基于短缺风险度量的数据驱动Wasserstein分布稳健优化问题

Data-Driven Wasserstein Distributionally Robust Optimization Problem based on the Shortfall Risk Measure

  • 摘要: 本文利用基于短缺风险度量的Wasserstein距离来构建模糊集,从而构建了更一般的基于短缺风险度量的Wasserstein分布稳健优化模型,并探究了其可求解性。当损失函数为凹函数或凸的逐段线性函数时,我们将最坏情况期望问题转化为了有限维优化问题。此外,我们还进行了投资组合案例模拟,基于短缺风险度量的Wasserstein分布稳健优化模型提供的策略在本文的案例中表现优于1/N投资策略和均值方差投资策略。

     

    Abstract: Inspired by various approaches to ambiguity set construction in the Data-driven Wasserstein DRO model, we extend the classic method by constructing the ambiguity set using the Wasserstein metric based on the utility-shortfall risk measure. We investigate the tractability of the resulting Wasserstein DRO problem. We transform the worst-case expectation problem to a finite dimension optimization problem for concave or convex piecewise linear loss functions. Additionally, we simulate the theoretical results in the A-share market. The strategy provided by the Wasserstein DRO model based on the shortfall risk measure outperforms both the 1/N investment strategy and the mean-variance investment strategy in this case, offering a promising approach to portfolio selection.

     

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