Stochastic Comparisons Of Dependent Risks

This paper studies the relation of dependency risks and its impact on the risk portfolio. Stochastic orders with given marginal distributions, including the stochas-tically increasing order, correlation order and supermodular order are studied. If one group of risks is smaller than another in the stochastically increasing order which with same given marginal distributions, then the two risk protfolios have correspond connection in the dispersive order, excess wealth order and stop-loss order.