  We consider the pricing of American put options in a model-independent
setting: that is, we do not assume that asset prices behave according to a
given model, but aim to draw conclusions that hold in any model. We incorporate
market information by supposing that the prices of European options are known.
  In this setting, we are able to provide conditions on the American Put prices
which are necessary for the absence of arbitrage. Moreover, if we further
assume that there are finitely many European and American options traded, then
we are able to show that these conditions are also sufficient. To show
sufficiency, we construct a model under which both American and European
options are correctly priced at all strikes simultaneously. In particular, we
need to carefully consider the optimal stopping strategy in the construction of
our process.
