Distributionally Robust Risk Evaluation With a Causality Constraint and Structural Information
研究了时间序列数据中期望值的分布鲁棒评估，通过因果最优传输定义替代测度集，证明了强对偶性，并用神经网络近似测试函数，在投资组合选择中优于经典方法。
ABSTRACT 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.