Title

Constrained dual representation of coherent risk measures

Publication Type

Working Paper

Publication Date

7-2005

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, 4. A Lagrange duality framework for optimization problems involving risk envelopes, and 5. A connection between risk measures in stochastic optimization and uncertainty sets in robust optimization.

Keywords

Coherent risk measures, optimization, risk envelopes

Discipline

Business

Research Areas

Operations Management

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