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On the Dual Representation of Coherent Risk Measures

arXiv 1502.06155 ↗First posted 22 Feb 2015math.OCcited by 8

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Abstract (arXiv)

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.

Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). First posted on arXiv 22 Feb 2015.

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Citing papers per year: 2021: 1; 2022: 0; 2023: 0; 2024: 4; 2025: 1; 2026: 2.

8 papers.

  1. 2021Doubly-Valid/Doubly-Sharp Sensitivity Analysis for Causal Inference with Unmeasured Confoundingcited by 28
  2. 2025State Entropy Regularization for Robust Reinforcement Learningcited by 6
  3. 2024Efficient and Sharp Off-Policy Evaluation in Robust Markov Decision Processescited by 3
  4. 2024Robust Risk-Sensitive Reinforcement Learning with Conditional Value-at-Riskcited by 2
  5. 2026Decision Making Needs Uncertainty Quantification [Lecture Notes]cited by 2
  6. 2024Risk Sensitivity in Markov Games and Multi-Agent Reinforcement Learning: A Systematic Reviewcited by 0
  7. 2024Robust Stochastic Shortest-Path Planning via Risk-Sensitive Incremental Samplingcited by 0
  8. 2026Instantiating Bayesian CVaR lower bounds in Interactive Decision Making Problemscited by 0