Claims reserving in the hierarchical generalized linear model framework

We consider an approach based on the hierarchical generalized linear models and h-likelihood estimators for claims reserving in non-life insurance. The hierarchical generalized linear models represent a class of flexible mixture models that extend the generalized linear models and the generalized linear mixed models. The fitting algorithm and the inferential analyses can be obtained by applying standard procedures to one or more generalized linear models, suitably defined. Our study examines how the models can be used to obtain predictors of the claims reserves and to determine their prediction uncertainty.

► We introduce hierarchical generalized linear models and their extensions for claims reserving. ► Random effects connected with the origin years are considered. ► The parameters of the distributions of the random effects allow us to take account of external information. ► We obtain predictors of the claims reserves and determine the prediction uncertainty by means of the conditional mean square error of prediction.