Transport plans with domain constraints
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.
Cite
@article{arxiv.1804.04283,
title = {Transport plans with domain constraints},
author = {Erhan Bayraktar and Xin Zhang and Zhou Zhou},
journal= {arXiv preprint arXiv:1804.04283},
year = {2020}
}
Comments
To appear in Applied Mathematics and Optimization. Keywords:Strassen's Theorem, Kellerer's Theorem, Martingale optimal transport, domain constraints, bounded volatility/quadratic variation, $G$-expectations, Kantorovich duality, monotonicity principle