关键词: 二阶随机占优, 鲁棒优化, 投资组合优化, 不确定集合

Abstract: This paper mainly focuses on a typical class of portfolio optimization problem with stochastic dominance constraints to measure the risk, which is to maximize the expected return, subjecting that the expected return stochastically dominates pre-defined targeted return in the second order. Unlike the existing studies, we consider the uncertain return with unknown probability distribution, but reside in an uncertainty set.We propose a novel robust stochastic dominance constrained model, and derive the corresponding robust counterpart reformulation. Finally, using the real-life stock data of S&P 500, we perform the analysis of the optimal portfolio, the robustness in both in-sample and out-of-sample datasets and the solution efficiency, in terms of different sizes of in-sample problems and types of uncertainty sets. The numerical results show that, one can achieve a high out-of-sample expected return by using the set of the latest historical observations. Moreover, our model can achieve the optimal in-sample solution, without sacrificing the guaranteed quality of out-of-sample expected return and feasibility of stochastic dominance constraints.

Key words: second-order stochastic dominance, robust optimization, portfolio optimization, uncertainty set