Let $X_1,\ldots,X_n$ 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 ${\bf l}=(l_1 , \ldots l_n)$ and ${\bf l}^*=(l^*_1 , \ldots l^*_n)$ be two vectors of policy limits such that ${\bf l}^*$ is majorized by ${\bf l}$ . It is shown that $\sum_{i=1}^{n} (X_i - l_{i})_+$ is larger than $\sum_{i=1}^{n} (X_i - l_{i}^*)_+$ according to stochastic dominance if $f$ is exchangeable . It is also shown that $\sum_{i=1}^{n} (X_i - l_{(i)})_+$ is larger than $\sum_{i=1}^{n} (X_i - l_{(i)}^*)_+$ according to stochastic dominance if either $f$ is decreasing arrangement or $X_1,\ldots,X_n$ are independent and ordered according to reversed hazard rate ordering . We applied the new results to multivariate Pareto distribution.
