Construction and Evaluation of Optimal BMS:Comprehensive Perspective Based on Number of Claims and Individual Claim Size
Bonus-malus system(BMS)is a premium adjustment mechanism widely used in the commer-cial auto insurance to set the posterior premium for the next contract period based on a policyholder's claim history.It is usually assumed that the a priori premium assigned to each policyholder adjusts based only on the number of claims.However,not all accidents produce the same individual claim size and thus it does not seem fair to penalize all policyholders in the same way when claims are presented.By a Bayesian methodology,this paper is devoted to the design of BMS involving different sources of a priori information,including the experiences of the number of claims and the individual claim size.The parameters of the BMS are estimated by applying the maximum likelihood method.An empirical analysis using an auto insurance claims database from an insurance company of China is presented.The results indicate that the proposed models could distinguish between claims with different size and then penalize policyholders depending on their experience with respect to the different types of claim,which effectively improve the accuracy of the a posteriori ratemaking.
bonus-malus systemBayesian methodologynumber of claimsindividual claim sizea posteriori rating
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