Bonus-malus system: statistical foundation

Abstract

Bayesian methods have been successfully applied in actuarial statistics and have proved to be a good tool for resolving problems related to the setting of insurance premiums. In particular, a merit rating method that is widely used in automobile insurance is the bonus-malus system. This system is characterized by the premium increasing with the number of claims and decreasing with the period in which the policyholder does not make a claim. In this case, the insurance company, looking for market competitiveness, must use a rating structure that matches the premiums for the risks as closely as possible, avoiding that policyholders transfer their policy to another insurance company, seeking lower premiums or higher discounts.