  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, $\pi=\sup_{(c_i,Q_i)_i}\sum_ic_i\phi^{Q_i}$, where $c_i \in
\mathbb{R}_+$ 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.
