2022/03/20 by Bingyan Han, Han, Bingyan · 2 citations
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Ambiguity #Causality (physics) #Computer science #Constraint (computer-aided design) #Discrete mathematics #Duality (order theory) #FOS: Computer and information sciences #FOS: Economics and business #Machine Learning (stat.ML) #Market Dynamics and Volatility #Mathematical Finance (q-fin.MF) #Mathematical optimization #Mathematics #Risk and Portfolio Optimization #Set (abstract data type) #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2203.10571
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2022/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.