조건부다층혼합분포를 이용한 비비례 재보험료 계산

In nonproportional reinsurance contract, if the losses for which reinsurer is responsible bear the characteristics of high severity and low frequency, then extremal losses ​​may occur, which makes it difficult to calculate the reinsurance premium. One of the reason for such difficulty is that it is hard to obtain a good fit of distribution in entire domain of loss random variable, in special, as the heavy-tailedness of the loss increases. Mixture distribution methodology associated with extreme value theory for tail distribution has been frequently applied as an alternative, but the problems of threshold estimation and model selection remain an unresolved task. This study proposed a method for estimating conditional layer mixture distributions that can compensate for these shortcomings of known mixture distributions. It has been shown that it can be applied to the calculation of reinsurance premiums such as excess of loss reinsurance treaty or ECOMOR. As an application of the results of the study, empirical analysis was performed to estimate the component distribution of conditional layer mixture distribution, using the empirical data on the environmental damage liability. Also, a method of measuring risk-diversification effect by reinsurance contract was discussed.