Dynamic mean-risk portfolio selection with multiple risk measures in continuous-time

• Study dynamic portfolio selection with multiple risk measures in continuous-time.
• Help investors control both central-moment risk measure and downside risk measure.
• Solve analytically dynamic mean-variance-CVaR formulation.
• Solve analytically dynamic mean-variance-SFP (Safety-First Principle) formulation.
• Reveal a curved V-shape property in optimal portfolio policies of our models.

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.