本文研究随机变量分布不确定下的风险-回报优化模型。针对传统的风险-回报三类典型问题和分布不确定性背景, 提出了更一般性条件下的分布鲁棒风险-回报优化新模型; 基于矩不确定集合和优化对偶理论, 化简复杂的新优化模型为常规结构的非线性优化问题。理论上证明了分布鲁棒风险-回报三类优化模型效率前沿的等价性。数值实验验证了理论分析的有效性。

This article studies the reward-risk optimization model under the uncertain distribution of random variables. In view of the three typical problems of traditional reward-risk and the background of uncertainty of distributions, a new model of distributionally robust reward-risk optimization is proposed under more general conditions. Based on moment ambiguity set and optimal duality theory, the complex new optimization model is simplified to a nonlinear optimization problem of conventional structure. The equivalence of efficient frontier of three types of distributionally robust reward-risk optimization models is proved theoretically. Numerical example verifies the effectiveness of the theoretical analysis.