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Rearrangement algorithm and maximum entropy

Author

Listed:
  • Carole Bernard

    (Grenoble Ecole de Management
    Vrije Universiteit Brussel (VUB))

  • Oleg Bondarenko

    (University of Illinois at Chicago)

  • Steven Vanduffel

    (Vrije Universiteit Brussel (VUB))

Abstract

We study properties of the block rearrangement algorithm (BRA) in the context of inferring dependence among variables given their marginal distributions and the distribution of their sum. We show that when all distributions are Gaussian the BRA yields solutions that are “close to each other” and exhibit almost maximum entropy, i.e., the inferred dependence is Gaussian with a correlation matrix that has maximum possible determinant. We provide evidence that, when the distributions are no longer Gaussian, the property of maximum determinant continues to hold. The consequences of these findings are that the BRA can be used as a stable algorithm for inferring a dependence that is economically meaningful.

Suggested Citation

  • Carole Bernard & Oleg Bondarenko & Steven Vanduffel, 2018. "Rearrangement algorithm and maximum entropy," Annals of Operations Research, Springer, vol. 261(1), pages 107-134, February.
    • Handle: RePEc:spr:annopr:v:261:y:2018:i:1:d:10.1007_s10479-017-2612-2
    DOI: 10.1007/s10479-017-2612-2
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    References listed on IDEAS

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    1. Bernard, Carole & Vanduffel, Steven, 2015. "A new approach to assessing model risk in high dimensions," Journal of Banking & Finance, Elsevier, vol. 58(C), pages 166-178.
    2. Ait-Sahalia, Yacine & Lo, Andrew W., 2000. "Nonparametric risk management and implied risk aversion," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 9-51.
    3. 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.
    4. 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.
    5. Stutzer, Michael, 1996. "A Simple Nonparametric Approach to Derivative Security Valuation," Journal of Finance, American Finance Association, vol. 51(5), pages 1633-1652, December.
    6. Jackwerth, Jens Carsten & Rubinstein, Mark, 1996. "Recovering Probability Distributions from Option Prices," Journal of Finance, American Finance Association, vol. 51(5), pages 1611-1632, December.
    7. Durante, Fabrizio & Sánchez, Juan Fernández, 2012. "On the approximation of copulas via shuffles of Min," Statistics & Probability Letters, Elsevier, vol. 82(10), pages 1761-1767.
    8. Stephen A. Ross, 1976. "Options and Efficiency," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 90(1), pages 75-89.
    9. Bondarenko, Oleg, 2003. "Estimation of risk-neutral densities using positive convolution approximation," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 85-112.
    10. E. G. Coffman & M. Yannakakis, 1984. "Permuting Elements Within Columns of a Matrix in Order to Minimize Maximum Row Sum," Mathematics of Operations Research, INFORMS, vol. 9(3), pages 384-390, August.
    11. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-651, October.
    12. Carole Bernard & Ludger Rüschendorf & Steven Vanduffel, 2017. "Value-at-Risk Bounds With Variance Constraints," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(3), pages 923-959, September.
    13. Embrechts, Paul & Puccetti, Giovanni & Rüschendorf, Ludger, 2013. "Model uncertainty and VaR aggregation," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 2750-2764.
    14. Rubinstein, Mark, 1994. "Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
    15. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    16. Banz, Rolf W & Miller, Merton H, 1978. "Prices for State-contingent Claims: Some Estimates and Applications," The Journal of Business, University of Chicago Press, vol. 51(4), pages 653-672, October.
    17. Carole Bernard & Ludger Rüschendorf & Steven Vanduffel & Jing Yao, 2017. "How robust is the value-at-risk of credit risk portfolios?," The European Journal of Finance, Taylor & Francis Journals, vol. 23(6), pages 507-534, May.
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    3. Takaaki Koike & Liyuan Lin & Ruodu Wang, 2022. "Joint mixability and notions of negative dependence," Papers 2204.11438, arXiv.org, revised Jan 2024.
    4. Xu, Chi & Zheng, Chunling & Wang, Donghua & Ji, Jingru & Wang, Nuan, 2019. "Double correlation model for operational risk: Evidence from Chinese commercial banks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 516(C), pages 327-339.
    5. Rabeh Khalfaoui & Sakiru Adebola Solarin & Adel Al-Qadasi & Sami Ben Jabeur, 2022. "Dynamic causality interplay from COVID-19 pandemic to oil price, stock market, and economic policy uncertainty: evidence from oil-importing and oil-exporting countries," Annals of Operations Research, Springer, vol. 313(1), pages 105-143, June.

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