Premium Determination on Bonus Malus System Using Mixed Poisson Distribution.

Abstract

Bonus malus system is an insurance system that conciders classes of premium division. Its premium depends on the number of claims that are proposed by policyholder each year. Therefore, the rate of premium on current year is determined by the number of claims which were made on previous year. This paper studies determination methods of insurance premium with bonus malus system using mixed Poisson distribution. Further, it also studies construction of a bonus malus table using the net premium principle (principle of zero utility) on mixed Poisson distribution. There are two cases in determining the premium estimates using mixed Poisson distribution, i.e. the parametric and non-parametric estimation. Determination of the best premium on parametric estimation can be made using Hofmann distribution. Determining the best premium with nonparametric estimation can be made using different parameters on the three groups of risk. The nonparametric case is better than the parametric case in context of goodness of fit test. The best distribution of both estimation cases are then used to construct the best optimal bonus malus table and a bonus malus table for weighted premium. In this case, the parametric estimation fits better than the nonparametric estimation.