Spatial Statistical Modelling of Insurance Claim Frequency

Abstract: In this thesis a fully Bayesian hierarchical model that estimates the number of aggregated insurance claims per year for non-life insurances is constructed using Markov chain Monte Carlo based inference with Riemannian Langevin diffusion. Some versions of the model incorporate a spatial effect, viewed as the relative spatial insurance risk that originates from a policyholder's geographical location and where the relative spatial insurance risk is modelled as a continuous spatial field. It is shown that the inclusion of a spatial effect derived from a Gaussian Markov random field with Matérn covariance in a generalised linear mixed model (GLMM) has better predictive performance regarding the number of aggregated claims in an insurance portfolio compared to GLMMs that lack such a spatial effect.