Tightness and duality of martingale transport on the Skorokhod space

TL;DR

This paper investigates the properties of continuous-time martingale optimal transport on the Skorokhod space, establishing duality results using advanced topological and dynamic programming techniques relevant for financial mathematics.

Contribution

It introduces dual problems and proves duality results for continuous-time martingale transport on the Skorokhod space, extending classical optimal transport theory.

Findings

Established duality results for martingale transport on Skorokhod space

Introduced new dual problems using S-topology and dynamic programming

Extended classical optimal transport duality to a continuous-time martingale setting

Abstract

The martingale optimal transport aims to optimally transfer a probability measure to another along the class of martingales. This problem is mainly motivated by the robust superhedging of exotic derivatives in financial mathematics, which turns out to be the corresponding Kantorovich dual. In this paper we consider the continuous-time martingale transport on the Skorokhod space of cadlag paths. Similar to the classical setting of optimal transport, we introduce different dual problems and establish the corresponding dualities by a crucial use of the S-topology and the dynamic programming principle.