資源描述：
《lee diagrams, retrospective rating》由會員上傳分享，免費(fèi)在線閱讀，更多相關(guān)內(nèi)容在工程資料-天天文庫。
1、2014-CAS8§13LeeDiagrams,RetroRatingHCM5/13/14,Page799Section13,LeeDiagrams,RetrospectiveRating552553In“TheMathematicsofExcessofLossCoveragesandRetrospectiveRating--AGraphicalApproach,”PCAS1988,Yoong-SinLeeusesgraphstoillustratemathematicalconceptsthatapplytobothsizeoflossdistributionsa
2、ndaggregatedistributions.InaprevioussectionIcoveredLee?sfirstthreesections,whichcontainlotsofveryusefulideas.MoreofthequestionsonrecentexamshavedealtwithLee?sfourthsectiononRetrospectiveRating,whichiscoveredinthissection.ThosewhoaregraphicallyorientedwillfindthatLeeDiagramshelpthemtore
3、memberorquicklyderivemanyimportantformulas.Notation:Leeuseswhatisnowoldernotation,whichdiffersfromwhatiscurrentlyusedonExam4:G(x)?S(x)=1-F(x)?SurvivalFunctionE[g(X;b)]?E[X∧b]?LimitedExpectedValue.554AdditionalReading:“TheInteractionofMaximumPremiums,MinimumPremiums,andAccidentLimitsinR
4、etrospectiveRating”,byHowardC.Mahler,PCAS1996.www.casact.org/pubs/proceed/proceed96/96075.pdfThis1996paperusesLeeDiagramstodiscussRetrospectiveRating,andwaswrittenbymeafterteachingExam9students.Whileitisnotonthesyllabus,someofyouwillfindaquickreadofthispaperusefulafteryouhavereadthepap
5、ersonthesyllabus.ItdirectlyrelatestomaterialintheLeeandSkurnickpapers.552“TheMathematicsofExcessofLossCoverageandRetrospectiveRating---AGraphicalApproach”,byY.S.Lee,PCASLXXV,1988.“OtherApplications”onpp.75-76arenotonthesyllabus.Leecites“APracticalGuidetotheSingleParameterParetoDistribu
6、tion”,byStevenPhilbrick,PCAS1985.PhilbrickinturnpointsoutthesimilaritytothetreatmentofInsuranceChargesandSavingsin“FundamentalsofIndividualRiskRatingandRelatedTopics”,byRichardSnader.553Section4coversCASLearningObjectivesB2,B5,andB6.554AlsousedinthesyllabusreadingsofMiccolis,Clark,andM
7、ahler.2014-CAS8§13LeeDiagrams,RetroRatingHCM5/13/14,Page800AggregateAnnualLosses:Retrospectiveratingusestheannualaggregatelossesforaninsured.Wecanapplymostofthesamemathematicstoaggregatedistributionsaswasappliedtosizeoflossdistributions.HereisaLeeDiagramofthedistributionfunctionofthe
