Transport Plans with Domain Constraints

Erhan Bayraktar, Xin Zhang, Zhou Zhou

Research output: Contribution to journalArticlepeer-review

Abstract

This paper focuses on martingale optimal transport problems when the martingales are assumed to have bounded quadratic variation. First, we give a result that characterizes the existence of a probability measure satisfying some convex transport constraints in addition to having given initial and terminal marginals. Several applications are provided: martingale measures with volatility uncertainty, optimal transport with capacity constraints, and Skorokhod embedding with bounded times. Next, we extend this result to multi-marginal constraints. Finally, we consider an optimal transport problem with constraints and obtain its Kantorovich duality. A corollary of this result is a monotonicity principle which gives a geometric way of identifying the optimizer.

Original languageEnglish (US)
Pages (from-to)1131-1158
Number of pages28
JournalApplied Mathematics and Optimization
Volume84
Issue number1
DOIs
StatePublished - Aug 2021

Keywords

  • Bounded volatility/quadratic variation
  • Domain constraints
  • G-expectations
  • Kantorovich duality
  • Martingale optimal transport
  • Monotonicity principle

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics

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