Robust multi-period portfolio selection based on downside risk with asymmetrically distributed uncertainty set

Motivated by the asymmetrical attitudes of investors towards downside losses and upside gains, this paper proposes a robust multi-period portfolio selection model based on downside risk with asymmetrically distributed uncertainty set, in which the downside losses of a portfolio are controlled by the lower partial moment (LPM). A computationally tractable approximation approach based on second-order cone optimization is used for solving the proposed model. We show in theory that the optimal solution of the robust model can generate a given probability guarantee for individual and joint stochastic constraints. The effect of the asymmetrically distributed uncertainty set on performance of the optimal solution is analyzed by the usual comparative static method. Comprehensive numerical comparisons with real market data are reported and indicate that the proposed model can obtain the smaller standard deviation and turnover ratios which reduce the Sharpe ratios of optimal portfolio, compared with some well-known models in the literature.