兩類模型下的最優(yōu)投資、消費(fèi)和人壽保險(xiǎn)問題的研究.pdf

1、分類號(hào)兩類模型下的最優(yōu)投資、消費(fèi)和人壽保險(xiǎn)問題的研究Researchonoptimalinvestment，consumptionandlifeinsuranceDroblemsont、ⅣomodelsanQ11relnSUranCeDroDlemSont、ⅣomoQelS研究生姓名：彭靈芝指導(dǎo)教師姓名、職稱：陳旭副教授學(xué)科專研究方概率論與數(shù)理統(tǒng)計(jì)湖南師范大學(xué)學(xué)位評(píng)定委員會(huì)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(rèn)(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(rèn)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(rèn)aIldCARApreferencesunde

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