Bayesian modelling of health insurance losses

Zeinab Amin and Maram Salem

Journal of Applied Statistics, 2015, vol. 42, issue 2, 231-251

Abstract: The purpose of this paper is to build a model for aggregate losses which constitutes a crucial step in evaluating premiums for health insurance systems. It aims at obtaining the predictive distribution of the aggregate loss within each age class of insured persons over the time horizon involved in planning employing the Bayesian methodology. The model proposed using the Bayesian approach is a generalization of the collective risk model, a commonly used model for analysing risk of an insurance system. Aggregate loss prediction is based on past information on size of loss, number of losses and size of population at risk. In modelling the frequency and severity of losses, the number of losses is assumed to follow a negative binomial distribution, individual loss sizes are independent and identically distributed exponential random variables, while the number of insured persons in a finite number of possible age groups is assumed to follow the multinomial distribution. Prediction of aggregate losses is based on the Gibbs sampling algorithm which incorporates the missing data approach.

Date: 2015
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DOI: 10.1080/02664763.2014.947247

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