Regime-dependent Robust Risk Measures with Application in Portfolio Selection

Current robust risk measures or portfolio selection models are usually derived under the worst-case analysis, which makes the investment decision too conservative and could not reflect the change of uncertainty sets with respect to different market environ- ments. We use the regime switching technique to describe the time-varying uncertainty set of the first and second order moments, and propose two kinds of robust risk measures: worst regime risk measure and mixed worst-case risk measure. These new risk measures have good properties and the robust portfolio selection models derived from them can be efficiently solved in polynomial time. Empirical results show the reasonability and efficiency of our new models.