ֻ12ज୍2௹ܵ ॓ ࿐ ࿐ Б 2009ֻ4ᄅ ௹ຬໃটാჿඏ༯֥ቋႪሧ໙ี 郭福华1,邓飞其2(1.ᆄࡾഽٓն࿐۽അܵ࿐ჽ,ࣁ321004;2.ଲ۽ն࿐༢۽ӱ࣮෮,ܼᇜ510640)ᅋေ:在标准的Black Scholes型金融市场下,建立了期望未来损失(expectedfutureloss;EFL)约束下基于终端财富效用最大化的投资组合选择模型.运用鞅和优化方法,得到了一般效用投资者在投资计划期内任意时刻的最优财富和最优投资组合选择策略.在对数效用函数下,得到了投资者在投资计划期内任意时刻的最优财富和最优投资组合选择策略的显式表达式.ܱՍ:期望未来损失;效用函数;最优财富;最优投资ᇏٳোݼ: ໓ངѓ്:A ໓ᅣщݼ:1007-9807(2009)02-0054-060 ႄ ၹູVaRٚم֥ಌཊ,Artzner֩[3]ิԛਔ!၂ᇁڄག؇ਈ∀ᆃ၂ۀ.ಪູڄག൞၂۱႘ഝ #࣍؟୍টRn∃R,ೂݔ၂۱ڄག࠹ਈٚمᄝඔઆࠠބࣜ࠶,ݓଽຓྸ؟࿐ᆀᇁ৯ႿVaR(value at riskઆࠠഈ൞ކ,֥ᄵႋھડቀ༯૫่֥ࠫ܄[5]:)֥࣮,VaRࠧሧቆކᄝ۳ק֥ᇂྐඣ༯ࠣหק֥ሧ࠹߃௹ଽॖିᄥ൳֥ቋ1)ሇ၍҂эྟ܄.ഡX%Rn, ൞ӈඔ,ᄵնാ[1,2].၂؍ൈ௹ၛট,ࣁವ໓ངරެႵ۱ (X+ )= (X)- ,ఃࣜ࠶ၩၬ൞ೂݔࡼӈඔ܋֥ྐֆ໊֥ҕॉࣁವ۽ऎࡆೆ֞ሧӁቆކᇏಀ,ᄵᆺ,ପࣼ൞VaR൞ܵބ॥ᇅڄག֥Ⴕིٚم.ᆞೂ໓ངླေႵཌྷඔਈ֥ڄགҀӊ.ఃᆰࢤࢲݔ൞๙ӈ[2]ᆷԛ֥ପဢ,VaRٚمၘФࠎࣁܼࣜٗᄎႨ.ط,Ϙೖغၿྛࡓܵჴ߶෮໌֥ڄགሧӁ္൞թᄝڄག.֥ေၿྛᄎႨVaRٚمটथקჷႿ൧ӆڄགВ2)ᆞఊՑྟ܄.ؓၩ֥k&0,X%Rn,Ⴕ֥ሧЧԉቀྟေ.ಖط,໓ང[3]ԛགྷᆭު, (kX)=k (X),ఃࣜ࠶ၩၬ൞ೂݔӻႵሧӁཁಖಪ്֞VaRٚمѩ٤؇ਈބ॥ᇅڄག֥ॖժ֥ܿଆᆰࢤ႕ཙ֞ڄགҩ؇(২ೂႮႿӻႵሧौٚم,ၹູVaRٚم҂൞၂ᇁྟڄག؇ਈٚӁժնၛᇀႿሧӁੀྟᇗ၇ঠႿሧӁܿم[4].Szegoᆷԛ,၂Ϯඪট,VaRമᇀ҂൞၂ᇁଆ),ᄵႋھॉ੮ႮႿሧӁಌكੀྟջট֥ުྟڄག؇ਈٚم,ఃᇗಌཊ൞҂ડቀՑॖࡆྟ.ݔ,ၹູՎൈڄགၘ҂ࣇࣇ၇ঠႿໃটҍڶ࣪ᆴ.္ࣼ൞ඪ,ٳሧّط߶ᅱᇁ۷ն֥ڄག,ᆃཁھ܄္іૼᆃ֥ڄག൞ཌྟ၇ঠႿӻႵሧӁಖႵᙣႿMarkowitz֥ٳሧჰ.֒ಖ,ೂݔժ,ѩႋھх૧ڄགןࡆ֥ܿଆིႋ.ሧቆކᇏ෮ႵڄགሧӁ߭Бੱ֥৳ކٳ҃൞ງ3)Ցॖࡆྟ܄.ؓ X,Y%Rn, (X+Y) ౯֥,VaRડቀՑॖࡆྟ,ࠧ (X)+ (Y),ఃࣜ࠶ၩၬ൞ሧቆކॖၛٳVaR (P1+P2) VaR (P1)+VaR (P2)ሧڄག,ၹູቐшॖၛູܼሧቆކ֥ڄག,طᆃ,P1ބP2ᆷਆ۱ሧቆކ֥߭Б,ੱ ᆷᇂႷшіൕֆሧ֥ڄགሹބ.ྐඣ.4)ֆטྟ܄.ೂݔX Y,ᄵ (X)& ൬۠ರ௹:2005-08-16;ྩרರ௹:2007-12-21.ቔᆀࡥࢺ:ݒڞ(1969∋),ଳ,ଲၭဝದ,Ѱൖ,ࢃഽ.Emai:lscutgfh@
