An Extreme Value Approach to Modelling Construction Defect Insurance Claims

Sammanfattning: Predicting future large claims, as well as the total cost, of a specific insurance is essential for insurance companies, for example when setting premium levels or purchasing reinsurance coverage. The purpose of this thesis is to investigate if extreme value theory can be applied to construction defect insurance claims. Data is provided by an insurance company offering construction insurance and two approaches are tested; the block maxima method using the generalized extreme value distribution and the peaks over threshold method using the generalized Pareto distribution. For both approaches, estimates for 10 and 50 year return levels, as well as 95$\%$ confidence intervals for the estimates, are calculated. Due to large variances for long periods of predictions, the confidence intervals are rather wide for both methods and hence the estimates need to be updated when more data become available in the future. Additionally, a model to estimate the expected total annual payout for the construction defect insurance of this specific insurance company is proposed. The estimated total annual payout should also be used as an indication of how large buffers the insurance companies need to build up in order to have enough coverage for possible large payouts in the future.