On the Martingale Schr\"odinger Bridge between Two Distributions

Marcel Nutz and Johannes Wiesel

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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.

Date: 2024-01
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