We provide conditions for the stochastic dominance comparisons of a risk $X$ and an associated risk $X+Z$, where $Z$ represents the uncertainty due to the environment and where $X$ and $Z$ can be dependent. The comparisons depend on both the copula $C$ between the distributions of $X$ and $Z$ and on the distribution of $Z$. We provide two different conditions for $C$ which represents new positive dependence properties. Regarding $Z$, we need some symmetry or asymmetry (skew) properties. Some illustrative examples are provided.

翻译：本文针对风险$X$及其关联风险$X+Z$的随机占优比较提供了充分条件，其中$Z$表征环境因素引致的不确定性，且$X$与$Z$可具有相依性。该比较既取决于$X$与$Z$分布间的连接函数$C$，也依赖于$Z$的分布特性。我们为$C$提出了两种不同的条件，这些条件表征了新的正相依性质。对于$Z$，则需要其具备一定的对称性或非对称性（偏斜）性质。文中给出了若干说明性示例。