Coskewness under dependence uncertainty

Carole Bernard, Jinghui Chen, Ludger Ruschendorf and Steven Vanduffel ()

Papers from arXiv.org

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 $[-1,\ 1]$.

Date: 2023-03
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http://arxiv.org/pdf/2303.17266 Latest version (application/pdf)

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Journal Article: Coskewness under dependence uncertainty (2023)
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