On the hedging of American options in discrete time markets with proportional transaction costs

In this note, we consider a general discrete time financial marked with proportional transaction costs as in Kabanov and Stricker [4], Kabanov et al. [5], Kabanov et al. [6] and Schachermayer [10]. We provide a dual formulation for the set of initial endowments which allow to super-hedge some American claim. We show that this extends the result of Chalasani and Jha [1] which was obtained in a model with constant transaction costs and risky assets which evolve on a finite dimensional tree. We also provide fairly general conditions under which the expected formulation in terms of stopping times does not work.