Open Access
January 2017 Duality for increasing convex functionals with countably many marginal constraints
Daniel Bartl, Patrick Cheridito, Michael Kupper, Ludovic Tangpi
Banach J. Math. Anal. 11(1): 72-89 (January 2017). DOI: 10.1215/17358787-3750133


In this work we derive a convex dual representation for increasing convex functionals on a space of real-valued Borel measurable functions defined on a countable product of metric spaces. Our main assumption is that the functionals fulfill marginal constraints satisfying a certain tightness condition. In the special case where the marginal constraints are given by expectations or maxima of expectations, we obtain linear and sublinear versions of Kantorovich’s transport duality and the recently discovered martingale transport duality on products of countably many metric spaces.


Download Citation

Daniel Bartl. Patrick Cheridito. Michael Kupper. Ludovic Tangpi. "Duality for increasing convex functionals with countably many marginal constraints." Banach J. Math. Anal. 11 (1) 72 - 89, January 2017.


Received: 17 October 2015; Accepted: 18 February 2016; Published: January 2017
First available in Project Euclid: 10 November 2016

zbMATH: 06667688
MathSciNet: MR3571145
Digital Object Identifier: 10.1215/17358787-3750133

Primary: 47H07
Secondary: ‎46G12 , 91G20

Keywords: increasing convex functionals , Kantorovich duality , model-independent finance , representation results , transport problem

Rights: Copyright © 2017 Tusi Mathematical Research Group

Vol.11 • No. 1 • January 2017
Back to Top