While our society began to recognize the importance to balance the risk performance under different risk measures, the existing literature has confined its research work only under a static mean-risk framework. This paper represents the first attempt to incorporate multiple risk measures into dynamic portfolio selection. More specifically, we investigate the dynamic mean-variance-CVaR (Conditional value at Risk) formulation and the dynamic mean-variance-SFP (Safety-First Principle) formulation in a continuous-time setting, and derive the analytical solutions for both problems. Combining a downside risk measure with the variance (the second order central moment) in a dynamic mean-risk portfolio selection model helps investors control both a symmetric central risk measure and an asymmetric catastrophic downside risk. We find that the optimal portfolio policy derived from our mean-multiple risk portfolio optimization models exhibits a feature of curved V-shape. Our numerical experiments using real market data clearly demonstrate a dominance relationship of our dynamic mean-multiple risk portfolio policies over the static buy-and-hold portfolio policy. 
Dynamic mean-risk portfolio selection with multiple risk measures in continuous-time