Portfolio optimization can lead to misspecified stock returns that follow a known distribution. To investigate tractable formulations of the portfolio selection problem, we study these problems with the ambiguity set defined by the Wasserstein metric. Robust optimization with Wasserstein models protects against ambiguity in the distribution when analyzing decisions. This study considers portfolio optimization using a robust mean absolute deviation model consistent with the Wasserstein metric. The core of our idea is to consider the sets of distributions that lie within a certain distance from an empirical distribution. However, since information in financial markets is often unclear, we extend this structure to the weighted mean absolute deviation model when the underlying probability distribution is not precisely known. We then construct a decomposition algorithm based on the Benders decomposition approach to solve such problems. For more efficient comparison, the acquired optimization programs are applied to real data.

中文翻译：

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使用稳健平均绝对偏差模型进行投资组合优化：Wasserstein 度量方法


投资组合优化可能会导致遵循已知分布的错误指定股票回报。为了研究投资组合选择问题的易于处理的公式，我们使用 Wasserstein 度量定义的模糊集来研究这些问题。使用 Wasserstein 模型进行稳健优化可防止分析决策时分布出现模糊性。本研究考虑使用与 Wasserstein 指标一致的稳健平均绝对偏差模型进行投资组合优化。我们想法的核心是考虑与经验分布一定距离内的分布集。然而，由于金融市场中的信息通常不明确，因此当底层概率分布未知时，我们将这种结构扩展到加权平均绝对偏差模型。然后我们基于 Benders 分解方法构建分解算法来解决此类问题。为了更有效地进行比较，将获得的优化程序应用于实际数据。