确定缴费型养老金的最优投资

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1、ABSTRACTAsthescaleofthepensionsfundisverylargeandthematuarityofthepensionsplanisverylong，investmentisveryimportantforthepensionsplan．Apparently，riskyinvestmentcanbedangerous，andthereforeitneedstofindtheoptimalinvestmentstrategy．Intheactualstockmarket

2、，therearemanyuncertainevents，suchasinflation，disaster,warandSOon，whichmayinfluencetheinterestrateandthevolatilitygreatly．Alargenumberofempiricalstudieshaveshownthatthereturnsandvarianceofstockarerandom．Therefore，introducingstochasticfactorsintobothin

3、terestrateandvolatilityininvestmentwillmakethepensionfundingplanmodelmorerealisticandmorepractical．‘Inthispaperwestudytheportfoliooptimizationproblemforthepensionsfundingplanwhoseekstomaximizetheexpectedutilityoftheterminalwealthinadefinedcontributio

4、npensionplan．Undertheconditionsthatthepensionfundingcanbeinvestedinarisk-freeassetandariskyasset，andthevolatilityoftheriskyassetisdescribedbyaHestonmodel，weobtaintheclosed—formexpressionsoftheoptimalinvestmentandthemaximalexpectedexponentialutility,p

5、owerutilityfunctionandlogarithmicutilityfunctionoftheterminalwealth，respectively．Moreover,therelationshipsbetweentheoptimalinvestmentandvariousparametersaregivenbynumericalcalculation．Therearetworisk—freeinterestrateoftherisk-freeassets：oneisconstant

6、，theotheroneisstochasticinterestratedsatisfingtheCox··Ingersoll--Ross(CIR)model．InchapterIIIandIV,thetwikindofrisk—freeinterestratesarestudied，respectively．BysolvingtheobjectivefunctioncorrespondingHJBequation，explicitexpressionsfortheoptimalinvestme

7、ntstrategyandtheoptimalvaluefunctionareobtained．KEYWORDSdefinedcontributionpensionplan，definedbenefitpensionplan，Hestonstochasticvolatilitymodel，Cox—Ingersoll—Rossmodel，optimalIlinvestment，utilityfunction，optimalcontrol，Hamilton—Jacobi-Bellmanequatmn

8、III第一章1．11．21．3第二章2．12．2第三章3．13．23．33．4第四章4．14．24．3第五章参考文附录“致谢．．攻读学硕十学位论文第一章绪论1．1选题的背景第一章绪论养老保险是社会保障制度的重要组成部分，是社会保险五大险种中最重要的险种之一。所谓养老保险(或养老保险制度)是国家和社会根据一定的法律和法规，为解决劳动者在达到国家规定的解除劳动义务的劳动年龄界限，或因年老丧失劳动能力退出劳动岗位后的基本生活而建立的一种社会保险制度(见参考文献【561，[59】)。由于养老金是到退休之