ֻ2௹ݒڞ֩:௹ຬໃটാჿඏ༯֥ቋႪሧ໙ี∋55∋ n(Y),ఃࣜ࠶ၩၬ൞ೂݔ၂۱ሧӁቆކݺႿਸ਼၂۱ሧӁቆކ,ᄵఃሧڄག္ႋھཬ၂,ུԮ֥dpi(t)=pi(t)bidt+) ijdBj(t)j=1(2)नᆴ-ٚҵथҦٚم҂ડቀھ่ࡱ.ቔэྙॖpi(0)=piᆩ֒X<0ൈ, (X)>0,ࠧՎԩ൞ႨᆞᆴіൕᆃT,B(∗)=(B1(∗),(,Bn(∗))൞קၬᄝջڄག.ੀۀੱॢࡗ(!,F,{Ft}0 t T,P)ഈ֥nົѓሙ҃ಖط,ଢభႨ֤ቋ؟֥ࠫᇕڄགҩ؇ٚمೂᄎ,༢ඔb=(b1,(T,bn)ࠣ =ٚҵaVaR҂൞၂ᇁڄགҩ؇,ᇶေ൞҂ડቀՑॖ{ ij}1 i,j n൞ܢௐ௹ຬ߭Бੱཟਈބѯੱइࡆ.ྟ္ࣼ൞ඪ֒Markowitzิԛ০Ⴈሧቆކॖၛᆔ,ૌડቀೂ༯ࡌഡ:ࢆ֮ሧڄག֥ჰൈ,ૌႨ֥ڄགҩ؇ᆷѓH1 bi>r,i=1,(,n;ಏ֝ᇁհ༂֥ሧቆކࢲݔ.ଢభದૌิԛਔ၂ུH2 T>0(٤߄่ࡱ)၂ᇁڄགҩ؇ᆷѓ,ఃᇏႨ֤ቋ؟֥൞่ࡱڄགᇿၩ,࣐ܵbބ ൞ൈэ,֥Ч໓ࡌקૌनູࡎᆴC[6~8]vaR(conditionalvalue at risk)aWCEӈඔ.n(w[9,10]orstconditionalexpectation)aES(expected[11]ሧቆކႮ)Ni(t)pi(t)ܒӮ,ᆃshortfall)֩.i=0ቋ࣍,໓ང[12]ᄎႨ!൳ཋ௹ຬാ∀ڄགNi(t)൞ᆷሧᄝֻiᇕܢௐpiഈ֥ܢඔ.ࡌഡԚҩ؇مট॥ᇅሧቆކ֥ڄག,ࡹ৫ਔ൳ཋ௹ຬҍڶູw(0)+w0>0,ၩൈख़t%[0,T]ാჿඏ༯ི֥Ⴈቋն߄ሧቆކ࿊ᄴଆ.൳ሧᆀ֥ሹҍڶ࠺ູw(t).ಸၞᆣૼ,w(t)ડቀෛཋ௹ຬാڄགҩ؇مડቀՑॖࡆྟaᆞఊՑྟࠏັٳٚӱࠣֆטྟ܄(҂ડቀሇ၍҂эྟ܄n).ၹՎdw(t)=w(t){[r1-)∀i(t)+i=1,൳ཋ௹ຬാٚمक़ڛਔVaRٚم҂ડቀՑॖࡆྟ֥ಌཊ.໓ངnnn[12]֥࣮іૼ,ა٤ڄག ܵᆀཌྷб)bi∀i(t)]dt+))∀i(t) ijdBj(t)}i=1i=1j=1,VaRڄགܵᆀሹ൞ቋႪֹ࿊ᄴڄགሧӁ֥۷նВ,ఃࢲݔ൞֒ാؿളൈ,߶ᅱ(3)ᇁ۷ն֥ാ;VaRڄགܵٚم༯֥௹ຬാൔᇏ,∀i(t)іൕൈख़tሧᄝֻiᇕܢௐഈ֥ҍ൞൳ཋ௹ຬാڄགܵٚم༯֥2~10П.ಖڶб২,ࠧط∀i(t)w(t)=Ni(t)Si(t),i=1,(,n,Ч໓ॉ੮֥൞௹ຬໃটാ(EFL)ჿඏ༯֥ቋႪሧ໙ี.