On spatial diversification and insurer’s solvency under Nat-Cat losses
Weather-related and catastrophe insurance losses typically exhibit strong spatial dependence, particularly at the local level. However, if the considered region is large enough, there may be sufficient diversification, which is essential for the insurability of related risks. In this paper we quantitatively study this question from several perspectives. Looking into real or simulated historical loss data for municipalities, we investigate the aggregation properties within a province or country, as well as for the aggregation of European countries towards a continent-wide portfolio solution, with a particular emphasis on implied solvency capital requirements. Beyond politically defined units, we then also look for the minimal size of an insured region such that a certain safety target is met for the insurance against a given peril, using a claim random field that combines a max-stable model for the dependence pattern of the natural phenomenon and a suitable damage function for the implied losses, where target values are coefficient of variation, expected return on invested solvency capital and necessary premium loading. We illustrate the results for a number of case studies for flood and storm losses in Europe.
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