Abstract

Journal of Actuarial Practice

Volume 13, 2006

Bayesian Analysis of a Health Insurance Model

Helio S. Migon and Edison M.O. Penna

Abstract

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 methodology is applied to two real data sets.

Key words and phrases: collective risk model, aggregate loss, rate making, predictive distribution, stochastic simulation, Monte Carlo Markov chain (MCMC)}

Corresponding Author:

Helio S. Migon

Universidade Federal do Rio de Janeiro (UFRJ)

Operational Research Section/COPPE

CP.: 68507

CEP 21941-972 - Rio de Janeiro RJ

BRAZIL

E-mail: migon@im.ufrj.br