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

In this note, we consider a general discrete time financial market with proportional transaction costs as in [4], [5], [6], and [10]. We provide a dual formulation for the set of initial endowments which allow to super-hedge some American claim. This extends the results of [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