Generalized Bonus-malus Systems with a Frequency and a Severity Component on an Individual Basis in Automobile Insurance* By

Dionne and Vanasse (1989, 1992) have presented a bonus-malus systems (BMS) that integrates risk classification and experience rating based on the number of claims of each policyholder. This BMS is derived as a function of the years that the policyholder is in the portfolio, of the number of accidents and of the significant – for the number of accidents – individual characteristics. Frangos and Vrontos (2001) extend BMS model by introducing the severity component. They proposed a BMS that integrates a priori and a posteriori information on an individual basis based on the both frequency and the severity component. This BMS will be derived as a function of the years that the policyholder is in the portfolio, of the number of accidents, of the exact size of loss that each one of these accidents incurred, and of the significant individual characteristics for the number of accidents and for the severity of the accidents. Some of the a priori rating variables that could be used are the age, the sex and the place of residence of the policyholder, the age, the type and the cubic capacity of the car, etc.