Hierarchical Bayesian collective risk model: an application to health insurance

This paper deals with the main statistical steps involved in building an insurance plan, with special emphasis on an application to health insurance. The pure premium is predicted based on the available past information concerning the number and the amount of losses, and also the population exposed to risk. Both the size and the number of losses are treated in a stochastic manner. The claims are assumed to follow a Poisson process and the claim sizes are independent and identically distributed non-negative random variables. The model proposed is a generalization of the collective risk model, usually applied in practice. The evolution of the population at risk is also stochastically described via a nonlinear hierarchical growth model. Furthermore, a theoretical decision framework is adopted for evaluating the premium. Model selection and premium calculation are obtained from the predictive distribution, incorporating all the uncertainties involved.