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1、 Chp.4LifetimePortfolioSelectionUnderUncertaintyHaiLinDepartmentofFinance,XiamenUniversity,3610051.Introduction。Examinethecombinedproblemofoptimalportfolioselectionandconsumptionrulesforindividualinacontinuoustimemodel.TheratesofreturnaregeneratedbyWienerBrownian-motionprocess.。Particularcase:-Twoas
2、setmodelwithconstantrelativeriskaversionorisoelasticmarginalutility.Constantabsoluteriskaversion.2.DynamicsoftheModel:TheBudgetEquationW(t):thetotalwealthattimetXi(t):thepriceofithassetattimeti=1,2,.,m:;C(t):theconsumptionperunittimeattimetwi(t):theproportionoftotalwealthinvestedintheithassetattimet
3、,|C1,2,.,m.萱二W(煮)=1闯1Thebudgetequation。Attimet0,theinvestmentbetweent0andt(t0+h)is:历)一Co)P。Thevalueofthisinvestmentattimetis:艺(to)(P(o)-Cr“/丽.(0)r“丽锹C(加)(-Trn工Lrn玑菩君DJ0a)-C(a)刀-CQa)6=艺)fexpB(0州一CP(a)-CQo)刀一C(a)口Theprocessofg(t)。Supposeg(t)isthegeometricBrownianmotion.Indiscretetimey,82i(0A=(a一萼)乃十丛翼
4、Q:theexpectedreturnofasseti*:thevolatilityofassetA一MN(0.a3)-I(a)=公maJfexpa-马)5+AX-T0(a)-Ca)切-Cajh012)h+AITwoassetmodel(2)()-I(f)=Gvto)texp(Q-o/2)h+AIFJ-D+L-wojxexp(列-ID(F(o)J-CQa)切-CQo)r:EQa)QP(0-(to)=orGa)e+L-w(o)hJ(o)-C(o)h+O()=orQo)(Q-口+7W(o)-Co)p+O(D:EQo)Qr(0-I(o)吊=(o)W2(o)E(o)(A7)+O()二M2Co)W2()o2pQ=(0r(D(a-)+)T(0)-C(D)df+(DaZ(f)W()VQf.应()=or(D(a-力+7W(0)-C(0)TheobjectiveproblemImaxtE亘exp(C-pD)U(C(D)ar+B(7.77,5一CUO0,I(0)0:IP(0)=厂0:Ln(CJ0:;Lm(C)0
