Determination Premiums Motor Vehicle Insurance Using Bonus-Malus Optimal

The increasing number of motor vehicles in Sumatera has heightened accident risks, emphasizing the need for motor vehicle insurance to distribute risk between policyholders and insurers. Determining fair and risk-based premium requires consideration of each policyholder’s claim history. This study aimed to determine motor vehicle insurance premiums using the optimal bonus-malus system based on claim data for the minibus category with comprehensive coverage in Sumatera during 2022. The proposed model extended the Bayesian bonus-malus framework by incorporating the trust region reflective (TRR) method for estimating claim severity and the Newton-Raphson method for estimating claim frequency, thereby enhancing parameter estimation accuracy and numerical stability. This approach offers a more equitable and precise premium adjustment mechanism aligned with individual risk levels, contributing to improved risk-based pricing, reduced underwriting losses, and greater transparency for policyholders. The results showed that the claim frequency followed the Poisson-Lindley distribution, while claim severity followed the lognormal-gamma distribution. Based on these models, the premium was computed by multiplying the basic premium by the relative value of the subsequent year and dividing it by the base relative value. Premium decrease in the absence of claims and increase when claims occur.