On the Dual Representation of Coherent Risk Measures
Optimization and Control
2018-02-28 v2
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.
Cite
@article{arxiv.1502.06155,
title = {On the Dual Representation of Coherent Risk Measures},
author = {Marcus Ang and Jie Sun and Qiang Yao},
journal= {arXiv preprint arXiv:1502.06155},
year = {2018}
}
Comments
Annals of Operations Research, 2017