IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v234y2014i1p140-154.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221713008692
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2013.10.046?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. Gneiting, Tilmann, 2011. "Making and Evaluating Point Forecasts," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 746-762.
    2. Cai, Zongwu & Wang, Xian, 2008. "Nonparametric estimation of conditional VaR and expected shortfall," Journal of Econometrics, Elsevier, vol. 147(1), pages 120-130, November.
    3. Trindade, A. Alexandre & Uryasev, Stan & Shapiro, Alexander & Zrazhevsky, Grigory, 2007. "Financial prediction with constrained tail risk," Journal of Banking & Finance, Elsevier, vol. 31(11), pages 3524-3538, November.
    4. Eldred, M.S. & Swiler, L.P. & Tang, G., 2011. "Mixed aleatory-epistemic uncertainty quantification with stochastic expansions and optimization-based interval estimation," Reliability Engineering and System Safety, Elsevier, vol. 96(9), pages 1092-1113.
    5. Franco Peracchi & Andrei V. Tanase, 2008. "On estimating the conditional expected shortfall," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 24(5), pages 471-493, September.
    6. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, September.
    7. So Yeon Chun & Alexander Shapiro & Stan Uryasev, 2012. "Conditional Value-at-Risk and Average Value-at-Risk: Estimation and Asymptotics," Operations Research, INFORMS, vol. 60(4), pages 739-756, August.
    8. Leorato, Samantha & Peracchi, Franco & Tanase, Andrei V., 2012. "Asymptotically efficient estimation of the conditional expected shortfall," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 768-784.
    9. Hall, Peter & Muller, Hans-Georg, 2003. "Order-Preserving Nonparametric Regression, With Applications to Conditional Distribution and Quantile Function Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 598-608, January.
    10. Rockafellar, R.T. & Royset, J.O., 2010. "On buffered failure probability in design and optimization of structures," Reliability Engineering and System Safety, Elsevier, vol. 95(5), pages 499-510.
    11. Kengo Kato, 2012. "Weighted Nadaraya--Watson Estimation of Conditional Expected Shortfall," Journal of Financial Econometrics, Oxford University Press, vol. 10(2), pages 265-291, 2012 15.
    12. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    13. R. Tyrrell Rockafellar & Stan Uryasev & Michael Zabarankin, 2008. "Risk Tuning with Generalized Linear Regression," Mathematics of Operations Research, INFORMS, vol. 33(3), pages 712-729, August.
    14. Warren Gilchrist, 2008. "Regression Revisited," International Statistical Review, International Statistical Institute, vol. 76(3), pages 401-418, December.
    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. Jun-ya Gotoh & Michael Jong Kim & Andrew E. B. Lim, 2020. "Worst-case sensitivity," Papers 2010.10794, arXiv.org.
    2. Rui Ding & Stan Uryasev, 2020. "CoCDaR and mCoCDaR: New Approach for Measurement of Systemic Risk Contributions," JRFM, MDPI, vol. 13(11), pages 1-18, November.
    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.
    5. Zhimin Wu & Guanghui Cai, 2024. "Can intraday data improve the joint estimation and prediction of risk measures? Evidence from a variety of realized measures," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 43(6), pages 1956-1974, September.
    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.
    14. Xia Han & Liyuan Lin & Ruodu Wang, 2023. "Diversification quotients based on VaR and ES," Papers 2301.03517, arXiv.org, revised May 2023.
    15. Xu, Qifa & Zhou, Yingying & Jiang, Cuixia & Yu, Keming & Niu, Xufeng, 2016. "A large CVaR-based portfolio selection model with weight constraints," Economic Modelling, Elsevier, vol. 59(C), pages 436-447.
    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.

