Optimal Bonus-Malus Premium with the Claim Frequency Distribution is Negative Binomial and the Claim Severity Distribution is Truncated Weibull
DOI:
https://doi.org/10.25077/jmua.15.2.179-195.2026Keywords:
Negative Binomial, optimal Bonus-Malus system, risk premium, truncated WeibullAbstract
The optimal bonus-malus system is a system for determining the amount of premium in the next period based on the frequency and severity of claims filed by policyholders in the previous period. In this article, we study the insurance premium formula using the optimal bonus-malus system with the claim frequency has a negative binomial distribution and the claim severity has a truncated Weibull distribution. The method to derive the bonus-malus formula uses a Bayes solution with a quadratic loss function. The formula obtained has been also applied to the data of motor vehicle insurance to calculate the risk premium that must be paid by the policyholder. From the calculation results, the insurance premiums that use the optimal bonus-malus system with a truncated Weibull distribution are more profitable for both the company and the insurer than the Weibull distribution.
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