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ABSTRACT: In this talk, we examine the scaling limit of multi-period distributionally robust optimization (DRO) via a semigroup approach. Each step involves a worst-case maximization over distributions in a Wasserstein ball around a reference process, and the multi-period problem arises through its sequential composition. When the Wasserstein ball’s radius scales linearly with time, we show that the scaling limit of the multi-period DRO yields a strongly continuous monotone semigroup on Cb. Furthermore, we show that its infinitesimal generator is equal to the generator associated with the non-robust scaling limit plus an additional perturbation term induced by the Wasserstein uncertainty. As an application, we show that when the reference process follows an Itô process, the viscosity solution of the associated nonlinear PDE coincides with the value of a continuous-time stochastic differential game. This is based on joint work with Max Nendel (U. Waterloo), Ariel Neufeld (NTU Singapore) and Alessandro Sgarabottolo (LMU Munich).