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Multivariate extensions of expectiles risk measures

Author

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  • Maume-Deschamps Véronique

    (Université de Lyon, Université Lyon 1, Institut Camille Jordan UMR 5208, Lyon, France)

  • Rullière Didier

    (Université de Lyon, Université Lyon 1, Laboratoire SAF EA 2429, Lyon , France)

  • Said Khalil

    (Université de Lyon, Université Lyon 1, Institut Camille Jordan UMR 5208, Lyon, France)

Abstract

This paper is devoted to the introduction and study of a new family of multivariate elicitable risk measures. We call the obtained vector-valued measures multivariate expectiles. We present the different approaches used to construct our measures. We discuss the coherence properties of these multivariate expectiles. Furthermore, we propose a stochastic approximation tool of these risk measures.

Suggested Citation

  • 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.
    • Handle: RePEc:vrs:demode:v:5:y:2017:i:1:p:20-44:n:2
    DOI: 10.1515/demo-2017-0002
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    Cited by:

    1. 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.
    2. Said Khalil, 2022. "Expectile-based capital allocation," Working Papers hal-03816525, HAL.
    3. Maume-Deschamps Véronique & Rullière Didier & Said Khalil, 2018. "Extremes for multivariate expectiles," Statistics & Risk Modeling, De Gruyter, vol. 35(3-4), pages 111-140, July.
    4. Joanna Bruzda, 2020. "Multistep quantile forecasts for supply chain and logistics operations: bootstrapping, the GARCH model and quantile regression based approaches," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 28(1), pages 309-336, March.
    5. V'eronique Maume-Deschamps & Didier Rulli`ere & Khalil Said, 2017. "Asymptotic multivariate expectiles," Papers 1704.07152, arXiv.org, revised Jan 2018.
    6. Hamel, Andreas H. & Ha, Thi Khanh Linh, 2025. "Set-valued expectiles for ordered data analysis," Journal of Multivariate Analysis, Elsevier, vol. 208(C).
    7. 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).
    8. Hashorva, Enkelejd, 2019. "Approximation of some multivariate risk measures for Gaussian risks," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 330-340.
    9. Maziar Sahamkhadam, 2021. "Dynamic copula-based expectile portfolios," Journal of Asset Management, Palgrave Macmillan, vol. 22(3), pages 209-223, May.
    10. Hu, Wei & Zheng, Zhenlong, 2020. "Expectile CAPM," Economic Modelling, Elsevier, vol. 88(C), pages 386-397.
    11. Klaus Herrmann & Marius Hofert & Melina Mailhot, 2017. "Multivariate Geometric Expectiles," Papers 1704.01503, arXiv.org, revised Jan 2018.
    12. Ling, Chengxiu, 2019. "Asymptotics of multivariate conditional risk measures for Gaussian risks," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 205-215.
    13. Beck, Nicholas & Di Bernardino, Elena & Mailhot, Mélina, 2021. "Semi-parametric estimation of multivariate extreme expectiles," Journal of Multivariate Analysis, Elsevier, vol. 184(C).

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