lee carter error matrix simulation heteroschedasticity impact on actuarial valuations

《lee carter error matrix simulation heteroschedasticity impact on actuarial valuations》由会员上传分享，免费在线阅读，更多相关内容在工程资料-天天文库。

1、Lee-Cartererrormatrixsimulation:heteroschedasticityimpactonactuarialvaluationsValeriaD’AmatoandMariaRussolilloAbstract.Recentlyanumberofapproacheshavebeendevelopedforforecastingmortality.Inthispaper,weconsidertheLee-Cartermodelandweinvestigateinparticularthehypothesisabouttheerror

2、structureimplicitlyassumedinthemodelspecification,i.e.,theerrorsareho-moschedastic.Thehomoschedasticityassumptionisquiteunrealistic,becauseoftheobservedpatternofthemortalityratesshowingadifferentvariabilityatoldagesthanyoungerages.Therefore,theopportunitytoanalysetherobustnessofest

3、imatedparameterisemerging.Tothisaim,weproposeanexperimentalstrategyinordertoassesstherobustnessoftheLee-Cartermodelbyinducingtheerrorstosatisfythehomoschedasticityhypothesis.Moreover,weapplyittoamatrixofItalianmortalityrates.Finally,wehighlighttheresultsthroughanapplicationtoapens

4、ionannuityportfolio.Keywords:Lee-Cartermodel,mortalityforecasting,SVD1IntroductionThebackgroundoftheresearchisbasedonthebilinearmortalityforecastingmethods.Thesemethodsaretakenintoaccounttodescribetheimprovementsinthemortalitytrendandtoprojectsurvivaltables.WefocusontheLee-Carter(

5、hereinafterLC)methodformodellingandforecastingmortality,describedinSection2.Inparticular,wefocusonasensitivityissueofthismodelandinordertodealwithit,inSection3,weillustratetheimplementationofanexperimentalstrategytoassesstherobustnessoftheLCmodel.InSection4,weruntheexperimentandap

6、plyittoamatrixofItalianmortalityrates.TheresultsareappliedtoapensionannuityportfolioinSection5.Finally,Section6concludes.2TheLee-Cartermodel:asensitivityissueTheLCmethodisapowerfulapproachtomortalityprojections.ThetraditionalLCmodelanalyticalexpression[7]isthefollowing:!"lnMx,t=αx

7、+βxκt+Ex,t,(1)M.Corazzaetal.(eds.),MathematicalandStatisticalMethodsforActuarialSciencesandFinance©Springer-VerlagItalia2010114V.D’AmatoandM.Russolillodescribingthelogofatimeseriesofage-specificdeathratesmx,tasthesumofanage-specificparameterindependentoftimeαxandacomponentgivenbythe

8、productofatime-varyingparameterκt