Using the Poisson Inverse Gaussian in Bonus-Malus Systems

In this paper, we will cover the Bonus-malus system m 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 Js 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 LEMA~RE'S (1985) bonus system. KEYWORDS Mixed Poisson distribution; Poisson reverse Gaussian; generalized inverse Gaussian; Bayes theorem; quadratic loss function, exponential utility function.