Year: 2018
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Bayraktar, Erhan, Zhang, Xin, Zhou, Zhou
Institutions: The University of Sydney, University of Michigan
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W2890119835