Estimating Predictive Distributions for Loss Reserve Models

This paper demonstrates a Bayesian method for estimating the distribution of future loss payments of individual insurers. The main features of this method are: (1) the stochastic loss reserving model is based on the collective risk model; (2) predicted loss payments are derived from a Bayesian methodology that uses the results of large, and presumably stable, insurers as its prior information; and (3) this paper tests its model on large number of insurers and finds that its predictions are well within the statistical bounds expected for a sample of this size. the paper concludes with an analysis of reported reserves and their subsequent development in terms of the predictive distribution calculated by this Bayesian methodology.