231 citations · 874 across the 46 of their papers we have counts for
16 papers · 1 filter
On the Martingale Schrödinger Bridge between Two Distributions
Marcel Nutz, Johannes Wiesel
We study a martingale Schrödinger bridge problem: given two probability distributions, find their martingale coupling with minimal relative entropy. Our main result provides Schröd…
Martingale Transports and Monge Maps
Marcel Nutz, Ruodu Wang, Zhenyuan Zhang
It is well known that martingale transport plans between marginals are never given by Monge maps -- with the understanding that the map is over the first marginal , or…
Stability of Schrödinger Potentials and Convergence of Sinkhorn's Algorithm
Marcel Nutz, Johannes Wiesel
We study the stability of entropically regularized optimal transport with respect to the marginals. Given marginals converging weakly, we establish a strong convergence for the Sch…
Fine Properties of the Optimal Skorokhod Embedding Problem
Mathias Beiglböck, Marcel Nutz, Florian Stebegg
We study the problem of stopping a Brownian motion at a given distribution while optimizing a reward function that depends on the (possibly randomized) stopping time and the Br…
Multiperiod Martingale Transport
Marcel Nutz, Florian Stebegg, Xiaowei Tan
Consider a multiperiod optimal transport problem where distributions are prescribed and a transport corresponds to a scalar martingale with marginals $X_{t}…
Canonical Supermartingale Couplings
Marcel Nutz, Florian Stebegg
Two probability distributions and in second stochastic order can be coupled by a supermartingale, and in fact by many. Is there a canonical choice? We construct and investi…