IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-01923798.html
   My bibliography  Save this paper

Extremes for multivariate expectiles

Author

Listed:
  • Véronique Maume-Deschamps

    (ICJ - Institut Camille Jordan - ECL - École Centrale de Lyon - Université de Lyon - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - INSA Lyon - Institut National des Sciences Appliquées de Lyon - Université de Lyon - INSA - Institut National des Sciences Appliquées - UJM - Université Jean Monnet - Saint-Étienne - CNRS - Centre National de la Recherche Scientifique, PSPM - Probabilités, statistique, physique mathématique - ICJ - Institut Camille Jordan - ECL - École Centrale de Lyon - Université de Lyon - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - INSA Lyon - Institut National des Sciences Appliquées de Lyon - Université de Lyon - INSA - Institut National des Sciences Appliquées - UJM - Université Jean Monnet - Saint-Étienne - CNRS - Centre National de la Recherche Scientifique)

  • Didier Rullière

    (LSAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

  • Khalil Said

    (ICJ - Institut Camille Jordan - ECL - École Centrale de Lyon - Université de Lyon - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - INSA Lyon - Institut National des Sciences Appliquées de Lyon - Université de Lyon - INSA - Institut National des Sciences Appliquées - UJM - Université Jean Monnet - Saint-Étienne - CNRS - Centre National de la Recherche Scientifique, PSPM - Probabilités, statistique, physique mathématique - ICJ - Institut Camille Jordan - ECL - École Centrale de Lyon - Université de Lyon - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - INSA Lyon - Institut National des Sciences Appliquées de Lyon - Université de Lyon - INSA - Institut National des Sciences Appliquées - UJM - Université Jean Monnet - Saint-Étienne - CNRS - Centre National de la Recherche Scientifique)

Abstract

Multivariate expectiles, a new family of vector-valued risk measures, were recently introduced in the literature. Here we investigate the asymptotic behavior of these measures in a multivariate regular variation context. For models with equivalent tails, we propose an estimator of extreme multivariate expectiles in the Fréchet domain of attraction case with asymptotic independence, or for comonotonic marginal distributions.

Suggested Citation

  • Véronique Maume-Deschamps & Didier Rullière & Khalil Said, 2018. "Extremes for multivariate expectiles," Post-Print hal-01923798, HAL.
    • Handle: RePEc:hal:journl:hal-01923798
    DOI: 10.1515/strm-2017-0014
    Note: View the original document on HAL open archive server: https://hal.science/hal-01923798v1
    as

    Download full text from publisher

    File URL: https://hal.science/hal-01923798v1/document
    Download Restriction: no
    File URL: https://libkey.io/10.1515/strm-2017-0014?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
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Elena Di Bernardino & Clémentine Prieur, 2018. "Estimation of the multivariate conditional tail expectation for extreme risk levels: Illustration on environmental data sets," Environmetrics, John Wiley & Sons, Ltd., vol. 29(7), November.
    2. Maume-Deschamps Véronique & Rullière Didier & Said Khalil, 2017. "Multivariate extensions of expectiles risk measures," Dependence Modeling, De Gruyter, vol. 5(1), pages 20-44, January.
    3. Charpentier, Arthur & Segers, Johan, 2009. "Tails of multivariate Archimedean copulas," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1521-1537, August.
    4. Klaus Herrmann & Marius Hofert & Mélina Mailhot, 2018. "Multivariate geometric expectiles," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2018(7), pages 629-659, August.
    5. Fabio Bellini & Valeria Bignozzi, 2015. "On elicitable risk measures," Quantitative Finance, Taylor & Francis Journals, vol. 15(5), pages 725-733, May.
    6. Asimit, Alexandru V. & Furman, Edward & Tang, Qihe & Vernic, Raluca, 2011. "Asymptotics for risk capital allocations based on Conditional Tail Expectation," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 310-324.
    7. Joe, Harry & Li, Haijun & Nikoloulopoulos, Aristidis K., 2010. "Tail dependence functions and vine copulas," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 252-270, January.
    8. Claudia Klüppelberg & Gabriel Kuhn & Liang Peng, 2008. "Semi‐Parametric Models for the Multivariate Tail Dependence Function – the Asymptotically Dependent Case," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(4), pages 701-718, December.
    9. Fabio Bellini & Elena Di Bernardino, 2017. "Risk management with expectiles," The European Journal of Finance, Taylor & Francis Journals, vol. 23(6), pages 487-506, May.
    10. Mao, Tiantian & Yang, Fan, 2015. "Risk concentration based on Expectiles for extreme risks under FGM copula," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 429-439.
    11. Klaus Herrmann & Marius Hofert & Melina Mailhot, 2017. "Multivariate Geometric Expectiles," Papers 1704.01503, arXiv.org, revised Jan 2018.
    12. Weng, Chengguo & Zhang, Yi, 2012. "Characterization of multivariate heavy-tailed distribution families via copula," Journal of Multivariate Analysis, Elsevier, vol. 106(C), pages 178-186.
    13. Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-847, July.
    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. Said Khalil, 2022. "Expectile-based capital allocation," Working Papers hal-03816525, HAL.
    2. Beck, Nicholas & Di Bernardino, Elena & Mailhot, Mélina, 2021. "Semi-parametric estimation of multivariate extreme expectiles," Journal of Multivariate Analysis, Elsevier, vol. 184(C).

