A Markov-Modulated Tree-Based Gradient Boosting Model for Auto-Insurance Risk Premium Pricing in Ghana

Abstract

In most sub-Saharan African countries, the mechanism for pricing auto insurance policies is tariff based. This means that the key factor that influences price changes is usually based on margins, regulation and legislative dynamics. Additionally, where pricing is risk based, analysis has in most cases focused on internal historical data. These policy regimes have led to unfair price distortions among policyholders and have increased risk of portfolios for most insurance companies. In this study we consider historical risk and location risk that is influential to loss cost. The study develops a Markov-modulated Tree-based Gradient Boosting (MMGB) model for pricing autoinsurance premiums. The Markov-modulated Tree-based Gradient Boosting is a Tweedie generalized model-based pricing algorithm with a compound-Poisson distribution whose rate varies according to accident risk in a Markov process. Thus, the study extends the existing premium pricing framework by integrating both historical and location risk into the main pricing framework. The study applies the model to a motor insurance data set from Ghana. The results show that the proposed method is superior to other competing models since it generates relatively fair premium predictions for the non-life auto-insurance companies, helping to mitigate more the insured risk for the firm and the industry.