Computing Bayesian Bonus-Malus Premium Distinguishing Among Different Multiple Types of Claims
Tóm tắt
The premium calculation considered in the classical bonus-malus system in automobile insurances is dependent only on a number of claims. When a policyholder declared a small claim size, he or she was penalized in the same way as those who made a large claim size. Hence, it is unfair to penalize all policyholders in like manner. In this article, we propose a model for computing the premium based on the bonus-malus system by distinguishing multiple types of claims as follows: small, middle, large, and sever claim sizes. The number of claims is considered based on discrete distributions: Poisson and binomial distributions. Besides, we introduce prior distributions, gamma, and beta distributions, conjugated with these discrete distributions. The Bayesian method is applied for updating the parameters of the model as this approach yields bonus-malus premiums. We use a real example data to demonstrate the model. The randomized neighborhood search (RNS) technique is introduced for estimating the parameters to minimize the statistical value for Akaike’s Information Criterion (AIC). This methodology allows us to obtain a good fit to the data set considered.
Tài liệu tham khảo
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