    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. V'eronique Maume-Deschamps & Didier Rulli`ere & Khalil Said, 2017. "Asymptotic multivariate expectiles," Papers 1704.07152, arXiv.org, revised Jan 2018.
    2. Maziar Sahamkhadam, 2021. "Dynamic copula-based expectile portfolios," Journal of Asset Management, Palgrave Macmillan, vol. 22(3), pages 209-223, May.
    3. Beck, Nicholas & Di Bernardino, Elena & Mailhot, Mélina, 2021. "Semi-parametric estimation of multivariate extreme expectiles," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    4. Said Khalil, 2022. "Expectile-based capital allocation," Working Papers hal-03816525, HAL.
    5. Tadese, Mekonnen & Drapeau, Samuel, 2020. "Relative bound and asymptotic comparison of expectile with respect to expected shortfall," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 387-399.
    6. Maume-Deschamps Véronique & Rullière Didier & Said Khalil, 2017. "Multivariate extensions of expectiles risk measures," Dependence Modeling, De Gruyter, vol. 5(1), pages 20-44, January.
    7. Haoyu Chen & Tiantian Mao & Fan Yang, 2024. "Estimation of the Adjusted Standard-deviatile for Extreme Risks," Papers 2411.07203, arXiv.org.
    8. Haoyu Chen & Tiantian Mao & Fan Yang, 2024. "Estimation of the adjusted standard‐deviatile for extreme risks," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 51(2), pages 643-671, June.
    9. Bingzhen Geng & Yang Liu & Yimiao Zhao, 2024. "Value-at-Risk- and Expectile-based Systemic Risk Measures and Second-order Asymptotics: With Applications to Diversification," Papers 2404.18029, arXiv.org.
    10. Mohammedi, Mustapha & Bouzebda, Salim & Laksaci, Ali, 2021. "The consistency and asymptotic normality of the kernel type expectile regression estimator for functional data," Journal of Multivariate Analysis, Elsevier, vol. 181(C).
    11. Matthias Fischer & Thorsten Moser & Marius Pfeuffer, 2018. "A Discussion on Recent Risk Measures with Application to Credit Risk: Calculating Risk Contributions and Identifying Risk Concentrations," Risks, MDPI, vol. 6(4), pages 1-28, December.
    12. Di Bernardino, Elena & Laloë, Thomas & Pakzad, Cambyse, 2024. "Estimation of extreme multivariate expectiles with functional covariates," Journal of Multivariate Analysis, Elsevier, vol. 202(C).
    13. Daouia, Abdelaati & Girard, Stéphane & Stupfler, Gilles, 2018. "Tail expectile process and risk assessment," TSE Working Papers 18-944, Toulouse School of Economics (TSE).
    14. Véronique Maume-Deschamps & Didier Rullière & Khalil Said, 2017. "Multivariate Extensions Of Expectiles Risk Measures," Working Papers hal-01367277, HAL.
    15. James Ming Chen, 2018. "On Exactitude in Financial Regulation: Value-at-Risk, Expected Shortfall, and Expectiles," Risks, MDPI, vol. 6(2), pages 1-28, June.
    16. Li, Haijun & Wu, Peiling, 2013. "Extremal dependence of copulas: A tail density approach," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 99-111.
    17. Kneib, Thomas & Silbersdorff, Alexander & Säfken, Benjamin, 2023. "Rage Against the Mean – A Review of Distributional Regression Approaches," Econometrics and Statistics, Elsevier, vol. 26(C), pages 99-123.
    18. Tobias Fissler & Jana Hlavinová & Birgit Rudloff, 2021. "Elicitability and identifiability of set-valued measures of systemic risk," Finance and Stochastics, Springer, vol. 25(1), pages 133-165, January.
    19. Man, Rebeka & Tan, Kean Ming & Wang, Zian & Zhou, Wen-Xin, 2024. "Retire: Robust expectile regression in high dimensions," Journal of Econometrics, Elsevier, vol. 239(2).
    20. Klaus Herrmann & Marius Hofert & Melina Mailhot, 2017. "Multivariate Geometric Expectiles," Papers 1704.01503, arXiv.org, revised Jan 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:hal:journl:hal-01923798. 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.