Bayesian Estimation of Outstanding Claim Reserves

In this paper we present an application of Bayesian forecasting methods to outstanding insurance claims. We assume that the time it takes for the claims to be completely paid is fixed and known, that payments are made annually and that the development of partial payments follow a stable pay-off pattern, from one year of origin to another. We present a Bayesian approach to forecasting either the total number claims or the total amount, given complete information for one or two past years and partial information on some development years for several occurrence years. Essentially the data corresponds to a run-off triangle in IBNR. Two different models are presented: one for the number of claims (intensity) and one for the amount of aggregate claims (severity). The advantage of using the Bayesian procedure presented here is that we can derive the complete predictive distribution of the reserve requirements, from which, in turn, we can obtain a point estimate as well as probability intervals and other summary measures, such as mean, variance and quantiles. So the possible range of values for the reserves can be formally quantified. We compare our method with others, using previously published data.