2024/01/29 by Yifan Jiang, Jiang, Yifan
Decision Sciences · Economics, Econometrics and Finance · #60G40 #90C46 #93E03 #Economic theories and models #FOS: Mathematics #Market Dynamics and Volatility #Optimization and Control (math.OC) #Probability (math.PR) #Risk and Portfolio Optimization
paper · pdf · doi:10.48550/arxiv.2401.16556
openalex publication_date 2024/01/29 · openalex created_date 2024/02/01 · openalex updated_date 2026/07/28
We study the distributionally robust optimization (DRO) in a dynamic context where the model uncertainty is captured by penalizing potential models in function of their adapted Wasserstein distance to a given reference model. We consider both discrete- and continuous-time settings and derive dynamic duality formulas that reformulate the worst-case expectation as a tractable minimax problem. The inner maximum can be computed recursively in discrete time, or solved by a path-dependent Hamilton--Jacobi--Bellman equation in continuous time. We further extend these duality results from the worst-case expectation to the worst-case expected shortfall, a non-linear expectation. Finally, we apply the DRO framework to optimal stopping problems in discrete time. We recast the original problem as a classical Wasserstein DRO on a nested space by introducing a novel relaxation that considers stopping times with respect to general flitrations.