Bayesian Estimation of Outstanding Claim Reserves

This paper presents a Bayesian approach to forecasting outstanding claims, either the total number of claims or the total amount, that is used for claims reserving. The assumption is made that there is complete information for one or two past years of origin and partial information for some development years of other years of origin. It also assumes payments are made annually and that the development of partial payments follows a stable payoff pattern from one year of origin to another. Two different models are presented: one for the number of claims (intensity) and one for claim amounts (severity). The advantage of using this procedure is that actuaries can derive the complete predictive distribution of the reserve requirements, from which, in turn, it is possible to obtain point estimates as well as probability intervals and other summary measures, such as mean, variance, and quantiles.

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