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Superquantile regression with applications to buffered reliability, uncertainty quantification, and conditional value-at-risk

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  • Rockafellar, R.T.
  • Royset, J.O.
  • Miranda, S.I.

Abstract

The paper presents a generalized regression technique centered on a superquantile (also called conditional value-at-risk) that is consistent with that coherent measure of risk and yields more conservatively fitted curves than classical least-squares and quantile regression. In contrast to other generalized regression techniques that approximate conditional superquantiles by various combinations of conditional quantiles, we directly and in perfect analog to classical regression obtain superquantile regression functions as optimal solutions of certain error minimization problems. We show the existence and possible uniqueness of regression functions, discuss the stability of regression functions under perturbations and approximation of the underlying data, and propose an extension of the coefficient of determination R-squared for assessing the goodness of fit. The paper presents two numerical methods for solving the error minimization problems and illustrates the methodology in several numerical examples in the areas of uncertainty quantification, reliability engineering, and financial risk management.

Suggested Citation

  • Rockafellar, R.T. & Royset, J.O. & Miranda, S.I., 2014. "Superquantile regression with applications to buffered reliability, uncertainty quantification, and conditional value-at-risk," European Journal of Operational Research, Elsevier, vol. 234(1), pages 140-154.
    • Handle: RePEc:eee:ejores:v:234:y:2014:i:1:p:140-154
    DOI: 10.1016/j.ejor.2013.10.046
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    References listed on IDEAS

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    Cited by:

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    3. Ye, Wuyi & Luo, Kebing & Liu, Xiaoquan, 2017. "Time-varying quantile association regression model with applications to financial contagion and VaR," European Journal of Operational Research, Elsevier, vol. 256(3), pages 1015-1028.
    4. Qinyu Wu & Fan Yang & Ping Zhang, 2023. "Conditional generalized quantiles based on expected utility model and equivalent characterization of properties," Papers 2301.12420, arXiv.org.
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    6. Rui Ding, 2023. "f-Betas and Portfolio Optimization with f-Divergence induced Risk Measures," Papers 2302.00452, arXiv.org, revised May 2023.
    7. Alex Golodnikov & Viktor Kuzmenko & Stan Uryasev, 2019. "CVaR Regression Based on the Relation between CVaR and Mixed-Quantile Quadrangles," JRFM, MDPI, vol. 12(3), pages 1-22, June.
    8. Liu, Congzheng & Zhu, Wenqi, 2024. "Newsvendor conditional value-at-risk minimisation: A feature-based approach under adaptive data selection," European Journal of Operational Research, Elsevier, vol. 313(2), pages 548-564.
    9. Xia Han & Liyuan Lin & Ruodu Wang, 2022. "Diversification quotients: Quantifying diversification via risk measures," Papers 2206.13679, arXiv.org, revised Jul 2024.
    10. R. Tyrrell Rockafellar & Johannes O. Royset, 2018. "Superquantile/CVaR risk measures: second-order theory," Annals of Operations Research, Springer, vol. 262(1), pages 3-28, March.
    11. Cheng Peng & Stanislav Uryasev, 2023. "Factor Model of Mixtures," Papers 2301.13843, arXiv.org, revised Mar 2023.
    12. Denis Chetverikov & Yukun Liu & Aleh Tsyvinski, 2022. "Weighted-average quantile regression," Papers 2203.03032, arXiv.org.
    13. Labopin-Richard T. & Gamboa F. & Garivier A. & Iooss B., 2016. "Bregman superquantiles. Estimation methods and applications," Dependence Modeling, De Gruyter, vol. 4(1), pages 1-33, March.
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    16. Han, Xia & Lin, Liyuan & Wang, Ruodu, 2023. "Diversification quotients based on VaR and ES," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 185-197.

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