Pareto严格稳定分布在保险理赔中的应用

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1、数学杂志Vo1．35(2015)J．ofMath．(PRC)No．4APPLICAT10N0FTHEPAREToP0SITIVESTABLEDISTRIBUTIoNININSURANCECLAIMXUANHai—yan．BAOHai—ming。SHIYong-xia。fJ．C。llegeofEcon。7n钯s6mdA如ngemenL6mz。u("ersityof丌ec^他。logy，。礼。乱730050，(n。)f2．nnzh。JinchengBranch，ChinⅡConstructi。礼Bank，Lanzh。u730030,Chin。)f．Co

2、UegeofScie礼ce，Lanzh。uUniversityofTechn。logy，Lanzh。“730050,Chinn)Abstract：Inthispaper，westudytheapplicationoftheParetopositivestabledistributionininsurance．TheparameterestimatesofParetopositivestabledistribution，normaldistributionandParetodistributionareobtainedusingthemethodof

3、maximumlikelihoodestimates．ByAkaikeinformationcriterion，itisindicatedthattheParetopositivestabledistributioncanfittheinsur—ancedatawel1．Keywords：Paretopositivestabledistribution；parameterestimation；insuranceclaim；AkMkeinformationcriterion2010MRSubjectClassification：62P20；91G10

4、Documentcode：AArticleID：0255—7797(2015)O4—0889—091IntroductionInsurancecompanyclaimiSanimportantfactorinitsdevelopment．Insurancecompa-niescommonlyuseexponentialdistribution，lognormaldistributionorParetodistributiontofitclaimsdataandcontrolrisk．Intheinsuranceclaimmodel，makingpr

5、emiumtoinsurancecompanyandresistingtherisk，Paretodistributionmodelisofguidingsignificance．Itissuitableforfittinglargeclaimsdata．Fromthehistoricaldata，insuranceclaimoftenshowshighpositivebias．Onthedistribution，itshowsfattailshape．ButParetodistributionhasaheavy—tailedcharcterist

6、ic．Sowhensimulatingthesedata，Paretodistributionispopularwiththescholars．TheParetopositivestable(PPS)distributionwasfirstlyproposedbySarabiaandPri—etointheirthesisin2009[11．TheyexplainedthereasonwhytheParetopositivestabledistributionisusedtomodellossesininsurance．Forinstance，th

7、eParetopositivestabledistributioneasilyfitandhaveasimplequantileexpression．ItmakestheMonteCarlosimulationsimple．Fortheriskvalue，ananalyticalexpressionisprovided．Ortobellieta1．『21proposedsomestableParetianmodelsforoptimalportfolioselectionandforquantifyingReceiveddate：2014．09—0

8、1Accepteddate：2014-12—24Foundationitem：SupportedbyNationalNat