We consider the super-hedging price of an American option in a discrete-time market in which stocks are available for dynamic trading and European options are available for static trading. We show that the super-hedging price \pi is given by the supremum over the prices of the American option under randomized models. That is, \pi=(c_i,Q_i)_i\sum_ic_i\phi^{Q_i}, where c_i \in %DIFDELCMD < \R%%%  _+ and the martingale measure Q^i are chosen such that \sum_i c_i=1 and \sum_i c_iQ_i prices the European options correctly, and \phi^{Q_i} is the price of the American option under the model Q_i  .
We consider the super-hedging price of an American option in a discrete-time market in which stocks are available for dynamic trading and European options are available for static trading. We show that the super-hedging price \pi is given by the supremum over the prices of the American option under randomized models. That is, \pi=(c_i,Q_i)_i\sum_ic_i\phi^{Q_i}, where c_i \in %DIFDELCMD < \R%%% \mathbb{R _+ and the martingale measure Q^i are chosen such that \sum_i c_i=1 and \sum_i c_iQ_i prices the European options correctly, and \phi^{Q_i} is the price of the American option under the model Q_i . Our result generalizes the example given in ArXiv:1604.02274 that the highest model based price can be considered as a randomization over models .
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. Our result generalizes the example given in ArXiv:1604.02274 that the highest model based price can be considered as a randomization over models