Claims reserving: A correlated Bayesian model

Estimation of adequate reserves for outstanding claims is one of the main activities of actuaries in property/casualty insurance and a major topic in actuarial science. The need to estimate future claims has led to the development of many loss reserving techniques. There are two important problems that must be dealt with in the process of estimating reserves for outstanding claims: one is to determine an appropriate model for the claims process, and the other is to assess the degree of correlation among claim payments in different calendar and origin years. We approach both problems here. On the one hand we use a gamma distribution to model the claims process and, in addition, we allow the claims to be correlated. We follow a Bayesian approach for making inference with vague prior distributions. The methodology is illustrated with a real data set and compared with other standard methods.