Pricing automobile insurance using mixed Poisson distributions

Automobile insurance, particularly motor third liability insurance covers dominant share in the portfolio of non-life insurance in almost all countries of the world. The aim of this paper is to analyze the process of determining premium rates in automobile liability insurance using the bonus-malus system as one of the key instruments to increase traffic safety. The paper presents a brief analysis of the automobile liability insurance market in Serbia, with special reference to the bonus-malus system introduced in practice. Using a sample from the year 2015 provided by one of the biggest Serbian automobile liability insurer it has been proved that the mixed Poisson distibutions are appropriate choice in the process of modeling of the afore mentioned tariff system. The main result of the study is the construction of bonus - malus system based on mixed Poisson models, where expected value principle is used to determine the net premium. According to the analysis, it has been concluded that during the creation of a bonus-malus system in practice it is important to use certain mathematical and statistical models, as well as that the existing tariff system of automobile liabilit