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Coskewness under dependence uncertainty

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  • Carole Bernard
  • Jinghui Chen
  • Ludger Ruschendorf
  • Steven Vanduffel

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 $[-1,\ 1]$.

Suggested Citation

  • Carole Bernard & Jinghui Chen & Ludger Ruschendorf & Steven Vanduffel, 2023. "Coskewness under dependence uncertainty," Papers 2303.17266, arXiv.org.
    • Handle: RePEc:arx:papers:2303.17266
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    References listed on IDEAS

    as
    1. Wang, Bin & Wang, Ruodu, 2015. "Extreme negative dependence and risk aggregation," Journal of Multivariate Analysis, Elsevier, vol. 136(C), pages 12-25.
    2. Wang, Bin & Wang, Ruodu, 2011. "The complete mixability and convex minimization problems with monotone marginal densities," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1344-1360, November.
    3. Roger Nelsen & Manuel Úbeda-Flores, 2012. "Directional dependence in multivariate distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(3), pages 677-685, June.
    4. Bignozzi, Valeria & Puccetti, Giovanni, 2015. "Studying mixability with supermodular aggregating functions," Statistics & Probability Letters, Elsevier, vol. 100(C), pages 48-55.
    5. Rüschendorf, Ludger & Uckelmann, Ludger, 2002. "On the n-Coupling Problem," Journal of Multivariate Analysis, Elsevier, vol. 81(2), pages 242-258, May.
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