Martingale optimal transport duality
Functional Analysis
2021-05-14 v3 Mathematical Finance
Abstract
We obtain a dual representation of the Kantorovich functional defined for functions on the Skorokhod space using quotient sets. Our representation takes the form of a Choquet capacity generated by martingale measures satisfying additional constraints to ensure compatibility with the quotient sets. These sets contain stochastic integrals defined pathwise and two such definitions starting with simple integrands are given. Another important ingredient of our analysis is a regularized version of Jakubowski's -topology on the Skorokhod space.
Cite
@article{arxiv.1904.04644,
title = {Martingale optimal transport duality},
author = {Patrick Cheridito and Matti Kiiski and David J. Prömel and H. Mete Soner},
journal= {arXiv preprint arXiv:1904.04644},
year = {2021}
}
Comments
29 pages