Dynamic Pricing Models for Automobile Insurance

The accurate pricing of automobile insurance remains a critical challenge, particularly in markets where traditional models fail to capture risk heterogeneity. This study addresses the limitations of conventional Poisson models, which assume uniform accident probabilities among insured individuals, by incorporating advanced probabilistic models that account for overdispersion and individual risk variability. The primary objective is to develop a more precise and equitable pricing model for automobile insurance premiums, integrating statistical and Bayesian inference techniques. The research focuses on Algeria, a market characterized by distinct driving conditions, regulatory frameworks, and demographic patterns that influence accident frequency. Using a dataset of 680 insured individuals from the Société Algérienne d'Assurances, collected over the period 2021–2024, this study applies the Poisson-Gamma and Poisson-Inverse Gaussian models to refine accident risk assessment. The findings reveal that accident frequency is significantly influenced by factors such as gender, age, driving experience, vehicle power, and usage. The Poisson-Gamma model outperforms the standard Poisson model by better capturing individual differences, while the Poisson-Inverse Gaussian model further refines risk estimation by addressing heavy-tailed distributions. Additionally, a Bayesian posterior pricing framework within a Bonus-Malus system is introduced, enabling gains to dynamically adjust premiums based on an individual’s accident history. The study confirms the superiority of these models through statistical validation and goodness-of-fit tests, demonstrating their potential for improving risk assessment and pricing accuracy. The results offer practical applications for insurance companies, policymakers, and regulators seeking to enhance premium fairness and financial sustainability.