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Algorithms for Finding Copulas Minimizing Convex Functions of Sums

Author

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  • Carole Bernard

    (Department of Accounting Law and Finance at Grenoble Ecole de Management, 12 Rue Pierre Sémard, 38000 Grenoble, France)

  • Don McLeish

    (Department of Statistics and Actuarial Science at the University of Waterloo, 200 University Avenue West, Waterloo, ON N2L3G1, Canada)

Abstract

In this paper, we develop improved rearrangement algorithms to find the dependence structure that minimizes a convex function of the sum of dependent variables with given margins. We propose a new multivariate dependence measure, which can assess the convergence of the rearrangement algorithms and can be used as a stopping rule. We show how to apply these algorithms for example to finding the dependence among variables for which the marginal distributions and the distribution of the sum or the difference are known. As an example, we can find the dependence between two uniformly distributed variables that makes the distribution of the sum of two uniform variables indistinguishable from a normal distribution. Using MCMC techniques, we design an algorithm that converges to the global optimum.

Suggested Citation

  • Carole Bernard & Don McLeish, 2016. "Algorithms for Finding Copulas Minimizing Convex Functions of Sums," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(05), pages 1-26, October.
    • Handle: RePEc:wsi:apjorx:v:33:y:2016:i:05:n:s0217595916500408
    DOI: 10.1142/S0217595916500408
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    References listed on IDEAS

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    Cited by:

    1. Carole Bernard & Oleg Bondarenko & Steven Vanduffel, 2018. "Rearrangement algorithm and maximum entropy," Annals of Operations Research, Springer, vol. 261(1), pages 107-134, February.
    2. Carole Bernard & Oleg Bondarenko & Steven Vanduffel, 2021. "A model-free approach to multivariate option pricing," Review of Derivatives Research, Springer, vol. 24(2), pages 135-155, July.
    3. Bernard, Carole & Kazzi, Rodrigue & Vanduffel, Steven, 2020. "Range Value-at-Risk bounds for unimodal distributions under partial information," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 9-24.
    4. Kris Boudt & Edgars Jakobsons & Steven Vanduffel, 2018. "Block rearranging elements within matrix columns to minimize the variability of the row sums," 4OR, Springer, vol. 16(1), pages 31-50, March.

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