ა൳ཋ௹ຬാཌྷб,௹ຬໃটႿ൞ാ҂ॉ੮ാ֥์གྷ(t)=)∀i(t)w(t)i=0n1 EFLჿඏ༯֥ሧቆކ࿊ᄴଆఃᇏ,∀0(t)=1-)∀i(t)൞ൈख़tሧᄝڄi=1གᅏಊᇏ֥ҍڶб২.ӫሧӁቆކݖӱ ࣁವ൧ӆ૭ඍ∀(t)=(∀1(t),(T,∀n(t))%Rnॉ੮ѓሙ֥Black Scholesࣁವ൧ӆ,ࡌഡູ၂۱ሧቆކ࿊ᄴҦ.൧ӆഈթᄝn+1ᇕሧӁ,෮Ⴕ֥ሧӁᄝሧ࠹֒ಖ,༢(3)ିཿӮཟਈྙൔ߃௹[0,T]ଽ৵࿃ࢌၞ.ఃᇏ၂ᇕሧӁູڄགdwT(t)=w(t){[r+(b-r1)∀(t)]dt+ᅏಊ,ఃࡎ۬ݖӱp0(t)ડቀӈັٳٚӱ ∀T(t) dB(t)}(4)dp0(t)=rp0(t)dtൔᇏ,1൞nົਙཟਈ,ఃૄ۱ჭູ1.(1)p0(0)=1൧ӆ֥ປಆྟၩሢթᄝຸ၂֥ሑࡎൔᇏ,r(>0)൞ڄགᅏಊ֥০ੱ.ఃჅnᇕሧ۬ૡ؇ݖӱ#(t),ડቀෛࠏັٳٚӱӁູܢௐ,ఃࡎ۬ݖӱpi(t)(i=1,2,(,n)ડቀd#(t)=-#(t)[rdt+∃TdB(t)](5)ෛࠏັٳٚӱൔᇏ,#(0)+#0;∃+ -1(b-r1)൞ڄག൧ӆࡎ
∋56∋ܵ ॓ ࿐ ࿐ Б2009୍4ᄅ۬ݖӱ.1ቋުE[#(T){I[%#1#(T)]&(d)+(t),ࡌקིႨݦඔu(x)൞ਆՑ৵࿃ॖັ,۬־ᄹ,۬χݦඔ,ડቀI[min%1#(T),u,(w0-c)]}[1-&(d)]F|t]limu,(x)=−,limu,(x)=0x∃0x∃ఃᇏ,%1൞٤ڵӈඔ,Ⴎൔ(14)ಒק;&(d)൞ѓ−ൈ,۬־ᄹ,৵࿃֥ш࠽ིႨݦඔሙᆞ࠹ٳ҃ݦඔ2u'#(0,−)∃(0,−)Ⴕ۬־ࡨ,৵࿃֥ݦඔ#/∃/ln#+r+TI#(0,−)∃(0,−).0(2)u,(w0-w)d=;#= EFLჿඏ༯֥ሧቆކ࿊ᄴଆ/∃/T%.1ᆞೂႄᇏ෮ᆷԛ֥VaRٚم֥ಌཊ,Ч໓ᆣૼ ഡ٤ڵӈඔ%1a%2ູঘ۬ರӰሰ,ҐႨEFLٚمট॥ᇅሧቆކڄག(ა໓ང[12]࠺ঘ۬ರݦඔL(w(T);%1,%2)ູ֥൳ཋ௹ຬാཌྷб,EFL҂ॉ੮ാ֥์གྷ),L(w(T);%1,%2)=Eu(w(T))-ఃඔ࿐іղൔູ %1{E[#(T)w(T)]-#0w0}-E[(w0-w(T))1{w0-w(T)&w}] c(6) %2{E[(w0-w(T))1{w0-w(T)&w}]-c}ൔᇏ,ᚐᆴwຓള۳ק;c൞ӈඔ;w0൞ሧᆀ֥ᄵԚҍڶ;w(T)൞ᇔ؊ҍڶ;w0-w(T)іൕ∋Lሧᆀ֥ໃটാ=E[u,(w(T))-%1#(T)+.ൔ(6)֥ࣜ࠶ݣၬ൞၂֊ാ∋wؿള(ӑݖᚐᆴw),ေनໃটാ҂ӑݖ۳ %21{w0-w(T)&w}]ק֥ଖӈඔc,ႮႿ∋LE∋w=0,֤[(w0-w(T))1{w0-w(T)&w}]=u,(w*(T))=%1#(T)-%21{w0-w*(T)&w}(8) E[(w0-w(T))w(T) w|0-w].