Risk model in fuzzy random environments

Abstract

In this paper, we consider a risk model in which the claim number process is characterized as a fuzzy random Poisson process and the individual claim amount is assumed to be a fuzzy random variable. The mean chance of the ultimate ruin is researched. The expressions of the mean chance of the ultimate ruin are obtained for zero initial surplus and arbitrary initial surplus. The results obtained in this paper coincide with those in stochastic case when the fuzzy random variables degenerate to random variables. Finally, a numerical example is presented. Keywords: Risk model; Mean chance; Ruin; Aggregate claims; Fuzzy variable; Fuzzy random variable