Issues in claims reserving and credibility: a semiparametric approach with mixed models

Using the statistical methodology of semi-parametric regression and its connection with mixed models, this article revisits smoothing models for loss reserving and credibility. Apart from the flexibility inherent to all semiparametric methods, advantages of the semiparametric approach developed here are threefold. First, a Bayesian implementation of these smoothing models is relatively straightforward and allows simulation from the full predictive distribution of quantities of interest. Second, because the constructed models have an interpretation as (generalized) linear mixed models ((G)LMMs), standard statistical theory and software for (G)LMMs can be used. Third, more complicated data sets, dealing, for example, with quarterly development in a reserving context, heavy tails, semi-continuous data, or extensive longitudinal data, can be modeled within this framework.