֮b၂֊ԛགྷഈඍ౦ঃఒြິჿ֥ۀੱ߶٤ӈնb֒ᇅᄯഅࡼᇉವሧࠆ֤ሧࣁႨႿࣉ၂֥҄ളࣉ၂֥࣮҄ॖၛٳ༅Ӂླෛࠏࡎ۬ѯӁൈ,B=16,Ic=,Ir=,T=3,ࠧሧࣁൈ֥ᇉੱ໙,ีൈթࠊᇉವሧ֥০༏ٮႨჿඏ֥ᇅᄯഅ֥ԚളӁਈູ໙ี္ᆴ֤ࣉ၂֥҄ധೆ࣮bq0=1,֮ႿቋႪ֥5ളӁਈ*1q=qm=b3ҕॉ໓ང:ࡼഈඍҕඔսೆ၂ࢨ่ࡱࠧ(36)ൔ,ॖ֤:[1]ၪ࿐,ڈ۶ᇏ,ྷ.ࡎ۬ෛࠏѯ༯թࠊᇉವሧ , if (=ြༀᇉੱ࣮[J].༢۽ӱંაൌ,2007,, otherwise(12):42-48.ࣉطႵ *1=, *2=;E( b( *1))=-[2]Jokivuolle,E.,Peura,S..Incorporatingcollateralval
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