Coskewness under dependence uncertainty

03/30/2023

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by   Carole Bernard, et al.

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We study the impact of dependence uncertainty on the expectation of the product of d random variables, 𝔼(X_1X_2⋯ X_d) when X_i ∼ 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].