(1)ೂݔw0-w*(T)<w,ᄵEFLჿඏ҂ఏ P(w(T) w0-w)ቔႨ,Ⴎൔ(8)ᆩၹՎჿඏ(6)࠻!Ӳـ∀ਔໃটാؿള֥ۚۀu,(w*(T))=%1#(T),ੱႻ!Ӳـ∀ਔ၂֊ാؿളൈ֥ۚनໃটၹՎቋႪᇔ؊ҍڶູാ[12].w*1(T)=I(%1#(T))ᄎႨ᷉ٚم,ࡹ৫ೂ༯EFLჿඏ༯֥ሧቆ(2)ೂݔw0-w*(T)&w,ᄵႮൔ(8)ᆩކ࿊ᄴଆu,(w*(T))=%1#(T)-%2(9)maxE[u(w(T))]w(T)۴ऌ%2{E[w0-w*(T)-c]}=0,ᆩ֡s..tE[#(T)w(T)]=#0w0 ֒E[w0-w*(T)-c]>0ൈ,%2=0; E[(w0-w(T))1{w0-w(T)&w}] c(7)0֒E[w0-w*(T)-c]=0ൈ,%2>0,ఃᇏ,ֻ1۱ჿඏູყෘჿඏ,ֻ2۱ჿඏູEFLw*(T)=w0-c(10)ჿඏ.ࡼൔ(10)սೆൔ(9)֤u,(w0-c)=%1#(T)-%22 ଆࢳࠧ%2=%1#(T)-u,(w0-c)ࢳEFLჿඏ༯֥Ⴊ߄໙ี(7),ק1აקၹՎ2ٳљ૭ඍਔ၂ϮིႨሧᆀᄝሧ࠹߃௹%2=max(0,%1#(T)-u,(w0-c))(11)[0,T]ଽၩൈख़t֥ቋႪҍڶބቋႪሧቆކቋު,ࡼൔ(11)սೆൔ(9)֤࿊ᄴҦ.u,(w*(T))=min(%1#(T)-u,(w0-c))ק1 ၂ϮིႨሧᆀᄝሧ࠹߃௹[0,ࠧT]ଽၩൈख़t֥ቋႪҍڶF(#(t),t)ູw*2(T)=I(min(%1#(T),u,(w0-c)))
ֻ2௹ݒڞ֩:௹ຬໃটാჿඏ༯֥ቋႪሧ໙ี∋57∋ၹՎ,ቋႪᇔ؊ҍڶູ1 =E[#(T)(I(%#1#(T))&(d)+w*(T)=P{w(t)0-w*(T)<w}w*1(T)+ I(min( [1-P{w0-w*(T)<w%}1#(T),u,(w0-c))).]w*2(T)(12 (1-&(d)))F|t](15))༯૫࠹ෘ*P{wᆣи.0-w(T)<w}.࠺#=u,(wק2 ೂݔ၂ϮིႨሧᆀᄝሧ࠹߃௹0-w)%,Ⴟ൞[0,T]ଽၩൈख़t֥ቋႪҍڶF(#(t),t)ܱႿ1P{w0-w*(T)<w}#(t)ؽՑ৵࿃ॖ,ັܱႿt၂Ցॖ,ັᄝ(#(t),t)ऎႵ৵࿃ொ֝ඔ,ପહቋႪሧቆކ࿊ᄴҦູ =P{I(%1#(T))>I(%1#)} =P{ln#(T)<ln#}∀(t)=-w-1(t)#∋F(t)∋# -1∃(16)Ⴎൔ(5)ࠣIT ັٳ܄ൔᆩ2ᆣૼ Ⴎ؟