Entropy martingale optimal transport and nonlinear pricing–hedging duality

Abstract The objective of this paper is to develop a duality between novel entropy martingale optimal transport (EMOT) problem and an associated optimisation problem. In EMOT, we follow the approach taken in (EOT) developed Liero et al. (Invent. Math. 211:969–1117, 2018), but add constraint, typical (MOT) theory, that infimum cost functional over probability measures. problem, functional, related via Fenchel conjugacy entropic term no longer linear as (martingale) transport. This leads which also has clear financial interpretation nonlinear subhedging Our theory allows us establish robust pricing–hedging covers wide range known results. We focus on Wasserstein-induced penalisations study how affected by variations penalty terms, with special convergence EMOT extreme case MOT.