IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v100y2015icp48-55.html
   My bibliography  Save this article

Studying mixability with supermodular aggregating functions

Author

Listed:
  • Bignozzi, Valeria
  • Puccetti, Giovanni

Abstract

We introduce the concepts of ϕ-complete mixability and ϕ-joint mixability and we investigate some necessary and sufficient conditions to the ϕ-mixability of a set of distribution functions for some supermodular functions ϕ. We give examples and numerical verifications which confirm our findings.

Suggested Citation

  • Bignozzi, Valeria & Puccetti, Giovanni, 2015. "Studying mixability with supermodular aggregating functions," Statistics & Probability Letters, Elsevier, vol. 100(C), pages 48-55.
    • Handle: RePEc:eee:stapro:v:100:y:2015:i:c:p:48-55
    DOI: 10.1016/j.spl.2015.01.032
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715215000474
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2015.01.032?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Puccetti, Giovanni & Wang, Bin & Wang, Ruodu, 2013. "Complete mixability and asymptotic equivalence of worst-possible VaR and ES estimates," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 821-828.
    2. 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.
    3. Paul Embrechts & Giovanni Puccetti & Ludger Rüschendorf & Ruodu Wang & Antonela Beleraj, 2014. "An Academic Response to Basel 3.5," Risks, MDPI, vol. 2(1), pages 1-24, February.
    4. Embrechts, Paul & Puccetti, Giovanni & Rüschendorf, Ludger, 2013. "Model uncertainty and VaR aggregation," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 2750-2764.
    5. 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.
    6. Bernard, Carole & Jiang, Xiao & Wang, Ruodu, 2014. "Risk aggregation with dependence uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 93-108.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Bernard, Carole & Chen, Jinghui & Rüschendorf, Ludger & Vanduffel, Steven, 2023. "Coskewness under dependence uncertainty," Statistics & Probability Letters, Elsevier, vol. 199(C).
    2. Bin Wang & Ruodu Wang, 2016. "Joint Mixability," Mathematics of Operations Research, INFORMS, vol. 41(3), pages 808-826, August.

    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. Wang, Bin & Wang, Ruodu, 2015. "Extreme negative dependence and risk aggregation," Journal of Multivariate Analysis, Elsevier, vol. 136(C), pages 12-25.
    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. Paul Embrechts & Bin Wang & Ruodu Wang, 2015. "Aggregation-robustness and model uncertainty of regulatory risk measures," Finance and Stochastics, Springer, vol. 19(4), pages 763-790, October.
    4. Mao, Tiantian & Wang, Ruodu, 2015. "On aggregation sets and lower-convex sets," Journal of Multivariate Analysis, Elsevier, vol. 138(C), pages 170-181.
    5. Jose Blanchet & Henry Lam & Yang Liu & Ruodu Wang, 2020. "Convolution Bounds on Quantile Aggregation," Papers 2007.09320, arXiv.org, revised Sep 2024.
    6. Takaaki Koike & Liyuan Lin & Ruodu Wang, 2022. "Joint mixability and notions of negative dependence," Papers 2204.11438, arXiv.org, revised Jan 2024.
    7. Lauzier, Jean-Gabriel & Lin, Liyuan & Wang, Ruodu, 2023. "Pairwise counter-monotonicity," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 279-287.
    8. Ruodu Wang & Zuo Quan Xu & Xun Yu Zhou, 2019. "Dual utilities on risk aggregation under dependence uncertainty," Finance and Stochastics, Springer, vol. 23(4), pages 1025-1048, October.
    9. 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.
    10. Bin Wang & Ruodu Wang, 2016. "Joint Mixability," Mathematics of Operations Research, INFORMS, vol. 41(3), pages 808-826, August.
    11. Bignozzi, Valeria & Puccetti, Giovanni & Rüschendorf, Ludger, 2015. "Reducing model risk via positive and negative dependence assumptions," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 17-26.
    12. 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.
    13. Lux, Thibaut & Papapantoleon, Antonis, 2019. "Model-free bounds on Value-at-Risk using extreme value information and statistical distances," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 73-83.
    14. Cornilly, D. & Rüschendorf, L. & Vanduffel, S., 2018. "Upper bounds for strictly concave distortion risk measures on moment spaces," Insurance: Mathematics and Economics, Elsevier, vol. 82(C), pages 141-151.
    15. 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.
    16. Edgars Jakobsons & Steven Vanduffel, 2015. "Dependence Uncertainty Bounds for the Expectile of a Portfolio," Risks, MDPI, vol. 3(4), pages 1-25, December.
    17. 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.
    18. 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.
    19. Paul Embrechts & Giovanni Puccetti & Ludger Rüschendorf & Ruodu Wang & Antonela Beleraj, 2014. "An Academic Response to Basel 3.5," Risks, MDPI, vol. 2(1), pages 1-24, February.
    20. 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.

    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:eee:stapro:v:100:y:2015:i:c:p:48-55. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.