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Designing Optimal Bonus-Malus Systems from Different Types of Claims

Abstract This paper provides bonus-malus systems which rest on different types of claims. Consistent estimators are given for some moments of the mixing distribution of a multi equation Poisson model with random effects. Bonus-malus coefficients are then obtained with the expected value principle, and from linear credibility predictors. Empirical results are presented for two types of claims, namely claims at fault and not at fault with respect to a third party.