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.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Increasing convex functionals
- Kantorovich duality
- Model-independent finance
- Representation results
- Transport problem