Finance Department


Date of this Version


Document Type



Journal of Actuarial Practice 13 (2006), pp. 61-80


Copyright 2006 Absalom Press


We consider the problem of determining health insurance premiums based on past information on size of loss, number of losses, and size of population at risk. The size of loss and the number of losses are treated as mutually independent random variables. The number of losses is assumed to follow a Poisson process, and the loss sizes are independent and identically distributed non-negative random variables, and the population at risk is assumed to follow a non-linear growth model. An expression for the premium is obtained through maximization of the insurer's expected utility under a Bayesian model. The parameter estimation process is based on Monte Carlo Markov chain (MCMC). Our methology is applied to two real data sets.