Constructing Risk Measures from Uncertainty Sets

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. ∗Department of Mathematics and NUS Risk Management Institute, National University of Singapore. Email: [email protected]. The research of the author was partially supported by Singapore-MIT Alliance and NUS startup grants R-146-050-070-133 & R146-050-070-101. †Division of Mathematics and Sciences, Babson College, Babson Park, MA 02457, USA. E-mail: [email protected]. Research supported by the Gill grant from the Babson College Board of Research. ‡NUS Business School and NUS Risk Management Institute, National University of Singapore. Email: [email protected]. The research of the author was partially supported by Singapore-MIT Alliance and NUS academic research grant R-314-000-066-122 and R-314-000-068-122.