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1、J.R.BirgeandV.Linetsky(Eds.),HandbooksinOR&MS,Vol.15Copyright©2008ElsevierB.V.AllrightsreservedDOI:10.1016/S0927-0507(07)15019-2Chapter19DynamicPortfolioChoiceandRiskAversionCostisSkiadasKelloggSchoolofManagement,DepartmentofFinance,NorthwesternUniversity,200
2、1SheridanRoad,Evanston,IL60208,USAE-mail:c-skiadas@kellogg.northwestern.eduAbstractThischapterpresentsatheoryofoptimallifetimeconsumption-portfoliochoiceinacontinuousinformationsetting,withemphasisonthemodelingofriskaversionthroughgeneralizedrecursiveutility.
3、Anovelcontributionisadecisiontheoreticde-velopmentofthenotionsofsource-dependentfirst-orsecond-orderriskaversion.Backwardstochasticdifferentialequations(BSDEs)areexplainedheuristicallyascontinuous-informationversionsofbackwardrecursionsonaninformationtree,anda
4、reusedtoformulateutilityfunctionsaswellasoptimalityconditions.TheroleofscaleinvarianceandquadraticBSDEsinobtainingtractablesolutionsisexplained.Afinalsectionoutlinesextensions,includingoptimalityconditionsundertradingcon-straints,andtractableformulationswithno
5、ntradeableincome.1IntroductionThischapteranalyzestheoptimalconsumption-portfoliochoiceofarisk-averseagent,withemphasisonthemodelingofriskaversiongivenastochasticinvestmentopportunityset.ThemainpartoftheanalysisisbasedonSchroderandSkiadas(2003).Anovelcontribut
6、ionisadecisiontheoreticdevelopmentofthenotionsofsource-dependentfirst-orsecond-orderriskaversionthatareimplicitintheutilityrepresentationsofSchroderandSkiadas(2003).Theseideasunify,atleastinthecontextofcontinuousinformation,standardnotionsofriskaversionwithsom
7、emodelsofambiguityaversionorrobustnessthathaverecentlyreceivedconsiderableattentionintheliterature.Thedynamicportfoliomethodologypresentedshould,however,alsobeofinteresttoread-ersonlyconcernedwithconventionalsource-independentriskaversioninadynamicsetting.Fol
8、lowingMerton’s(1969,1971)seminalwork,mostpapersondynamicportfoliochoiceassumethattheinvestormaximizestime-additiveexpected789790C.Skiadasutility,thatwerefertoas“additiveutility”forthepurp
