Coherent Worst-Case Value-at-Risk with Applications to Robust Portfolio Optimization

In this paper, we investigate a risk measure, namely, the worst-case value-at-risk with support information. We obtain its tractable and equivalent representations. Then by using properly defined uncertainty sets, we show that this risk measure is coherent. We extend the case with exactly known moments to uncertain situations and get corresponding optimization formulations. We report some numerical experiments for robust portfolio optimization to illustrate the efficiency of this method.