具有随机保费的二维扰动稀疏风险模型的破产概率.pdf

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1、应用概率统计第三十卷ChineseJournalofAppliedProbability第四期2014年8月andStatisticsVo1．30No．4Aug．2014RuinProbabilityforaTwo-DimensionalPerturbedRiskModelwithThinningDependenceandStochasticPremiumsZHOUYUN(SchoolofStatisticsandManagement，ShanghaiUniversityofFinanceandEconomics，Shanghai，200433)ZHUDONGJIN(SchoolofM0t

2、hemnticsandComputerScie佗ces，AnhuiNormnlUniersity，Wuhu，241000)AbstractThismansuscriptfocusesonakindoftwo—dimensionalriskmodelwithstochasticpremiumincomeandthemodelallowsfordependencebetweenpremiumsandclaims．ByLaplacetransform-S，weprovethatthemodelproposedinthispapercanbereducedintoakindofriskmodelw

3、ithstochasticpremiumincomes，andthepremiumincomeisindependentoftheclaimprocess．Whentheindividualclaimsarethe“light—tailed”case．anupperboundforruinprobabilityisderivedbymartingaleapproach．Whentheclaimsbelongtoakindofheavy-taileddistribution，theasymp—toticestimationforruinprobabilityisgivenwhentheini

4、tialsurplustendstoinfinity．Keywords：Two-dimensionalriskmodel，ruinprobability,thinningdependence，upperbound，asymptoticestimation．AMSSubjectClassification：60K05，62P05，90A46．§1．IntroductionClassicalriskmodelisspecifiedasN(t)u(t)=u+ct一∑，i=1whereU0istheinitialcapitalofaninsurer；C>0istherateofpremiuminc

5、ome，N(t)representsthetotalnumberoftheclaimsuptotimet；denotestheamountoftheithclaim．{Ⅳ(t)，t0)isaPoissonprocesswithparameter>0，seeAsmussenTheresearchwassupportedbyNationalNaturalScienceFoundationofChina(11201006)，HumanitiesandSocialScienceProjectofMinistryofEducation(12YJC910012)，theCollegesandUnive

6、rsitiesofAnhuiProvinceNaturalScienceFoundationGrandProject(KJ2012ZD01)．ReceivedApril3，2014．RevisedMay18，2014．doi：10．3969／j．issn．1001—4268．2014．04．006第四期周昀祝东进：具有随机保费的二维扰动稀疏风险模型的破产概率399andAlbrecher(2010)orGrandell(1991)forcomprehensiveintroduction．Intheclassicalmodel，thepremiumrateisaconstantandthep

7、remiumprocessisalinearfunctionoftime．Inpastdecade，moreandmoreliteraturepayattentiontothemodelwithstochasticpremiumincomes，seeCaiandGeng(2007)，Yaoeta1．(2008)，XiangandWei(2011)andreferencesthereinforexample．Inreali