Dynamic Bayesian Ratemaking: A Markov Chain Approximation Approach

We contribute to the non-life experience ratemaking literature by introducing a computationally efficient approximation algorithm for the Bayesian premium in models with dynamic random effects, where the risk of a policyholder is governed by an individual process of unobserved heterogeneity. Although intuitive and flexible, the biggest challenge of dynamic random effect models is that the resulting Bayesian premium typically lacks tractability. In this article, we propose to approximate the dynamics of the random effects process by a discrete (hidden) Markov chain and replace the intractable Bayesian premium of the original model by that of the approximate Markov chain model, for which concise, closed-form formula are derived. The methodology is general because it does not rely on any parametric distributional assumptions and, in particular, allows for the inclusion of both the cost and the frequency components in pricing. Numerical examples show that the proposed approximation method is highly accurate. Finally, a real data pricing example is used to illustrate the versatility of the approach.