We propose a unified theory that links uncertainty sets in robust optimization to risk measures in portfolio optimization. We illustrate the correspondence between uncertainty sets and some popular risk measures in finance, and show how robust optimization can be used to generalize the concepts of these measures. We also show that by using properly defined uncertainty sets in robust optimization models, one can in fact construct coherent risk measures. Our approach to creating coherent risk measures is easy to apply in practice, and computational experiments suggest that it may lead to superior portfolio performance. Our results have implications for efficient portfolio optimization under different measures of risk.
Working paper, National University of Singapore