Constrained dual representation of coherent risk measures

• Main Authors: ANG, Marcus, SUN, Jie, YAO, Qiang
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2018
• Subjects: Coherent risk measures; optimization; risk envelopes; Business; Operations and Supply Chain Management
• Online Access: https://ink.library.smu.edu.sg/lkcsb_research/4490; https://ink.library.smu.edu.sg/context/lkcsb_research/article/5489/viewcontent/101007_2Fs10479_017_2441_3.pdf
• Institution: Singapore Management University

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.