Martingale optimal transport duality

Patrick Cheridito, Matti Kiiski, David J. Pr\"omel and H. Mete Soner

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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 $S$-topology on the Skorokhod space.

Date: 2019-04, Revised 2020-11
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Citations: View citations in EconPapers (6)

Published in Math. Ann. 379, 1685--1712 (2021)

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