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

摘要： 本文主要考虑一类经典的含有二阶随机占优约束的投资组合优化问题,其目标为最大化期望收益,同时利用二阶随机占优约束度量风险,满足期望收益二阶随机占优预定的参考目标收益。与传统的二阶随机占优投资组合优化模型不同,本文考虑不确定的投资收益率,并未知其精确的概率分布,但属于某一不确定集合,建立鲁棒二阶随机占优投资组合优化模型,借助鲁棒优化理论,推导出对应的鲁棒等价问题。最后,采用S&P 500股票市场的实际数据,对模型进行不同训练样本规模和不确定集合下的最优投资组合的权重、样本内和样本外不确定参数对期望收益的影响的分析。结果表明,投资收益率在最新的历史数据规模下得出的投资策略,能够获得较高的样本外期望收益,对未来投资更具参考意义。在保证样本内解的最优性的同时,也能取得较高的样本外期望收益和随机占优约束被满足的可行性。

关键词: 二阶随机占优, 鲁棒优化, 投资组合优化, 不确定集合