资源描述：
《Jones_Bruce_ResearchContributions4_203204-11-2011》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。
1、TheUseofPhase-TypeModelsforDisabilityInsuranceCalculationsAminHassanZadeh1BruceL.JonesandDavidA.StanfordDepartmentofStatisticalandActuarialSciences,UniversityofWesternOntario,London,OntarioN6A5B7,Canada.April19,2010AbstractThispaperexplorestheuseofphase-typemodelsinactuarialcalculationsfordi
2、sabilityinsurance.Wedemonstratethatthechangesinstatusofdis-abilityinsuredscanbeappropriatelycapturedbyaphase-typemodel.Ourmodelrepresentstheagingprocessasthepassagethroughanumberofphasesofdecreasingvitality.Whendisabled,individualsadditionallypassthroughseveralstagesthatrepresentdurationofdi
3、sability.Recoveryandmortalityratesfromtheearlierstagesaregreaterthanthoseinlaterstages.Usingsuchamodel,explicitandeasilycalculableexpressionsareobtainedforrelevantprobabilitiesandactuarialpresentvalues.Thisfacilitatesthecalculationofpremiumsandreserves.Keywords:Actuarialpresentvalue,aggregat
4、eMarkovchain,continuous-timeMarkovchain,disabilityinsurance,phase-typedistribution1Correspondingauthor;e-mail:jones@stats.uwo.ca;tel:(519)661-3149;fax:(519)661-3813.11.IntroductionVarioustypesofdisabilitybenefitsareprovidedbyavarietyofdifferentkindsofinsurancepolicies.Thecommonalityisthatcover
5、edindividualsmayatanytimebeinoneoftwostatuses:active(notdisabled),ordisabled.Thedefinitionofdisabilityisbasedontheindividual’sinabilitytoperformoccupationalduties.Benefitsaretypicallypayableperiodicallywhiletheindividualisinthedisabledstatus,afterawaitingperiod.Actuarialcalculationsfordisabili
6、tycoveragespresentchallengesbecauseofthepos-sibilityofrepeatvisitstothedisabledstatus.Traditionalapproachesinvolvetheuseofdisabilityincidenceratesandterminationrates(see,forexample,Bowersetal.[2],p.359).Theincidenceratesdependonage,andtheterminationratesdependondura-tionofdisabilityandage.Th
7、esesetsofratesallowinsurerstocalculatetheprobabilitythatadisabilitybeginsinagivenyearandcontinuesforagivenperiodoftime.Oftentheterminationratesdonotdistinguishrecoveriesfromdeaths,andthereforecalcula-tionsmayonlycontemplateonespellofdisability.Allo
