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Constructing Risk Measures from Uncertainty Sets

Department of Mathematics and NUS Risk Management Institute, National University of Singapore, Singapore
Division of Mathematics and Sciences, Babson College, Babson Park, Massachusetts 02457
NUS Business School and NUS Risk Management Institute, National University of Singapore, Singapore
matkbn{at}nus.edu.sg
dpachamanova{at}babson.edu
dscsimm{at}nus.edu.sg

We illustrate the correspondence between uncertainty sets in robust optimization and some popular risk measures in finance and show how robust optimization can be used to generalize the concepts of these risk measures. We also show that by using properly defined uncertainty sets in robust optimization models, one can construct coherent risk measures and address the issue of the computational tractability of the resulting formulations. Our results have implications for efficient portfolio optimization under different measures of risk.

Subject classifications: finance; portfolio management.
History: Received August 2005; revision received August 2008; accepted October 2008.

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