  We consider as given a discrete time financial market with a risky asset and
options written on that asset and determine both the sub- and super-hedging
prices of an American option in the model independent framework of
ArXiv:1305.6008. We obtain the duality of results for the sub- and
super-hedging prices. For the sub-hedging prices we discuss whether the sup and
inf in the dual representation can be exchanged (a counter example shows that
this is not true in general). For the super-hedging prices we discuss several
alternative definitions and argue why our choice is more reasonable. Then
assuming that the path space is compact, we construct a discretization of the
path space and demonstrate the convergence of the hedging prices at the optimal
rate. The latter result would be useful for numerical computation of the
hedging prices. Our results generalize those of ArXiv:1304.3574 to the case
when static positions in (finitely many) European options can be used in the
hedging portfolio.
