一類基于工資水平的養(yǎng)老金計(jì)劃的定價(jià)問題.pdf

1、復(fù)旦大學(xué)碩士學(xué)位論文一類基于工資水平的養(yǎng)老金計(jì)劃的定價(jià)問題姓名：劉宛音申請學(xué)位級別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)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