Monotone martingale transport plans and Skorokhod embedding

Mathias Beiglböck, Pierre Henry-Labordère, Nizar Touzi

Research output: Contribution to journalArticlepeer-review


We show that the left-monotone martingale coupling is optimal for any given performance function satisfying the martingale version of the Spence–Mirrlees condition, without assuming additional structural conditions on the marginals. We also give a new interpretation of the left monotone coupling in terms of Skorokhod embedding which allows us to give a short proof of uniqueness.

Original languageEnglish (US)
Pages (from-to)3005-3013
Number of pages9
JournalStochastic Processes and their Applications
Issue number9
StatePublished - Sep 2017


  • Martingales
  • Optimal transport
  • Skorokhod embedding

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics


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