ჭIT ັٳ܄ൔᆩln#(T)=ln#/∃/0-r+T-∃TB(T)dF(#(t),t)2∋FF21∋F2 =d#∋t+dt+2d1#,#2(t)E∋#∋t2[ln#(T)]=ln#0-/∃/T∋#r+2∋F∋F1ၹՎ =[-#(t)r++#2(t)∋t2/∃/]dt-∋# P{ln#(T)<ln#}∋F ∋##(t)∃TdB(t)ln#-Eln#(T) =Pln#(T)-Eln#(T)<ਸ਼ຓ,Ⴎൔ(4)ᆩҍڶݖӱູVar(ln#(T))Var(ln#(T))#2dw(t)=wT(t)[(r+(b-r1)∀(t))dt+ln+/∃/T ∀T(t) dB(t)]r+ =ၹູᆃਆ۱ݖӱ൞֩ࡎ,֥бࢠఃѯཛ֤/∃/T∋F-#(t)∃T=w(t)∀T(t) #2/∃/∋#lnr+T#+02d=,֤ࠧၹՎ/∃/T∀-1(t)=-w(t)#∋F(t) -1∃ᆣи.∋#P*{w0-w(T)<w}=&(d)ሸഈ,Ⴎൔཁಖ,ᆺေᆩ֡ၩൈख़t֥ቋႪҍڶw(t),ь(12)ॖၛ֤֞ॖႮൔ(16)֤ھൈख़֥ቋႪሧቆކ࿊ᄴҦ.w*(T)=I(%1#(T))&(d)+ I(min(%1#(T),u,(w0-c))).3 ؓඔིႨݦඔ༯֥ቋႪҍڶބ (1-&(d))(13)ၹູၩൈख़tሧᆀ֥ቋႪҍڶF(#ሧቆކ࿊ᄴҦ(t),t)ູοቋႪᄹӉݖӱ#(t)ሧղ֞w*(T)֥ሧӮЧ[13],ܣႵק3ࠣק4۳ԛਔؓඔིႨݦඔ༯ሧ#ᆀᄝሧ࠹߃௹[0,T]ଽၩൈख़t֥ቋႪҍڶ0w0=E[#(T)w*(T)F|0]ބቋႪሧቆކ࿊ᄴҦ֥ཁൔіղൔ. =E{#(T)[I(%1#(T))&(d)+ק3 ࡌഡིႨݦඔu(w)=lnw,ᄵሧ I(min(%1#(T),u,(w0-c))).ᆀᄝሧ࠹߃௹[0,T]ଽၩൈख़t֥ቋႪҍڶ (1-&(d))]|F0}(14)F(#(t),t)ॖၛཁൔֹіൕູႮՎൔьॖಒק%1.ਸ਼ຓ,ሧᆀᄝሧ࠹~߃௹F(#1(t),t)=%&(d)+[0,T]ଽၩൈख़t֥ቋႪҍڶູ1#(t)F1(#(t),t)=E#(T)w*(T)F {#|t(t)%&(d)+exp[-r(T-t)].1#(t)
∋58∋ܵ ॓ ࿐ ࿐ Б2009୍4ᄅ~E[#(T)]=#0exp{-rT} (w0-c)(1-&(d))}(1-&(d))21-#Var(#(T))=/∃/T0exp{-rT}~%1(w0-c)d=ၹՎ/∃/Tൔᇏ,%1൞٤ڵӈඔ,Ⴎൔ P#1(T)<%=P.(14)ಒק.1(w0-c)ᆣૼ ၹູu(w)=lnw,ᄵ11#(T)-E[#(T)]%-E[#(T)]1(w0-c)u,(w1)=,I(x)=<wx{Var[#(T)]Var[#(T)}]Ⴎק1֤֞1-#0exp(-rT) F(#(t),t)==&%1(w0-c)1/∃/T#E{#(T)[I(%1#(T))&(d)+(t)I(min(%1#(T),u,(w0-c)))(1-&(d))]F|t}1-#0exp(-rT)(1)ೂݔ~%1(w0-c)d=min(%1#(T),u,(w0-c))=%1#(T)/∃/Tࠧ#1Ⴟ൞(T)<%,ᄵ1(w0-c)1P#1~(T)<%=&(d)1(w0-c) F1(#(t),t)=E{#(T)[I(%1#(T)).