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On the Martingale Schr\"odinger Bridge between Two Distributions

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arxiv 2401.05209 v2 pith:TNFXKIVP submitted 2024-01-10 math.PR q-fin.MF

Marcel Nutz , Johannes Wiesel This is my paper · ORCID
classification math.PRq-fin.MF
keywords martingalecouplingodingerschrbridgedistributionsgivenpotentials
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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.

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  1. Multidimensional specific relative entropy between continuous martingales

    math.PR 2024-11 conditional novelty 7.0 of 10

    A multidimensional version of specific relative entropy between continuous martingales is defined, with Gantert's inequality extended and shown to be the convex lower semicontinuous envelope of the entropy.

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