BONUS-MALUS PREMIUM WITH A FREQUENCY AND A SEVERITY COMPONENT USING THE BAYESIAN METHOD - Belicia Laras Jatnika, Amara
Bonus-Malus System (BMS) is a widely system used in the industry of vehicle industry. This system assesses claim behavior as a consideration in determining premiums. BMS only reviews the frequency component of claims but can lead to unfairness because small-size claims is facing the same premium increase as large-size claims. This Final Project discusses the determination of bonus-malus premiums that simultaneously consider the frequency and size components of claims. The frequency component of claims is classified into four categories: small, medium, large, and very large, based on the claim size for each submitted claim. The claim size component is assumed to follow the Pareto, gamma-Lindley, and Weibull distributions, with parameter values obtained from previous research. Premium determination uses a Bayesian method approach, employing the principles of net premium and loss function. The bonus-malus premium value based on the frequency and claim size components is the product of the Bayesian premium for both components. In this final project, the results of premium increases/decreases using the bonus-malus system based on the three distribution assumptions are provided. The analysis results indicate that as the claim frequency increases, with each claim size becoming larger, the premium increase also becomes higher, and vice versa. However, for a certain total claim size, this does not applicable for the assumption of the Weibull-distributed claim size.