关于随机利率下经典风险模型分红问题的分析-analysis on dividend distribution problem of classical risk model under random interest rate.docx

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2018-06-05 发布于上海
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关于随机利率下经典风险模型分红问题的分析-analysis on dividend distribution problem of classical risk model under random interest rate.docx

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关于随机利率下经典风险模型分红问题的分析-analysis on dividend distribution problem of classical risk model under random interest rate

AbstractInactuarial mathematics, ithasalotofwork totheclassicalrisk modelundertheoptimaldividendproblems.Butwiththedevelopmentoffinancialbusinessandinsurancebusiness,thestudyoftheruinproblemwithinteresthasbeenoneoftheimportanttopicsinthefieldofinsurancemathematics.Inthepastfewdecades,insuranceriskmodelswithconstantandwithstochasticinteresthavebeenstudiedbymanyauthors.Paulsen(1993)discussedtheproblemofruintheoryinastochasticeconomicenvironment.PaulsenandGjessing(1997)studiedruintheorywithstochasticeconomicenvironment,andtheruinprobabilityisgivenunderthespecialconditions.CaiandYang(2005)discussedtheproblemwithruinintheperturbedcompoundPoissonriskprocessunderinterestforce.WangandWu(2000)discussedsomedistributionsforclassicalriskprocessthatisperturbedbydiffusion.WangandWu(2001)studiedtheclassicalriskprocesswithstochasticreturnoninvestmentsinwhichthereturnontheinvestmentgeneratingprocessisaBrownianmotionwithpositivedrift.Theyobtainedanintegralequationfortheruinprobabilityandgavesufficientconditionsunderwhichtheruinprobabilityistwicecontinuouslydifferentiable.WenowfollowtheriskmodelinWangandWu(2001)tointroducethebarrierstrategy.Thethesisisdividedintothreesectionsaccordingtocontents.InChapter1,weintroducesomerecentresearchresults,researchstatusofrelated theoryandtheclassicalriskmodelwithstochasticinterest,N(t)U(t)=u+ct?γXi, t≥0,i=1I(t)=rt+σW(t), t≥0.Itisusedtobethepointofresearchinthetest.Thenthetrendofdividendproblemsinrecentyearsisbrieflyrecommended.InChapter2,thischapteristhefocusofthispaperandimportantinnovationofthispaper.Weconsiderthebarrierdividendstrategyintheclassicalriskmodelwithstochasticinterest.Thefourpartsareincluded.Inthefirstpart,theintergral-differentialequationsatisfiedbythemomentsofthediscounteddividendpaymentsisgiven,thatis:1?2Mσ2u2?M?M2?u2(u,y;b)+(c+ru)?u(u,y;b)?δy?y(u,y;b)Iu=λM(u,y;b)?λM(u?x,y;b)dF(x)?λ[1?F(u)].0andtheclosedformforthemomentsofthediscounteddividendpaymentsisalsoobtainedinthecasewhereinterestisaconstantandprofitsfollowanexponentialdistr