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On the dual representation of coherent risk measures

Author

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  • Marcus Ang

    (Singapore Management University)

  • Jie Sun

    (Curtin University
    National University of Singapore)

  • Qiang Yao

    (East China Normal University)

Abstract

A classical result in risk measure theory states that every coherent risk measure has a dual representation as the supremum of certain expected value over a risk envelope. We study this topic in more detail. The related issues include: (1) Set operations of risk envelopes and how they change the risk measures, (2) The structure of risk envelopes of popular risk measures, (3) Aversity of risk measures and its impact to risk envelopes, and (4) A connection between risk measures in stochastic optimization and uncertainty sets in robust optimization.

Suggested Citation

  • Marcus Ang & Jie Sun & Qiang Yao, 2018. "On the dual representation of coherent risk measures," Annals of Operations Research, Springer, vol. 262(1), pages 29-46, March.
    • Handle: RePEc:spr:annopr:v:262:y:2018:i:1:d:10.1007_s10479-017-2441-3
    DOI: 10.1007/s10479-017-2441-3
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    References listed on IDEAS

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    1. Wenqing Chen & Melvyn Sim & Jie Sun & Chung-Piaw Teo, 2010. "From CVaR to Uncertainty Set: Implications in Joint Chance-Constrained Optimization," Operations Research, INFORMS, vol. 58(2), pages 470-485, April.
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    Cited by:

    1. Marcelo Brutti Righi, 2019. "A composition between risk and deviation measures," Annals of Operations Research, Springer, vol. 282(1), pages 299-313, November.
    2. Gabriele Torri & Rosella Giacometti & Darinka Dentcheva & Svetlozar T. Rachev & W. Brent Lindquist, 2023. "ESG-coherent risk measures for sustainable investing," Papers 2309.05866, arXiv.org.
    3. Ying Cui & Ziyu He & Jong-Shi Pang, 2021. "Nonconvex robust programming via value-function optimization," Computational Optimization and Applications, Springer, vol. 78(2), pages 411-450, March.
    4. Jie Sun & Di Wu & Changjun Yu, 2024. "Risk-Averse Optimal Control Model Under Uncertainty and Its Modified Progressive Hedging Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 203(1), pages 960-984, October.
    5. Haodong Yu & Jie Sun & Yanjun Wang, 2021. "A time-consistent Benders decomposition method for multistage distributionally robust stochastic optimization with a scenario tree structure," Computational Optimization and Applications, Springer, vol. 79(1), pages 67-99, May.

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