The HGLM approach to claims reserving with diagonal effects

The claims reserving problem is often addressed in the context of regression models, with parameters that are fixed effects related to observable covariates, typically the origin and the development years. However, also the effects related to the payment or calendar year may be important. In fact, the presence of accounting year effects (also named diagonal effects), imply dependences between different accident years because they act on all accident years, simultaneously. Therefore, the common assumption that accident years behave independently, could not be stated any more. For these reasons, reserving models with random effects and diagonal effects related to unobservable risk parameters connected with diagonal effects have been introduced. They are often studied by following the Bayesian or the Credibility approaches. In this paper, we tackle the problem of the diagonal effects in the context of Hierarchical Generalized Linear Models with the introduction of fixed or random diagonal effects. Besides of the estimation of claims reserves, the model allows for the evaluation of prediction errors.