We consider the martingale optimal transport duality for càdlàg processes with given initial and terminal laws. Strong duality and existence of dual optimizers (robust semistatic superhedging strategies) are proved for a class of payoffs that includes American, Asian, Bermudan and European options with intermediate maturity. We exhibit an optimal superhedging strategy for which the static part solves an auxiliary problem and the dynamic part is given explicitly in terms of the static part.
"Robust pricing and hedging around the globe." Ann. Appl. Probab. 29 (6) 3348 - 3386, December 2019. https://doi.org/10.1214/19-AAP1482