RISK-SENSITIVE AUTOMOBILE INSURANCE PREMIUM PRICING UNDER A BONUS-MALUS SYSTEM

Abstract

This study proposes an automobile insurance premium pricing model under a Bonus-Malus System (BMS), considering both claim frequency and claim severity. The claim frequency is assumed to follow the Poisson-New Sushila distribution, while claim severity is assumed to follow the Exponential-New Sushila distribution. A Bayesian approach is applied to estimate insurance premiums based on the policyholder’s claim history. Using a real-world motor insurance dataset comprising 67,856 policies, the results show that the Poisson-New Sushila distribution provides a better fit to the claim frequency data than the competing distributions, while the Exponential-New Sushila distribution provides the best fit to the claim severity data, with a Kolmogorov-Smirnov statistic of 0.043192. The premium calculations demonstrate that the proposed premiums reflect both the frequency and severity of claims, resulting in more appropriate and equitable premium pricing for both policyholders and insurers. The findings can be applied as a guideline for developing risk-based motor insurance premium pricing systems based on policyholders’ risk levels, thereby supporting effective risk management and premium determination by insurance companies.

Keywords: Automobile Insurance, Bonus-Malus System, Bayesian Approach, Claim Frequency, Claim Severity