Spatial Statistical Modeling of Insurance Risk

Abstract: The aim of this thesis is to provide a statistical method for assessing the relative insurance risk associated with the policyholders geographical location. Number of claims and claims cost are modeled separately, where the Poisson distribution is assumed for the former and the Gamma distribution is assumed for the latter. The models are based on a Bayesian approach, and inference is made using Integrated Nested Laplace Approximation (INLA). It is shown that an ordinary generalized linear model is sufficient for the Gamma distributed claims cost - while the model for number of claims can be improved by combining the ordinary generalized linear model with a spatial component in a conditional auto regressive model. In this study car insurance data from If P\&C Insurance was used together with spatial referenced data of high resolution, provided by Insightone.