Abstract:
The bonus-malus system is an insurance system that divides premium classes. If a policyholder files a claim in the previous year, a malus or penalty is charged, which increases the amount of premium that must be paid the following year. If, on the other hand, the policyholder does not file a claim in the preceding year, a bonus or discount will be applied to the premium to be paid the following year. The primary goal of this thesis is to develop the bonus-malus premium system as one of the most important tools for improving traffic safety. The Poisson-Gamma and Poisson – Inverse Gaussian distributions will be used to determine the expected frequencies of the observed data in this thesis. The maximum likelihood approach will be used to estimate the parameters, whereas Bayesian estimation method will be utilized to calculate the premium. Throughout this thesis, it has been shown that the Poisson-Gamma and Poisson Inverse Gaussian distributions are appropriate choices in the process of modeling the bonus-malus premium system using a sample from generation data in R packages. The study's key result is the development of a bonus-malus premium table based on the Bayesian estimator, where the net premium is determined using the expected value principle. According to the findings, the proposed premium system could be enhanced by integrating additional priori policyholder characteristics.
