Selected Reinsurance Models

Abstract

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.