Duality for increasing convex functionals with countably many marginal constraints

Daniel Bartl, Patrick Cheridito, Michael Kupper, Ludovic Tangpi

Research output: Contribution to journalArticle

8 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)72-89
Number of pages18
JournalBanach Journal of Mathematical Analysis
Volume11
Issue number1
DOIs
StatePublished - Jan 1 2017
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory

Keywords

  • Increasing convex functionals
  • Kantorovich duality
  • Model-independent finance
  • Representation results
  • Transport problem

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