Bonus-malus Systems in Vehicle Insurance

Actuaries in insurance companies try to design a tariff structure that will fairly distribute the burden of claims among policyholders. Therefore they try to find the best model for an estimation of the insurance premium. The paper deals with an estimate of a priori annual claim frequency and application of bonus-malus system in the vehicle insurance.In this paper, analysis of the portfolio of vehicle insurance data using generalized linear model (GLM) is performed. Based on large real-world sample of data from 67 857 vehicles, the present study proposes a classification analysis approach addressing the selection of predictor variables. The models with different predictor variables are compared by the analysis of deviance. Based on this comparison, the model for the best estimate of annual claim frequency is chosen. Then the bonus-malus (BM) system is used for each class of drivers and Bayesian relative premium is calculated. Finally a fairer premium for different groups of drivers is proposed.