论文标题
通过因果关系限制和结构信息，分配强劲的风险评估
Distributionally robust risk evaluation with a causality constraint and structural information
论文作者
论文摘要
这项工作研究了对时间数据对期望值的分布强劲评估。一组替代措施的特征是因果最佳运输。我们证明了强大的二元性并重铸了因无限维测试功能空间的最小化因果关系的约束。我们通过神经网络近似测试函数，并证明了Rademacher复杂性的样品复杂性。给出了一个示例来验证技术假设的可行性。此外，当有结构信息可以进一步限制歧义集时，我们证明了双重公式并提供有效的优化方法。我们的框架在分配强大的投资组合选择问题中优于经典的框架。还通过数值研究了与幼稚策略的联系。
This work studies the distributionally robust evaluation of expected values over temporal data. A set of alternative measures is characterized by the causal optimal transport. We prove the strong duality and recast the causality constraint as minimization over an infinite-dimensional test function space. We approximate test functions by neural networks and prove the sample complexity with Rademacher complexity. An example is given to validate the feasibility of technical assumptions. Moreover, when structural information is available to further restrict the ambiguity set, we prove the dual formulation and provide efficient optimization methods. Our framework outperforms the classic counterparts in the distributionally robust portfolio selection problem. The connection with the naive strategy is also investigated numerically.
