Let X1, . . ., Xn be a set of n risks, with decreasing joint density function f, faced by a policyholder who is insured for this n risks, with upper limit coverage for each risk. Let l=(l1, . . .ln) and l*=(l1*,. . .ln*) be two vectors of policy limits such that l* is majorized by l. It is shown that ∑i=1n(Xi-li)+ is larger than ∑i=1n(Xi-li*)+ according to stochastic dominance if f is exchangeable. It is also shown that ∑i=1n(Xi-l(i))+ is larger than ∑i=1n(Xi-l(i)*)+ according to stochastic dominance if either f is a decreasing arrangement or X1, . . ., Xn are independent and ordered according to the reversed hazard rate ordering. We apply the new results to multivariate Pareto distribution.
