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Arbitrage and hedging with American options

We consider a financial market in discrete time where stocks are available for dynamic trading, and liquid American options are available for static trading. We assume that the American options are infinitely divisible, and can only be bought but not sold. We establish the fundamental theorem of asset pricing and the dualities for the hedging prices of European and American options, for both the case without model ambiguity and the case with non-dominated model uncertainty.

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