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On the Martingale Schr\"odinger Bridge between Two Distributions

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  • Marcel Nutz
  • Johannes Wiesel

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.

Suggested Citation

  • Marcel Nutz & Johannes Wiesel, 2024. "On the Martingale Schr\"odinger Bridge between Two Distributions," Papers 2401.05209, arXiv.org.
    • Handle: RePEc:arx:papers:2401.05209
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