    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. So Yeon Chun & Alexander Shapiro & Stan Uryasev, 2012. "Conditional Value-at-Risk and Average Value-at-Risk: Estimation and Asymptotics," Operations Research, INFORMS, vol. 60(4), pages 739-756, August.
    2. Zhongde Luo, 2020. "Nonparametric kernel estimation of CVaR under $$\alpha $$α-mixing sequences," Statistical Papers, Springer, vol. 61(2), pages 615-643, April.
    3. Denis Chetverikov & Yukun Liu & Aleh Tsyvinski, 2022. "Weighted-average quantile regression," Papers 2203.03032, arXiv.org.
    4. Leorato, Samantha & Peracchi, Franco & Tanase, Andrei V., 2012. "Asymptotically efficient estimation of the conditional expected shortfall," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 768-784.
    5. Johanna F. Ziegel, 2013. "Coherence and elicitability," Papers 1303.1690, arXiv.org, revised Mar 2014.
    6. Julia S. Mehlitz & Benjamin R. Auer, 2021. "Time‐varying dynamics of expected shortfall in commodity futures markets," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(6), pages 895-925, June.
    7. Dingshi Tian & Zongwu Cai & Ying Fang, 2018. "Econometric Modeling of Risk Measures: A Selective Review of the Recent Literature," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201807, University of Kansas, Department of Economics, revised Oct 2018.
    8. Ruodu Wang & Ričardas Zitikis, 2021. "An Axiomatic Foundation for the Expected Shortfall," Management Science, INFORMS, vol. 67(3), pages 1413-1429, March.
    9. 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.
    10. Roger W. Barnard & Kent Pearce & A. Alexandre Trindade, 2018. "When is tail mean estimation more efficient than tail median? Answers and implications for quantitative risk management," Annals of Operations Research, Springer, vol. 262(1), pages 47-65, March.
    11. Patton, Andrew J. & Ziegel, Johanna F. & Chen, Rui, 2019. "Dynamic semiparametric models for expected shortfall (and Value-at-Risk)," Journal of Econometrics, Elsevier, vol. 211(2), pages 388-413.
    12. Wei, Bo & Tan, Kean Ming & He, Xuming, 2024. "Estimation of complier expected shortfall treatment effects with a binary instrumental variable," Journal of Econometrics, Elsevier, vol. 238(2).
    13. Merlo, Luca & Petrella, Lea & Raponi, Valentina, 2021. "Forecasting VaR and ES using a joint quantile regression and its implications in portfolio allocation," Journal of Banking & Finance, Elsevier, vol. 133(C).
    14. Adil Rengim Cetingoz & Jean-David Fermanian & Olivier Gu'eant, 2022. "Risk Budgeting Portfolios: Existence and Computation," Papers 2211.07212, arXiv.org, revised Sep 2023.
    15. L. Jeff Hong & Zhaolin Hu & Liwei Zhang, 2014. "Conditional Value-at-Risk Approximation to Value-at-Risk Constrained Programs: A Remedy via Monte Carlo," INFORMS Journal on Computing, INFORMS, vol. 26(2), pages 385-400, May.
    16. Natalia Nolde & Johanna F. Ziegel, 2016. "Elicitability and backtesting: Perspectives for banking regulation," Papers 1608.05498, arXiv.org, revised Feb 2017.
    17. Faugeras, Olivier P. & Pagès, Gilles, 2024. "Risk quantization by magnitude and propensity," Insurance: Mathematics and Economics, Elsevier, vol. 116(C), pages 134-147.
    18. repec:cte:wsrepe:35425 is not listed on IDEAS
    19. Luca Merlo & Lea Petrella & Valentina Raponi, 2021. "Forecasting VaR and ES using a joint quantile regression and implications in portfolio allocation," Papers 2106.06518, arXiv.org.
    20. Tobias Fissler & Johanna F. Ziegel, 2015. "Higher order elicitability and Osband's principle," Papers 1503.08123, arXiv.org, revised Sep 2015.
    21. Gaglianone, Wagner Piazza & Marins, Jaqueline Terra Moura, 2017. "Evaluation of exchange rate point and density forecasts: An application to Brazil," International Journal of Forecasting, Elsevier, vol. 33(3), pages 707-728.

    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:ejores:v:234:y:2014:i:1:p:140-154. 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/locate/eor .

    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.