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1、DEPARTMENTOFUNIVERSITÀDEGLISTUDIECONOMICSANDSTATISTICSDITORINOWORKINGPAPERSERIESALMAUNIVERSITASTAURINENSISQuadernidelDipartimentodiScienzeEconomico-SocialieMatematico-StatisticheFoundedin1404ISSN2279-7114PORTFOLIOOPTIMIZATIONOVERAFINITEHORIZONWITHFIXE
2、DANDPROPORTIONALTRANSACTIONCOSTSANDLIQUIDITYCONSTRAINTSSTEFANOBACCARINDANIELEMARAZZINAWorkingpaperNo.17-January2013PortfolioOptimizationoveraFiniteHorizonwithFixedandProportionalTransactionCostsandLiquidityConstraintsStefanoBaccarina,,DanieleMarazzin
3、abaUniversitadegliStudidiTorino,DipartimentodiScienzeEconomico-SocialieMatematico-Statistiche,CorsoUnioneSovietica218/bis,10134Torino,Italy.bPolitecnicodiMilano,DipartimentodiMatematica,ViaBonardi9,20133Milano,Italy.AbstractWeinvestigateaportfolioopt
4、imizationproblemforanagentwhoinvestsintwoassets,arisk-freeandariskyassetmodeledbyageometricBrownianmotion.Theinvestorfacesboth xedandproportionaltransactioncostsandliquidityconstraints.Hisobjectiveistomaximizetheexpectedutilityfromtheport-folioliquida
5、tionataterminal nitehorizon.Themodelisformulatedasaparabolicimpulsecontrolproblemandwecharacterizethevaluefunctionastheuniqueconstrainedviscositysolutionoftheassociatedquasi-variationalinequal-ity.Wecomputenumericallytheoptimalpolicybyaaniterative nit
6、eelementdiscretizationtechnique,presentingextendednumericalresultsinthecaseofaconstantrelativeriskaversionutilityfunction.Ourresultsshowthat,evenwithsmalltransactioncostsanddistanthorizons,theoptimalstrategyisessen-tiallyabuy-and-holdtradingstrategywh
7、eretheagentrecalibrateshisportfolioveryfewtimes.ThiscontrastssharplywiththecontinuousinterventionsoftheMerton'smodelwithouttransactioncosts.Keywords:PortfolioOptimization,Quasi-variationalInequalities,TransactionCosts,ViscositySolutions1.IntroductionO
8、ptimalportfolioinvestmentstrategieshavebeenwidelystudiedintheliter-ature.Inhisseminalarticle,Merton(1969)developedacontinuoustimemodeltostudytheoptimalportfoliostrategyforaninvestormanagingaportfolioofriskyassets,whosepricesevolveaccordingtoge
