Using the Poisson Inverse Gaussian in Bonus-Malus Systems

Abstract

In this paper, we will cover the bonus-malus system in automobile insurance. Bonus-malus systems are based on the distribution of the number of car accidents. Therefore, the modelling and fitting of that distribution are considered. Fitting of data is done using the Poisson inverse Gaussian distribution, which shows a good fit. Building the bonus system is done by minimizing the insurer's risk, according to Lemaire's (1985) bonus system.