The goal of this talk is to price American-type financial contracts in the presence of Knightian uncertainty. In particular, instead of choosing a particular probabilistic model to represent the price process of some underlying asset (on which an American option is written), we first restrict our attention to the whole class of models that are consistent with the market data. Then the aim is to pick two consistent models for which the price of an American option is minimized and maximized. Our analysis is based on the (weak) optimal transport theory.