Abstract
The traditional automobile insurance bonus-malus system (BMS) merit-rating depends on thenumber of claims. An insured individual who makes a small severity claim is penalized unfairly compared to aninsured person who makes a large severity claim. A model for assigning the bonus-malus premium wasproposed. Consideration was based on both the number and size of the claims that were assumed to follow aPoisson-Lindley distribution and a Lognormal-Gamma distribution, respectively. The Bayesian method wasapplied to compute the bonus-malus premiums, integrated by both frequency and severity components based onthe posterior criteria. Practical examples using a real data set are provided. This approach offers a fairer methodof penalizing all policyholders in the portfolio.
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