组合投资选择均值最小最大化多目标规划模型

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1、万方数据2009年9月第40卷第5期内蒙古大学学报(自然科学版)JournalofInnerMongoliaUniversityArticleID：1000～1638(2009)05—0548—07Sept．2009V01．40No．5Mean--minmaximizedMulti-·objectiveProgrammingModelforPortfolioSelection。ZHANGZhen—hual。LIANGZhi—an2(1．SchoolofFinance，ShanghaiUniversi

2、ty0厂FinanceandEconomics，Shanghai200433，China；2．Departmento÷AppliedMathematicsIShanghaiUniversityofFinanceandEconomics，Shanghai200433，China)Abstract：Amean—minimummaximizedmulti—objectiveprogrammingmodelisproposedforsolvingportfolioselectionproblems．Mini

3、mumreturnisusedinthismodeltomeasurethedownsideriskofaportfolio。andmulti—objectivemodelprovidesmoreflexibletrade—offamongprofit．riskandcost(orevenmorefactors)。Boththeoretiealanalysisandnumericalexperimentsarecommitted．Theseresultsindicatethat，whenthedis

4、tributionsofportfolioreturnsaremoderatelyskewed，thismodeloutperformsthenormalmean．varianceefficientmodelobviously．Keywords：Portfolioselection；downsiderisk；multi—objectiveprogrammingCLCnumber：0221．6；F224．3Documentcode：AIntroductionArationalinvestorwants

5、tomakethemostfromhisinvestmentandavoidextremeloss．Markowitz[¨noticedthatoneshoulddiversifytoreducerisk．Heconstructedthefamousmean．varianceefficientportfolioselectionmodelwhereportfolioriskisevaluatedbyitscovariancematrix．Afterwards，Sharpe‘2’andLintner∞

6、proposedtheCapitalAssetPricingModel(CAPM)．undertheassumptionthateveryinvestorpursuesamean-varianceefficientportfolio．Alargenumberofpapers，basedontheMarkowitzmean—varianceefficientframeworkorCAPM，haveemergedsincethen．Manyofthesepaperswereconcernedwithho

7、wriskshouldbemeasured，sinceminimizingvariancesuccessfullyreducesfluctuation，whichmayalsopenalizeoutperformance．ThereforeappearedresearchesinasymmetricriskmeasureslikeValueatRisk(VaR)andsemivariance。seethereferenceinSteinbachc¨．Young㈣introduceda“minimax

8、”principlein1998：TheoptimalportfolioisdefinedtominimizethemaximumlOSS(inotherwords，maximizestheminimumreturn)overallpasthistoricalperiods．subjecttotheconstraintthattheaveragereturnacrosstheseperiodsisnolessthananacceptable·Receiveddate：