IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2309.17346.html
   My bibliography  Save this paper

Symmetric Bernoulli distributions and minimal dependence copulas

Author

Listed:
  • Alessandro Mutti
  • Patrizia Semeraro

Abstract

The key result of this paper is to find all the joint distributions of random vectors whose sums $S=X_1+\ldots+X_d$ are minimal in convex order in the class of symmetric Bernoulli distributions. The minimal convex sums distributions are known to be strongly negatively dependent. Beyond their interest per se, these results enable us to explore negative dependence within the class of copulas. In fact, there are two classes of copulas that can be built from multivariate symmetric Bernoulli distributions: the extremal mixture copulas, and the FGM copulas. We study the extremal negative dependence structure of the copulas corresponding to symmetric Bernoulli vectors with minimal convex sums and we explicitly find a class of minimal dependence copulas. Our main results stem from the geometric and algebraic representations of multivariate symmetric Bernoulli distributions, which effectively encode several of their statistical properties.

Suggested Citation

  • Alessandro Mutti & Patrizia Semeraro, 2023. "Symmetric Bernoulli distributions and minimal dependence copulas," Papers 2309.17346, arXiv.org.
    • Handle: RePEc:arx:papers:2309.17346
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2309.17346
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ruodu Wang & Liang Peng & Jingping Yang, 2013. "Bounds for the sum of dependent risks and worst Value-at-Risk with monotone marginal densities," Finance and Stochastics, Springer, vol. 17(2), pages 395-417, April.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Thibaut Lux & Antonis Papapantoleon, 2016. "Model-free bounds on Value-at-Risk using extreme value information and statistical distances," Papers 1610.09734, arXiv.org, revised Nov 2018.
    2. Carole Bernard & Ludger Rüschendorf & Steven Vanduffel & Ruodu Wang, 2017. "Risk bounds for factor models," Finance and Stochastics, Springer, vol. 21(3), pages 631-659, July.
    3. Hofert Marius & Memartoluie Amir & Saunders David & Wirjanto Tony, 2017. "Improved algorithms for computing worst Value-at-Risk," Statistics & Risk Modeling, De Gruyter, vol. 34(1-2), pages 13-31, June.
    4. Lin, Feng & Peng, Liang & Xie, Jiehua & Yang, Jingping, 2018. "Stochastic distortion and its transformed copula," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 148-166.
    5. Daniël Linders & Jan Dhaene & Wim Schoutens, 2015. "Option prices and model-free measurement of implied herd behavior in stock markets," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 2(02), pages 1-35.
    6. Shao, Hui, 2017. "Decomposing aggregate risk into marginal risks under partial information: A top-down method," Statistics & Probability Letters, Elsevier, vol. 124(C), pages 97-100.
    7. Corrado De Vecchi & Max Nendel & Jan Streicher, 2024. "Upper Comonotonicity and Risk Aggregation under Dependence Uncertainty," Papers 2406.19242, arXiv.org.
    8. Giovanni Puccetti & Pietro Rigo & Bin Wang & Ruodu Wang, 2019. "Centers of probability measures without the mean," Journal of Theoretical Probability, Springer, vol. 32(3), pages 1482-1501, September.
    9. Ra'ul Torres & Rosa E. Lillo & Henry Laniado, 2015. "A Directional Multivariate Value at Risk," Papers 1502.00908, arXiv.org.
    10. Furman, Edward & Kuznetsov, Alexey & Su, Jianxi & Zitikis, Ričardas, 2016. "Tail dependence of the Gaussian copula revisited," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 97-103.
    11. Cristófoli, María Elizabeth & García Fronti, Javier, 2019. "Macroeconomic Reverse Stress Testing: An Early-Warning System for Spanish Banking Regulators. Analysis Based on the 2008 Global Financial Crisis / Prueba de resistencia inversa Macroeconómica: una pru," Estocástica: finanzas y riesgo, Departamento de Administración de la Universidad Autónoma Metropolitana Unidad Azcapotzalco, vol. 9(2), pages 181-204, julio-dic.
    12. Ruodu Wang & Ričardas Zitikis, 2021. "An Axiomatic Foundation for the Expected Shortfall," Management Science, INFORMS, vol. 67(3), pages 1413-1429, March.
    13. Stephan Eckstein & Gaoyue Guo & Tongseok Lim & Jan Obloj, 2019. "Robust pricing and hedging of options on multiple assets and its numerics," Papers 1909.03870, arXiv.org, revised Oct 2020.
    14. Wang, Bin & Wang, Ruodu, 2015. "Extreme negative dependence and risk aggregation," Journal of Multivariate Analysis, Elsevier, vol. 136(C), pages 12-25.
    15. 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.
    16. Raphael Hauser & Sergey Shahverdyan & Paul Embrechts, 2014. "A General Duality Relation with Applications in Quantitative Risk Management," Papers 1410.0852, arXiv.org.
    17. Tuitman, Jan & Vanduffel, Steven & Yao, Jing, 2020. "Correlation matrices with average constraints," Statistics & Probability Letters, Elsevier, vol. 165(C).
    18. Asimit, Alexandru V. & Gerrard, Russell, 2016. "On the worst and least possible asymptotic dependence," Journal of Multivariate Analysis, Elsevier, vol. 144(C), pages 218-234.
    19. Lauzier, Jean-Gabriel & Lin, Liyuan & Wang, Ruodu, 2023. "Pairwise counter-monotonicity," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 279-287.
    20. Das, Bikramjit & Kratz, Marie, 2017. "Diversification benefits under multivariate second order regular variation," ESSEC Working Papers WP1706, ESSEC Research Center, ESSEC Business School.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2309.17346. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.