随机利率和最优投资策略下的破产概率上界

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1、随机利率和最优投资策略下的破产概率上界李津竹，吴荣南开大学数学科学学院，天津300071摘要：本文研究了保险公司破产概率的上界问题。在本文的风险模型屮，保险公司除去固定的保费收入外，还参与金融市场的股票和债券投资。本文用CIR过程来描述债券所对应的随机利率。对于股票价格，本文分别考虑常数波动率情形和随机波动率情形，前者通过O・U过程描述，而后者用CIR过程描述。在两种情况下，本文利用纯概率的方法分别得出了保险公司破产概率的最小上界及相应的最优投资策略。关键词：随机过程；跳扩散模型；最优投资；破产概率；随机利率中图分类号：0211.6Upperbou

2、ndsforruinprobabilitiesunderstochasticinterestrateandoptimalinvestmentstrategiesJinzhuLi,RongWuSchoolofMathematicalSciencesandLPMC,NankaiUniversity,Tianjin,300071Abstract:Inthispaper,westudytheupperboundsforruinprobabilitiesofaninsurancecompanywhichinvestsitswealthinastockanda

3、bond・WeassumetheinterestrateofthebondisstochasticanditisdescribedbyaCox-Ingersoll-Ross(CIR)model.Forthestockpriceprocess,weconsiderboththecaseofconstantvolatility(drivenbyanO-Uprocess)andthecaseofstochasticvolatility(drivenbyaCIRmodel)・【neachcase,undercertainconditions,weobtai

4、ntheminimalupperboundforruinprobabilityaswellasthecorrespondingoptimalinvestmentstrategybyapureprobabilisticmethod.Keywords:stochasticprocesses;Cox-Ingcrsoll-Rossmodel;Jump-Diffusionmodel;Optimalinvestment;Ornstein・Uhlenbeck(O-U)process;ruinprobability;Stochasticinterestrate.1

5、IntroductionInrecentyears,therehasbeenanincreasingattentiononthetopicaboutruinprobabilityofaninsurancecompanywhichhasthepossibilitytoinvestinariskasset.Oneoftheseminal基金项目：ResearchFundfortheDoctoralProgiamofHigherEducation,NationalBasicResearchProgramofChina(973Program)(No.200

6、7CB8I4905)作者简介:Correspondenceauthor：JinzhuLi(1982-)•Male.Doctor,MajorResearchDirection：StochasticProcesses»Email:lijinzhunk@gniail.com.RongWu(1940-),Female>Professor.MajorResearchDirection：StochasticProcesses.papersis[1],inwhichanoptimalinvestmentstrategyminimizingtheruinproba

7、bilityisobtained.Inthatpaper,itisassumedthatnomoneyisinvestedinthebondandtheriskprocessisdescribedbyitsdiffusionapproximation.HippandPlum[2]consideredthejump-diffusionwealthmodelandobtainedtheinvestmentstrategywhichminimizestheruinprobabilitybysolvingaHamilton-Jacobi-Bcllman(

8、HJB)cquation.Underthesamehypothesesasin[2],Gaier,GranditsandS