Duality for increasing convex functionals with countably many marginal constraints
D. Bartl, P. Cheridito, L. Tangpi · 2015
Abstract. The main result of this paper is a convex dual representation for increasing convex functionals that are defined on a space of real-valued Borel measurable functions living on a countable product of metric spaces. Our principal assumption is that the func-tionals fulfill convex marginal constraints satisfying a 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.