  In this paper we extend discrete time semi-static trading strategies by also
allowing for dynamic trading in a finite amount of options, and we study the
consequences for the model-independent super-replication prices of exotic
derivatives. These include duality results as well as a precise
characterization of pricing rules for the dynamically tradable options
triggering an improvement of the price bounds for exotic derivatives in
comparison with the conventional price bounds obtained through the martingale
optimal transport approach.
