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

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We consider a Tweedie's compound Poisson regression model with fixed and random effects, to describe the payment numbers and the incremental payments, jointly, in claims reserving. The parameter estimates are obtained within the framework of hierarchical generalized linear models, by applying the h-likelihood approach. Regression structures are allowed for the means and also for the dispersions. Predictions and prediction errors of the claims reserves are evaluated. Through the parameters of the distributions of the random effects, some external information (e.g. a development pattern of industry wide-data) can be incorporated into the model. A numerical example shows the impact of external data on the reserve and prediction error evaluations

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