Generalized geoadditive models for insurance claims data

Generalized regression models provide a flexible framework for analyzing insurance claims data. Most applications are still based on generalized linear models, assuming that covariate effects can be modeled by a parametric linear predictor. In many cases, however, the data contain detailed information on metrical and geographical covariates. Their effects are often highly nonlinear, and are at least rather difficult to assess with conventional parametric models. In this paper, we propose generalized geoadditive models which can simultaneously incorporate usual linear effects as well as nonlinear effects of metrical and spatial covariates within a unified semiparametric Bayesian approach. Statistical inference is based on Markov chain Monte Carlo techniques. We apply our methods to analyse the amount of loss and claim frequency for car insurance data from a German insurance company.