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Asymptotic multivariate expectiles

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  • V'eronique Maume-Deschamps

    (ICJ)

  • Didier Rulli`ere

    (SAF)

  • Khalil Said

Abstract

In [16], a new family of vector-valued risk measures called multivariate expectiles is introduced. In this paper, we focus on the asymptotic behavior of these measures in a multivariate regular variations context. For models with equivalent tails, we propose an estimator of these multivariate asymptotic expectiles, in the Fr{\'e}chet attraction domain case, with asymptotic independence, or in the comonotonic case.

Suggested Citation

  • V'eronique Maume-Deschamps & Didier Rulli`ere & Khalil Said, 2017. "Asymptotic multivariate expectiles," Papers 1704.07152, arXiv.org, revised Jan 2018.
    • Handle: RePEc:arx:papers:1704.07152
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Véronique Maume-Deschamps & Didier Rullière & Khalil Said, 2017. "Multivariate extensions of expectiles risk measures," Post-Print hal-01478930, HAL.
    4. 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.
    5. 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.
    6. Charpentier, Arthur & Segers, Johan, 2009. "Tails of multivariate Archimedean copulas," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1521-1537, August.
    7. 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.
    8. 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.
    9. Fabio Bellini & Valeria Bignozzi, 2015. "On elicitable risk measures," Quantitative Finance, Taylor & Francis Journals, vol. 15(5), pages 725-733, May.
    10. Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-847, July.
    11. Véronique Maume-Deschamps & Didier Rullière & Khalil Said, 2017. "Multivariate Extensions Of Expectiles Risk Measures," Working Papers hal-01367277, HAL.
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    Cited by:

    1. Mustapha Rachdi & Ali Laksaci & Noriah M. Al-Kandari, 2022. "Expectile regression for spatial functional data analysis (sFDA)," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(5), pages 627-655, July.

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