Model risk in claim reserving with generalised linear models

According to the newly developing International Accounting Standards, the evaluation of the liabilities arising from the outstanding claims of a general insurance portfolio should contain a market-based adjustment for risk, referred to as the market value margin. Sources of risk to be taken into account in the assessment of the market value margin are the process risk, the parameter risk and the model risk. The aim of this paper is to illustrate how the stochastic models for the future payments, based on the framework of generalised linear models and quasi-likelihood models can be used to evaluate these types of risk and, in particular, to reduce the model risk. Following a classical approach in the statistical literature, the classes of models with variance and link functions of the power family are considered. The comparison of models is performed through the log-likelihood for models with distribution in the exponential dispersion family and through the extended quasi-likelihood in the semi-parametric case in which only the first and second moments of the response variables are specified. Numerical examples on real data illustrate the methodology. KW Stochastic claims reserving,Generalized linear models,Quasi-likelihood models,Mean squared error of prediction,Model risk.