An Actuarial Approach to Determining the Optimal Premium for Car Accident Insurance Based on Claim Frequency and Severity Data

Abstract

The determination of car accident insurance premiums requires a model capable of capturing variations in claim frequency and claim severity to ensure fairness and competitiveness. This study employs aggregate claim distributions—Negative Binomial–Exponential and Negative Binomial–Gamma—under two approaches: the Pure Premium Principle and the Expected Value Principle. the analysis indicates that the Expected Value Principle is more optimal, as it incorporates a premium loading factor (ψ) to account for additional risk adjustments. The calculations yield premiums of IDR 2,802,908,472.03 for the Negative Binomial–Exponential model and IDR 5,566,024,615.90 for the Negative Binomial–Gamma model. The Negative Binomial–Gamma model was selected as the optimal premium calculation model, resulting in a final premium of IDR 4,619,107.565 after dividing by the total claim frequency of 1,205. These findings confirm that the choice of aggregate claim distribution significantly affects the premium amount and provides a stronger foundation for insurance companies to establish sound and competitive pricing.