On the Martingale Schr\"odinger Bridge between Two Distributions
Probability
2025-09-01 v2 Mathematical Finance
Abstract
We study a martingale Schr\"odinger bridge problem: given two probability distributions, find their martingale coupling with minimal relative entropy. Our main result provides Schr\"odinger potentials for this coupling. Namely, under certain conditions, the log-density of the optimal coupling is given by a triplet of real functions representing the marginal and martingale constraints. The potentials are also described as the solution of a dual problem.
Cite
@article{arxiv.2401.05209,
title = {On the Martingale Schr\"odinger Bridge between Two Distributions},
author = {Marcel Nutz and Johannes Wiesel},
journal= {arXiv preprint arXiv:2401.05209},
year = {2025}
}
Comments
Final version, accepted for publication in Bernoulli