On the dual representation of coherent risk measures
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Open access
Authors
Ang, M.
Sun, Jie
Yao, Q.
Date
2017Type
Journal Article
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Ang, M. and Sun, J. and Yao, Q. 2017. On the dual representation of coherent risk measures. Annals of Operations Research. 262 (1): pp. 29-46.
Source Title
Annals of Operations Research
ISSN
School
Department of Mathematics and Statistics
Funding and Sponsorship
Remarks
The final publication is available at Springer via 10.1007/s10479-017-2441-3
Collection
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.
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