Feasibility of Portfolio Optimization under Coherent Risk Measures

Details Feasibility of Portfolio Optimization under Coherent Risk Measures Feasibility of Portfolio Optimization under Coherent Risk Measures

2008-03-15

arxiv.org/abs/0803.2283v3

Economy

Quantitative Finance

Risk Management

13 pages, 2 figures

Scientific paper

It is shown that the axioms for coherent risk measures imply that whenever there is an asset in a portfolio that dominates the others in a given sample (which happens with finite probability even for large samples), then this portfolio cannot be optimized under any coherent measure on that sample, and the risk measure diverges to minus infinity. This instability was first discovered on the special example of Expected Shortfall which is used here both as an illustration and as a prompt for generalization.

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