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Robust pricing-hedging duality for American options in discrete time financial markets

Deng, Shuoqing; Tan, Xiaolu; Aksamit, Anna; Obloj , Jan (2017), Robust pricing-hedging duality for American options in discrete time financial markets. https://basepub.dauphine.fr/handle/123456789/17090

Type
Document de travail / Working paper
External document link
https://hal.archives-ouvertes.fr/hal-01429550
Date
2017
Series title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Pages
19
Metadata
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Author(s)
Deng, Shuoqing
Tan, Xiaolu
Aksamit, Anna cc
Obloj , Jan
Abstract (EN)
We aim to generalize the duality results of Bouchard & Nutz [10] 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.
Subjects / Keywords
Super-replication; American option; nondominated model; martingale; optimal transport; Kantorovich duality

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