Prediction error for credible claims reserves: an h-likelihood approach

In this paper we consider a hierarchical overdispersed Poisson-gamma model for claims reserving as a hierarchical generalized linear model, in which the h-likelihood approach is applied to estimate the parameters. The model allows us to take account of external data, e.g. external estimates of ultimate claims. Predictions and prediction errors of the claims reserves are evaluated. For each origin year, the estimated reserve can be seen as a credible claims reserve: a mixture of a Chain–ladder type and a Bornhuetter–Ferguson type claims reserve.