发表机构
The Chinese University of Hong Kong (Shenzhen); Georgia State University（香港中文大学（深圳）; 佐治亚州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对Wasserstein模糊下的失真风险度量，提出稳健优化方法，包括直接凸化条件、精确最坏情况评估及近似分布误差界，并应用于投资组合选择。
AI 中文摘要
在分布模糊下进行风险评估是金融、经济学和运筹学中决策的核心问题。Wasserstein 球提供了一种描述参考分布周围不确定性的自然方式。我们解决了在仅以 Wasserstein 距离作为模糊约束的失真风险度量类别中，一个自然但尚未解决的稳健优化问题。该目标类别不要求失真函数具有凸性、单调性和连续性，涵盖了许多常见的风险度量和偏差度量。首先，我们刻画了直接凸化保持最坏情况值的条件。其次，当直接凸化条件不成立时，我们开发了一种精确最坏情况评估的构造性方法。第三，我们构造了显式的近似最坏情况分布，并提供了可计算的误差界，以在不求解精确问题的情况下评估其准确性。我们将这些结果应用于分布稳健的投资组合选择，并通过数值实验评估近似精度及由此产生的投资组合决策。
英文摘要
Risk evaluation under distributional ambiguity is central to decision making in finance, economics, and operations research. Wasserstein balls provide a natural way to describe uncertainty around a reference distribution. We solve a natural yet open problem of robust optimization for the class of distortion riskmetrics with Wasserstein distance as the sole ambiguity constraint. This chosen objective class does not require convexity, monotonicity, and continuity of distortion functions, encompassing many common risk measures and deviation measures. First, we characterize conditions under which direct convexification preserves the worst-case value. Second, we develop a constructive method for exact worst-case evaluation when the direct convexification conditions fail. Third, we construct explicit approximate worst-case distributions and provide computable error bounds to assess their accuracy without solving the exact problem. We apply these results to distributionally robust portfolio selection and use numerical experiments to assess approximation accuracy and the resulting portfolio decisions.
