一類基于工資水平的養(yǎng)老金計劃的定價問題.pdf

1、復旦大學碩士學位論文一類基于工資水平的養(yǎng)老金計劃的定價問題姓名：劉宛音申請學位級別：碩士專業(yè)：應用數(shù)學指導教師：沈瑋熙2000.6.1ValuationofretirementbenefitbasedonfinalsalaryAbstractBasedonthefinancialandactuarialtheories，apricingmodelforretirementbenefitisconsidered，andthenPDE(pa

2、rtialdifferentialequations)thatthebenefitsatisfiesarederivedinthispapertheretirementbenefitisbasedonfinalsalarywhichisastochasticprocessFirstlyitisassumedthatthereisailarbitragefreemarket；andthenaccordingtotheriskneutral

3、principle，theretirementbenefitvaluationmodelisdeveloped，whichissimilartotheoption—pricingmodelSecondlywediscusstheEDEintwodifferentscenarios：whentherearemanyelementsinfluencingthedecisionofearlyretirement，withtheassumpti

4、onthattheforceofretirementrate∥，callbeobtained，wederiveageneralPDE；otherwise，ifthememberofpensionplanretiresonlywhentheretirementbenefitamountiSthemaximum，ieearlyretirementisallowedwhentheearlyretirementbenefitisgreatert

5、hanthecurrentpensionbenefit，whichiSsimilartothedecisionoftheoptimumexercisetimeofAmericanoptionSOthePDEwithfree—boundarysimilartothepricingoftheAmericanoptioniSderivedThenthreemethodsareusedtogiveanalyticalsolutiontothef

6、irstgeneralPDE；thethreesolutionsareperfectlysameAstothesecondPDEwhichhasfreeboundaryitCanbetreatedinasimilarmaRRertotheAmericanoptionpricingproblemandsolvedintwostepsInthefirststepthePDEwithfree—boundaryconditionsiStrans

7、formedtoalinearcomplimentarityformulation；thegreatadvantageofthisformulationiSthatthefreeboundaryneedednottobetrackedexplicitlyInthesecondstep，thefinitedifierencemethodiSutilizedtoprovidenumericalsolutionandtheeffectsoft