The Root solution to the multi-marginal embedding problem: an optimal stopping and time-reversal approach

Alexander M. G. Cox, Jan Obłój, Nizar Touzi

Research output: Contribution to journalArticle

4 Citations (Scopus)
28 Downloads (Pure)


We provide a complete characterisation of the Root solution to the Skorokhod embedding problem (SEP) by means of an optimal stopping formulation. Our methods are purely probabilistic and the analysis relies on a tailored time-reversal argument. This approach allows us to address the long-standing question of a multiple marginals extension of the Root solution of the SEP. Our main result establishes a complete solution to the n-marginal SEP using first hitting times of barrier sets by the time–space process. The barriers are characterised by means of a recursive sequence of optimal stopping problems. Moreover, we prove that our solution enjoys a global optimality property extending the one-marginal Root case. Our results hold for general, one-dimensional, martingale diffusions.

Original languageEnglish
Pages (from-to)211-259
Number of pages49
JournalProbability Theory and Related Fields
Issue number1-2
Early online date10 Feb 2018
Publication statusPublished - 28 Feb 2019


ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this