An extension of martingale transport and stability in robust finance

Benjamin Jourdain and Gudmund Pammer
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Benjamin Jourdain: CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - ENPC - École nationale des ponts et chaussées, MATHRISK - Mathematical Risk Handling - UPEM - Université Paris-Est Marne-la-Vallée - ENPC - École nationale des ponts et chaussées - Centre Inria de Paris - Inria - Institut National de Recherche en Informatique et en Automatique
Gudmund Pammer: Department of Mathematics - ETH - ETH Zürich - Eidgenössische Technische Hochschule - Swiss Federal Institute of Technology [Zürich]

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Abstract: While many questions in robust finance can be posed in the martingale optimal transport framework or its weak extension, others like the subreplication price of VIX futures, the robust pricing of American options or the construction of shadow couplings necessitate additional information to be incorporated into the optimization problem beyond that of the underlying asset. In the present paper, we take into account this extra information by introducing an additional parameter to the weak martingale optimal transport problem. We prove the stability of the resulting problem with respect to the risk neutral marginal distributions of the underlying asset, thus extending the results in \cite{BeJoMaPa21b}. A key step is the generalization of the main result in \cite{BJMP22} to include the extra parameter into the setting. This result establishes that any martingale coupling can be approximated by a sequence of martingale couplings with specified marginals, provided that the marginals of this sequence converge to those of the original coupling. Finally, we deduce stability of the three previously mentioned motivating examples.

Keywords: Martingale Optimal Transport; Adapted Wasserstein distance; Robust finance; Weak trans- port; Stability; Convex order; Martingale couplings (search for similar items in EconPapers)
Date: 2024
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Published in Electronic Journal of Probability, 2024, 29 (57)

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-04075283

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