mahler, shifting risk parameters

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1、2014-CAS8§7Mahler,ShiftingRiskParametersHCM5/13/14,Page326Section7,Mahler,ShiftingRiskParameters235Erratafor“AnExampleofCredibilityandShiftingRiskParameters”byHowardC.Mahler:236Page286,firstsentence:237τisdistributedontherange[-1,1].Iftheactualcorrelation,ρ=0,thenτissymmetricallydistr

2、ibutedontherange[-1,1].Page297,fourthline:238⎡l(

3、j-i

4、)ζ2i≠jCov[Xi,Xj]=⎢ζ22⎣+δi=j235“AnExampleofCredibilityandShiftingRiskParameters”,byHowardC.Mahler,PCAS1990.CandidateswillnotbetestedontheAppendices.CASLearningObjectiveA1.236Notofficial.237InAppendixB,notonthesyllabus.238InAppendixD

5、,notonthesyllabus.2014-CAS8§7Mahler,ShiftingRiskParametersHCM5/13/14,Page327ShiftingRiskParameters:Shiftingriskparameters:Theparametersdefiningtheriskprocessforanindividualinsuredarenotconstantovertime.Thereare(aseriesofperhapssmall)permanentchangestotheinsuredʼsinitialriskprocessason

6、elooksoverseveralyears.239Forexample,aprivatepassengerautomobileinsuredʼsriskparametersmightshiftifamajornewroadwereopenedinhislocalityorifhechangedthelocationtowhichhecommutestowork.Inanotherexample,theprivatepassengerautomobileinsuranceexperienceofatownrelativetotherestofthestate,in

7、otherwordsthetownʼsrelativity,couldshiftasthattownbecomesmoredenselypopulated.Inyetanotherexample,theproceduresandmachinesusedtomanufacturewidgetschangeovertime.ThiscouldresultinchangesovertimeintheexpectedpurepremiumandthereforetherelativityfortheWidgetManufacturingClassforWorkersCom

8、pensationInsurance.Forinsurancesituations,riskparametersarenevertotallyconstantoverdecades.However,dependingonthelengthofthetimeperiodconsideredandtheparticulardata,themagnitudeoftheshiftscanbelargeorsmall.Ifriskparametersshiftsignificantlyovertime,thiswillsignificantlyeffecttheoptima

9、lcredibilitytoassigntoyearsofpastdatainordertopredictthefuture.TheBaseballParadigm:InMahlerʼs“AnExampleofCredibilityandShiftingRiskParameters,”theauthorevaluatesvariousestimatesforbaseballteamsʼfuturelosingpercentagesusinghistoricallosingpercentagesHediscussestheimpactofshiftingparame

10、terso