We consider empirical measures of R d-valued stochastic process in finite discrete-time. We
show that the adapted empirical measure introduced in the recent work (Ann. Appl. Probab …

Wasserstein distance induces a natural Riemannian structure for the probabilities on the
Euclidean space. This insight of classical transport theory is fundamental for tremendous …

This paper studies distributionally robust optimization (DRO) in a dynamic context. We
consider a general penalized DRO problem with a causal transport-type penalization. Such …

We consider multiperiod stochastic control problems with non-parametric uncertainty on the
underlying probabilistic model. We derive a new metric on the space of probability …

We consider empirical measures of $\R^{d} $-valued stochastic process in finite discrete-
time. We show that the adapted empirical measure introduced in the recent work\cite …

In recent years, Wasserstein Distributionally Robust Optimization (DRO) has garnered
substantial interest for its efficacy in data-driven decision-making under distributional …