Stochastic comparisons of the largest claim amounts from two sets of interdependent heterogeneous portfolios

Abstract

Let Xλ1 ,..., Xλn be continuous and dependent non-negative random variables and Yi = Ipi Xλi , i = 1,..., n, where Ip1 ,..., Ipn are independent Bernoulli random variables independent of Xλi ’s, with E[Ipi ] = pi , i = 1,..., n. In actuarial sciences, Yi corresponds to the claim amount in a portfolio of risks. In this paper, we compare the largest claim amounts of two sets of interdependent portfolios, in the sense of usual stochastic order, when the variables in one set have the parameters λ1,..., λn and p1,..., pn and the variables in the other set have the parameters λ1∗,..., λn∗ and p∗1,..., p∗n . For illustration, we apply the results to some important models in actuary.