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1、MathFinanEcon(2012)6:113DOI10.1007/s11579-011-0052-3Utilitymaximization,riskaversion,andstochasticdominanceMathiasBeiglböck·JohannesMuhle-Karbe·JohannesTemmeReceived:4April2011/Accepted:14September2011/Publishedonline:25September2011©Springer-Verlag2011AbstractConsideraninvestort
2、radingdynamicallytomaximizeexpectedutilityfromterminalwealth.Ouraimistostudythedependencebetweenherriskaversionandthedis-tributionoftheoptimalterminalpayoff.Economicintuitionsuggeststhathighriskaversionleadstoaratherconcentrateddistribution,whereaslowerriskaversionresultsinahighe
3、raveragepayoffattheexpenseofamorewidespreaddistribution.DybvigandWang(J.Econ.Theory,2011,toappear)findthatthisideacanindeedbeturnedintoarigorousmathematicalstatementinone-periodmodels.Morespecifically,theyshowthatlowerriskaversionleadstoapayoffwhichislargerintermsofsecondorderstoc
4、hasticdominance.Inthepresentstudy,weextendtheirresultsto(weakly)completecontinuous-timemodels.Wealsocom-plementanad-hoccounterexampleofDybvigandWang,byshowingthattheseresultsarefragile,inthesensethattheyfailinessentiallyanymodel,ifthelatterisperturbedonasetofarbitrarilysmallproba
5、bility.Ontheotherhand,weestablishthattheyholdforpowerinvestorsinmodelswith(conditionally)independentincrements.KeywordsUtilitymaximization·Riskaversion·StochasticdominanceJELClassificationG11·C611IntroductionAclassicalprobleminmathematicalfinanceandfinancialeconomicsistomaximizeexpe
6、ctedutilityfromterminalwealth.ThismeansthatgivenatimehorizonTandautilityfunctionM.Beiglböck·J.TemmeFakultätfürMathematik,UniversitätWien,Nordbergstrasse15,1090Wien,Austriae-mail:mathias.beiglboeck@univie.ac.atJ.Temmee-mail:johannes.temme@univie.ac.atJ.Muhle-Karbe(B)DepartementMat
7、hematik,ETHZürich,Rämistrasse101,8092Zürich,Switzerlande-mail:johannes.muhle-karbe@math.ethz.ch1232MathFinanEcon(2012)6:113UdescribingtheinvestorspreferencesonetriestochooseatradingstrategysuchthattheterminalvalueXˆTofthecorrespondingwealthprocessmaximizesE[U(XT)]overallwealthpro
8、cessesofcompetingstrategies.Existenceand
