Duality in nondominated discrete-time models for Americain options. (arXiv:1604.05517v1 [math.OC])

We aim to generalize the duality results of Bouchard and Nutz (2015) to the case of American options. By introducing an enlarged canonical space, we reformulate the superhedging problem for American options as a problem for European options. Then in a discrete time market with finitely many liquid options, we show that the minimum superhedging cost of an American option equals to the supremum of the expectation of the payoff at all (weak) stopping times and under a suitable family of martingale measures. Moreover, by taking the limit on the number of liquid options, we obtain a new class of martingale optimal transport problems as well as a Kantorovich duality result.