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arXiv · 2503.05348

Stochastic dominance of sums of risks under dependence conditions

Jorge Navarro·José M. Zapata
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Abstract

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.

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Jorge Navarro, José M. Zapata. 2025-03-07. Stochastic dominance of sums of risks under dependence conditions. https://arxiv.org/abs/2503.05348

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