On the dual representation of coherent risk measures

Marcus Ang (), Jie Sun () and Qiang Yao ()
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Marcus Ang: Singapore Management University
Jie Sun: Curtin University
Qiang Yao: East China Normal University

Annals of Operations Research, 2018, vol. 262, issue 1, No 3, 29-46

Abstract: 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.

Keywords: Coherent risk measures; Duality; Optimization; Risk envelopes (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (6)

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DOI: 10.1007/s10479-017-2441-3

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