optimal dynamic asset allocation in a non–gaussian world

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1、Optimaldynamicassetallocationinanon–GaussianworldGianniPolaAbstract.AssetAllocationdealswithhowtocombinesecuritiesinordertomaximizetheinvestor’sgain.WeconsidertheOptimalAssetAllocationprobleminamulti-periodinvestmentsetting:theoptimalportfolioallocationissynthesisedtomaxi

2、misethejointprobabilityoftheportfoliofulfillingsometargetreturnsrequirements.Themodeldoesnotassumeanyparticulardistributiononassetreturns,thusprovidinganappropriateframeworkforanon–Gaussianenvironment.Anumericalstudyclearlyillustratesthatanoptimaltotal-returnfundmanagerisc

3、ontrariantothemarket.Keywords:assetallocation,portfoliomanagement,multi-periodinvestment,optimalcontrol,dynamicprogramming1IntroductionInthefinanceindustry,portfolioallocationsareusuallyachievedbyanoptimiza-tionprocess.StandardapproachesforOptimalAssetAllocationarebasedont

4、heMarkowitzmodel[15].Accordingtothisapproach,returnstochasticdynamicsaremainlydrivenbythefirsttwomoments,andasymmetryandfat-tailseffectsareas-sumedtobenegligible.Themodeldoesnotbehaveverywellwhendealingwithnon–Gaussian-shapedassetclasses,likeHedgeFunds,EmergingmarketsandCo

5、m-modities.Indeedithasbeenshownthatsometimesminimizingthesecondordermomentleadstoanincreaseinkurtosisandadecreaseinskewness,thusincreasingtheprobabilityofextremenegativeevents[3,10,22].Manyworkshaveappearedrecentlyintheliteraturethatattempttoovercometheseproblems:theseapp

6、roacheswerebasedonanoptimizationprocesswithrespecttoacostfunctionthatissensitivetohigher-ordermoments[2,11,12],oronageneralisationoftheSharpe[21]andLintner[14]CAPMmodel[13,16].ThesecondaspectoftheMarkowitzmodelisthatitisstaticinnature.Itpermitstheinvestortomakeaone-shotal

7、locationtoagiventimehorizon:portfoliore–balancingduringtheinvestmentlifetimeisnotfaced.DynamicAssetAllocationmodelsaddresstheportfoliooptimisationprobleminmulti-periodsettings[4,7,17,20,23].M.Corazzaetal.(eds.),MathematicalandStatisticalMethodsforActuarialSciencesandFinan

8、ce©Springer-VerlagItalia2010274GianniPolaInthispaperweconsidertheOptimalDynamicAssetAllocation(O