Selected Reinsurance Models

In this paper, we investigate non-classical reinsurance models. Two kinds of such models are presented. One is based on dependent binomial distributions and the second on fuzzy numbers. First, we study dependent random variables representing claims using copulas. We investigate the number of claims the reinsurer covers and the total value of covered claims. We present the influence of the degree of dependence and different copulas on the number and the value of the claims covered by the reinsurer. Second, we analyze the case in which the main parameter of the model, the probability that the reinsurer covers the claim, is uncertain. We treat such a parameter as a fuzzy number in this case and combine randomness and fuzziness. We also study the case when the parameter of a copula which describes the degree of dependence is uncertain.