Bayesian Bonus-Malus Premiums Under Different Loss Functions in Car Insurance

Abstract

In the traditional bonus-malus system, automobile insurance premiums are typically calculated based solely on claim frequency. This study introduces an alternative approach, incorporating both claim frequency and claim severity into the determination of premiums. Furthermore, the research explores the premiums under various loss functions, including quadratic, linex, and entropy, applied to both frequency and severity. The Bayesian approach is employed to compute the bonus-malus premiums. Additionally,this work relies on the R program to provide a numerical application based on a real automobile insurance dataset. By incorporating diverse loss functions, this approach aims to enhance flexibility, achieve balance, and provide greater control over premiums, all while ensuring the solvency of the insurance company.