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Superquantile/CVaR risk measures: second-order theory

Author

Listed:
  • R. Tyrrell Rockafellar

    (University of Washington)

  • Johannes O. Royset

    (Naval Postgraduate School)

Abstract

Superquantiles, which refer to conditional value-at-risk in the same way that quantiles refer to value-at-risk, have many advantages in the modeling of risk in finance and engineering. However, some applications may benefit from a further step, from superquantiles to second-order superquantiles. Measures of risk based on second-order superquantiles have recently been explored in some settings, but key parts of the theory have been lacking: descriptions of the associated risk envelopes and risk identifiers. Those missing ingredients are supplied in this paper, and moreover not just for second-order superquantiles, but also for a much broader class of mixed superquantile measures of risk. Such dualizing expressions facilitate the development of dual methods for mixed and second-order superquantile risk minimization as well as superquantile regression, a proposed second-order version of quantile regression.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:262:y:2018:i:1:d:10.1007_s10479-016-2129-0
    DOI: 10.1007/s10479-016-2129-0
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    References listed on IDEAS

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    1. R. Rockafellar & Stan Uryasev & Michael Zabarankin, 2006. "Generalized deviations in risk analysis," Finance and Stochastics, Springer, vol. 10(1), pages 51-74, January.
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    10. 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.
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    Cited by:

    1. Michael D. Teter & Johannes O. Royset & Alexandra M. Newman, 2019. "Modeling uncertainty of expert elicitation for use in risk-based optimization," Annals of Operations Research, Springer, vol. 280(1), pages 189-210, September.
    2. Cheng Peng & Stanislav Uryasev, 2023. "Factor Model of Mixtures," Papers 2301.13843, arXiv.org, revised Mar 2023.
    3. Gilles Bareilles & Yassine Laguel & Dmitry Grishchenko & Franck Iutzeler & Jérôme Malick, 2020. "Randomized Progressive Hedging methods for multi-stage stochastic programming," Annals of Operations Research, Springer, vol. 295(2), pages 535-560, December.
    4. 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.

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