#(t)ሸഈॖ֤ &(d)+I(%1#(T))(1-&(d))]}F(#(t),t)1~~=%=F1(#(t),t)&(d)+F2(#(t),t)(1-&(d))1#(t)1(2)ೂݔ=[%m1#&(d)+exp{-r(T-t)}].(t)in(%1#(T),u,(w0-c))=u,(w0-c)~1~ࠧ (1-&(d))+%&(d)(17)#(T)&1%,ᄵ1#(t)1(w0-c)ᆣи.F2(#1(t),t)=#E{#(T)[I(%1#(T)).(ק4 ࡌഡིႨݦඔu(w)=lnw,ᄵሧt)ᆀᄝሧ࠹߃௹[0,T]ଽၩൈख़t֥ቋႪሧ &(d)+I(u,(w0-c))(1-&(d))]F|t}ቆކ࿊ᄴҦॖၛཁൔֹіൕູ =1E1[#(t)%&(d)+1∀1~(t)=%[&(d)+1#(t)w(t) #(T)(w0-c)(1-&(d))|Ft]~ &(d)(1-&(d))] -1∃Ⴎൔ(5)ࠣIT ັٳ܄ൔᆩᆣૼ Ⴎൔ(17)ᆩE[#(T)F|t]=#(t)exp{-r(T-t)}∋F=-1ၹՎ∋#%1#2.(t)~~F1 [&(d)+&(d)(1-&(d))]2(#(t),t)=%&(d)+1#(t)၇ק2֤֞ exp{-r(T-t)}(w0-c)(1-&(d))ဢ,ֹႮൔ(5)ࠣIT ັٳ܄ൔᆩ∀(t)=-w-1-1(t)#∋F(t) ∃∋#2#∃1(T)=#0exp-/r+/T-∃TB(T) =2% -1∃.1#(t)w(t)ᄵ~~ [&(d)+&(d)(1-&(d))]ᆣи.
ֻ2௹ݒڞ֩:௹ຬໃটാჿඏ༯֥ቋႪሧ໙ี∋59∋หљ൞,ᄝؓඔིႨݦඔ༯,֤֞ਔሧᆀᄝሧ4 ࢲඏე࠹߃௹ଽၩൈख़֥ቋႪҍڶބቋႪሧቆކ࿊ᄴҦ֥ཁൔіղൔ.ಖط,Ч໓ીႵॉ੮൧ӆ֥Ч໓ࡹ৫ਔ௹ຬໃটാჿඏ༯ࠎႿᇔ؊ҍଉ҈ၹ,бೂࢌၞӮЧࠇඥ൬ؓሧᆀቋႪҍڶིႨቋն߄֥ሧቆކ࿊ᄴଆ.ᄎႨ᷉ބႪڶބሧቆކ࿊ᄴҦ֥႕ཙ.ၹՎ,ଉ҈൧ӆࠎ߄ٚم,֤֞ਔ၂ϮིႨሧᆀᄝሧ࠹߃௹ଽႿ௹ຬໃটാ֥ቋႪሧ໙ีᆴ֤ࣉ၂࣮҄.ၩൈख़֥ቋႪҍڶބቋႪሧቆކ࿊ᄴҦ.ҕॉ໓ང:[1]:TheNewBenchmarkforControllingMarketRisk[M].NewYork:McGrow Hil,l1997.[2],FuturesandOtherDerivatives[M].UpperSaddleRiver:Prentice Hal,l2000.[3]ArtznerP,DelbaenF,EberJ,[J].MathematicalFinance,1999,9(3):203∋228.