Stochastic Bounds for Discrete-time Claim Processes with Correlated Risks

The purpose of this paper is to derive bounds on the marginal distributions of a discrete-time claim process S with correlated claims. These bounds are based on stochastic comparison in convex order and in Laplace transform order of the process S with two corresponding processes Sˆ and S˜ having, respectively, uncorrelated and weakly correlated claims. The relevance of these comparisons is due to the simple structure of the processes Sˆ and S˜, which are nothing else than a random walk and a mixed random walk. The paper also contains the proof of the closure under mixture property of some dependence orders, like supermodular and PQD, and some applications of the main results. Keywords: Dependence Orders, Convex Order, Laplace Transform Order, Discrete-time And Continuous Time Claim Processes, Random Environments, Correlated Claims