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1、ChainLadderMethod:BayesianBootstrapversusClassicalBootstrapGarethW.Peters1,2MarioV.W¨uthrich3PavelV.Shevchenko21UNSWMathematicsandStatisticsDepartment,Sydney,2052,Australia;email:peterga@maths.unsw.edu.au2CSIROMathematicalandInformationSciences,LockedBag17,NorthRyde,NSW,167
2、0,Australia3ETHZurich,DepartmentofMathematics,CH-8092Zurich,SwitzerlandarXiv:1004.2548v1[q-fin.CP]15Apr2010PreprintsubmittedtoElsevierApril16,2010ChainLadderMethod:BayesianBootstrapversusClassicalBootstrapGarethW.Peters1,2MarioV.W¨uthrich3PavelV.Shevchenko2AbstractTheintent
3、ionofthispaperistoestimateaBayesiandistribution-freechainladder(DFCL)modelusingapproximateBayesiancomputation(ABC)methodology.Wedemonstratehowtoestimatequantitiesofinterestinclaimsreservingandcomparetheestimatestothoseobtainedfromclassicalandcredibilityapproaches.Inthiscont
4、ext,anovelnumericalprocedureutilisingMarkovchainMonteCarlo(MCMC),ABCandaBayesianbootstrapprocedurewasdevelopedinatrulydistribution-freesetting.TheABCmethodologyarisesbecauseweworkinadistribution-freesettinginwhichwemakenoparametricassumptions,meaningwecannotevaluatethelikel
5、ihoodpoint-wiseorinthiscasesimulatedirectlyfromthelikelihoodmodel.Theuseofabootstrapprocedureallowsustogeneratesamplesfromtheintractablelikelihoodwithouttherequirementofdistributionalassumptions,thisiscrucialtotheABCframework.Thedevelopedmethodologyisusedtoobtaintheempirica
6、ldistributionoftheDFCLmodelparametersandthepredictivedistributionoftheoutstandinglossliabilitiesconditionalontheobservedclaims.WethenestimatepredictiveBayesiancapitalestimates,theValueatRisk(VaR)andthemeansquareerrorofprediction(MSEP).Thelatteriscomparedwiththeclassicalboot
7、strapandcredibilitymethods.Keywords:Claimsreserving,distribution-freechainladder,meansquareerrorofprediction,Bayesianchainladder,approximateBayesiancomputation,MarkovchainMonteCarlo,annealing,bootstrapPreprintsubmittedtoElsevierApril16,20101.MotivationThedistribution-freech
8、ainladdermodel(DFCL)ofMack[14]isapopularmodelforstochasticclaimsreserving.Inthispa
