基于Vasicek隨機利率下具有冪型支付的期權(quán)保險精算定價方法.pdf

1、哈爾濱工程大學(xué)碩士學(xué)位論文基于Vasicek隨機利率下具有冪型支付的期權(quán)保險精算定價方法姓名：劉鳳波申請學(xué)位級別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：鄭曉陽20090501哈爾濱下程大學(xué)碩十學(xué)位論文ABSTRACTFinancecalculuswhichhasexperiencednearlyonehundredyearsmainlyresearchedonthepricingofriskyassets，thepricingofinterest

2、ratederivativesecuritiesandoptimalinvestmentandconsumptionstrategy，moreverthepricingofinterestratederivativesecuritiesisoneofthekernelproblemsDuetothelongdurationofthederivativesecurities，themomentofimerestratesbecomesmo

3、reimportantinpricingsuchlong—datedderivativeoptionsIn1977，Vasicekproposedamodelofshortterminterestrate，whichmademoreinvestorsfocusonthepricingofinterestratederivativesecuritiesThusthestudyofthepricingofderivativesecuriti

4、eswithstochasticinterestratenotonlyhasimportanttheoreticsignificancebutalsothepracticalvalueThispapermainlyappliesstochasticanalysis，martingaletheoryandstochasticprocessestosimulatethemathematicmodeloffinancialmarket，stu

5、diesthepricingofEuropeanoption、Ⅳimstochasticinterestrate，andgetsthepricingofgeometric—averageAsianoptionsMeanwhile，thispapergivethepricingofEuropeanoptioninthecaseofpoweroptionpricingformulaunderthemodelofVasicekstochast

6、icinterestratewiththeactuarialapproachThefollowingarethispaper’Smainresultsandinnovations：(1)UsingthemethodofItointegralandstochasticdifferentialequation，theproblemsofexoticoptions’pricingaretakenintoconsideration，ofwhic

7、hthemostrepresentativegeometricaverageAsianoptionswiththefunctionofVasicekstochasticinterestratesForthermorever，gettingthepromotedoptionpricingmodelofBlackScholeswiththefunctionofVasicekstochasticinterestrates(2)Usingthe