Abstract:We study distributionally robust optimization (DRO) in a dynamic context, where model uncertainty is captured by penalizing potential models based on their adapted Wasserstein distance to a 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 maximization admits a recursive representation in discrete time, while in continuous time, it is characterized by a path-dependent Hamilton--Jacobi--Bellman equation. We further extend these duality results from the worst-case expectation to the worst-case expected shortfall, a non-linear expectation. Finally, we apply this 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 filtrations.
From: Yifan Jiang [view email]
[v1]
Mon, 29 Jan 2024 20:49:39 UTC (93 KB)
[v2]
Sat, 27 Sep 2025 11:08:18 UTC (86 KB)
[v3]
Mon, 17 Aug 2026 13:25:25 UTC (80 KB)
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