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arXiv · 2303.17266

Coskewness under dependence uncertainty

Carole Bernard·Jinghui Chen·Ludger Ruschendorf·Steven Vanduffel
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Abstract

We study the impact of dependence uncertainty on the expectation of the product of $d$ random variables, $\mathbb{E}(X_1X_2\cdots X_d)$ when $X_i \sim F_i$ for all~$i$. Under some conditions on the $F_i$, explicit sharp bounds are obtained and a numerical method is provided to approximate them for arbitrary choices of the $F_i$. The results are applied to assess the impact of dependence uncertainty on coskewness. In this regard, we introduce a novel notion of "standardized rank coskewness," which is invariant under strictly increasing transformations and takes values in $[-1,\ 1]$.

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Carole Bernard, Jinghui Chen, Ludger Ruschendorf, Steven Vanduffel. 2023-03-30. Coskewness under dependence uncertainty. https://arxiv.org/abs/2303.17266

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