兩類模型下的最優(yōu)投資、消費和人壽保險問題的研究.pdf

1、分類號兩類模型下的最優(yōu)投資、消費和人壽保險問題的研究Researchonoptimalinvestment，consumptionandlifeinsuranceDroblemsont、ⅣomodelsanQ11relnSUranCeDroDlemSont、ⅣomoQelS研究生姓名：彭靈芝指導教師姓名、職稱：陳旭副教授學科專研究方概率論與數理統計湖南師范大學學位評定委員會辦公室二零一六年五月ABSTRACTInthi8p印er，Wem

2、ainlyusethedualitytheo珂anddynamicprogrammingprinciplesuchasmathematicalltooltostudythetwotypesofriskunderthemodelofoptimizationproblemsundertheHestonmodelandtheCEV(constaJltelasticityofvariance)riskmodel，discussedCfLI己A(

3、constaJltrelatiVeriskaⅣersion)andCAf認(constantabsoluteriska№rsion)respectivelyunderthepref打encesoftheoptiInali11vestment，consumptionaIldlifeinsurallceThemain、Ⅳorkofthispaperisasfollows：Inch印terl，Weintroducethebackgrounda

4、nddynamicofthelifeinsuraIlcesimply，andthenpresentthem出nworkofthisarticleInchapter2，wemaLinlyintroducesomerelevantinsuraIlcemodelsandthebasicknowledge，whichareprepadngforthefolloWingrese盯chinchapters3and4necessarilyInchap

5、ter3，westudytheoptimaLlinvestment，consumptionandlifeinsu卜anceconsumptionofthehireworkers而thC砒認andCAf漁preferencesundertheCEVmodelInourmodel，thewagee缸nerpurcllalsestermlifeinsuranceannuitytosimpli匆themodel0urobjectiveistom

6、aXimizeconsumption，he卜itageandtheterminalweaJth，Weusethest(JchasticcontroltheorytogettheHJBequationandboundaryconditionsoftheVaLlllefunction，solvetheintegr伊di髓rentialequationthroughtheLegendretransformation，andthenobt越nt

7、heimplicitequationoftheoptimaLlinvestment，consumptionand1ifeinsuranceun—dertheCRRAandCARApreferencesInchapter4，weresearch也eoptimalinVestment，consumptionandlifeinsuranceproblemofthehireworkers而thC砒認aIldCARApreferencesunde

8、rtheHestonmodelSimilarlyinourmodel，thewageearnerpurchasestermlifeinsurancean眥itytosimpli匆themodelOurobjectiveistomaXimizeconsumption，heritageandthetermin出wealth，weusethestodhalsticcontroltheorytogettheHJBequationandbound