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1、2014-CAS8§13LeeDiagrams,RetroRatingHCM5/13/14,Page799Section13,LeeDiagrams,RetrospectiveRating552553In“TheMathematicsofExcessofLossCoveragesandRetrospectiveRating--AGraphicalApproach,”PCAS1988,Yoong-SinLeeusesgraphstoillustratemathematicalconceptsthatapplytobothsizeoflossdistributionsa
2、ndaggregatedistributions.InaprevioussectionIcoveredLeeʼsfirstthreesections,whichcontainlotsofveryusefulideas.MoreofthequestionsonrecentexamshavedealtwithLeeʼsfourthsectiononRetrospectiveRating,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
