A Study of the Loss Distribution of Natural Disasters in Norway Comparing a Common Model with a Model Broken Down into Catastrophe Types

Abstract

Norway has been suffering from numerous natural disasters throughout its history. In order to be able to compensate losses caused by natural disasters such as storm, flood, earthquake, avalanche or other natural disasters, all buildings and all accessories in Norway with insurance policies that cover fires are automatically insured against natural catastrophes followed by the Natural Disaster Insurance Law. The arrangement is managed by Norwegian Natural Perils Pool. Based on the recorded data of the catastrophes between 1980 and 2013, we have tested different distributions for the model of the catastrophe frequency and the model of the amounts of compensation. The extreme amounts of compensation were modelled with a Pareto distribution, in accordance with Pickand's theorem. The main issue of this thesis was to compare the loss model based on all the catastrophes and the one based on a combination of the single catastrophe types. Therefore, we fitted both a common model and separate models for the different catastrophe types to the data. Further, we applied the best fitting distributions to construct the total loss model. Thereafter, the reserve was estimated from the upper $\epsilon$-percentile of the total loss model by Monte Carlo simulation. Uncertainties in the underlying models as well as the uncertainty in the reserve estimation were assessed by the bootstrap method. From the results we see that the separate models are preferable to the common model. The confidence intervals of the distribution parameters indicate a significant difference of the parameters in the separate models and the common model. Although the uncertainty in the reserve estimate based on the separate models is larger than the one based on the common model, it is more "correct" to have a higher reserve estimate to ensure that the Pool is able to cover significant losses under worst-case situations. Therefore, on the premise that the models are reasonable and correct, a break-down into catastrophe type model is suggested.