[4][J].JournalofBankingandFinance,2002,26(7):1253∋1272.[5]ۚಆ഻.ࣁವڄག࠹ਈંభခაႋႨ[J].ݓ࠽ࣁವ࣮,2004,(9):71∋ [J].StudiesofInternationalFinance,2004,(9):71∋78.(inChinese)[6]RockafellarRT, at risk:Forgenerallossdistribution[J].JournalofBankingandFinance,2002,26(7):1443∋1471.[7]AndersonF,MausserH,RosenD,[J].MathematicalProgramming,2001,89(2):273∋291.[8]KroknmalP,PalmquistJ,[J].JournalofRisk,2002,(2):124∋129.[9][J].JournalofMathematicalAnalysisandApplications,2003,286(1):237∋247.[10]:Thecomputationoftheworstconditionalexpectation[J].EuropeanJournalofOperationalResearch,2004,155(2):414∋425.[11]AcerbiD,[J].JournalofBankingandFinance,2002,26(7):1487∋1503.[12]BasakS, basedriskmanagement:Optimalpoliciesandassetprices[J].TheReviewofFinancialStudies,2001,14(2):371∋405.[13] timeFinance[M].London:Blackwel, hua,DENGF2ei ,ZhejiangNormalUniversity,Jinhua321004,China;,SouthChinaUniversityofTechnology,Guangzhou510640,ChinaAbstract:InthestandardBlack Scholestypeoffinancialmarkets,theportfolioselectionmodelbasedonutili tymaximizationfromterminalwealthundertheconstraintofexpectedfutureloss(EFL) ,underloga rithmicutility,:EFL;utilityfunction;optimalwealth;optimalinvestment
