索赔服从Phase-type分布的风险模型破产概率.pdfVIP

数 学 杂 志 Vo1．33(2013) J．ofMath．(PRC) NO．4 THE RUIN PR0BABILITIES FoR RISK M oDEL W ITH PHASE—TYPE CLAIM S YANG Shao—hun ．HUA Zhi-qiang SchoolofMathematicsandComputationalScience，FuyangN。rmalCollege，Fuyang23603ZChina) (2，C。llege M。them。tics，lnnerM。nglinUiversity，0rtheⅣ。ti。nnIities，Tongli。。028043，Chin。) Abstract：In thispaper，theruin probabilityofnth claim with Phase—typedistribution is investigated．Intheclassicalriskmodel，when theclaim sizesarethePhase—typedistribution，a recursivescheme fortheLaplacetransform ofreserve’Sdensity isderived withthepropertiesof Phase—typedistributionsandtherelationbetweenreserveandincrement，thentheruinprobability ofnthclaim isobtained withtheresult．Finally，anexampleisgiventoillustratetheapplication． KeYwords： ruinprobability；recursivemethods；Phase—typedistributions；Erlangdistribu—- tion 2010MR SubjectC：lassification：60K99 Documentcode： A ArticleID： 0255—7797(2013)04—0646-07 1 Introduction LetUSsupposethesurplusprocess{u(0he0hasthefollowingform N(t) ()=+ct一∑ where istheinitialsurplus，c 0istheconstantprem ium rate，withoutlossofgenerality， letc= 1inthisarticle，andclaimsamounts{ ) 1areassumedtonon—negative，i．i．d． randomvariableswithcommondensityfunctionf(x)， 0，anditsLaplacetransforms is (s)= e-sxf(x)dx，theprocess{Ⅳ() oisaPoissonprocesswithparameter ， 。 itcountsthenumbersofclaimsuptotimet，{ }z1areassumedtobeindependentof {Ⅳ())to．Fortheprobabilityofruin，exactresultswereobtainedforclaim sizesgivenby combinationsofexponentialdistributionsandcombinationsofgammadistributions(see[1])， inthisarticlewestudytheruin probabilityofnth claim assum