Evaluation of the Variance in the Premium Provision Estimate : Handling Inhomogeneous and Decreasing Risk in Premium Provision Purposes

Abstract: The costs related to events of losses within non-life insurance are stochastic and a prerequisite of running a successful insurance business is to predict risks and future costs. From both a business- and regulatory perspective, it is of high interest to have a genuine understanding of the precision and the sensitivity of the estimated costs and future risks. This thesis aims to provide an alternative procedure of how to estimate the costs related to the future and, above all, the variance, in the case of dealing with inhomogeneous and decreasing risk. The procedure is based on a separate modeling of the claim frequency and the claim severity, that later can be combined to yield a total cost distribution for a determined time period. The claim severities are modeled based on a parametric and a non-parametric approach and the claim frequencies are modeled with the resampling method bootstrap and by the use of scenarios. The thesis is made in collaboration with the insurance company, Anticimex Insurance, who has contributed with the data as well as expert knowledge related to the actuarial field. The results of the thesis show that the procedure is successful for evaluating estimated total costs distributions and their first and second moments, even in the case of inhomogeneous and decreasing risk.