Stability of the weak martingale optimal transport problem

Mathias Beiglböck; Benjamin Jourdain; William Margheriti; Gudmund Pammer

doi:10.1214/23-aap1950

Stability of the weak martingale optimal transport problem

Mathias Beiglböck, Benjamin Jourdain, William Margheriti, Gudmund Pammer

Research output: Contribution to journal › Article › peer-review

Abstract

While many questions in (robust) finance can be posed in the martingale optimal transport (MOT) framework, others require to consider also nonlinear cost functionals. Following the terminology of Gozlan, Roberto, Samson and Tetali (J. Funct. Anal. 273 (2017) 3327 3405) for classical optimal transport, this corresponds to weak martingale optimal transport (WMOT). In this article we establish stability of WMOT which is important since financial data can give only imprecise information on the underlying marginals. As application, we deduce the stability of the superreplication bound for VIX futures as well as the stability of the stretched Brownian motion and we derive a monotonicity principle for WMOT.

Original language	English
Pages (from-to)	5382 - 5412
Journal	The Annals of Applied Probability
Volume	33
Issue number	6B
DOIs	https://doi.org/10.1214/23-aap1950
Publication status	Published - 1 Dec 2023
Externally published	Yes

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AU - Jourdain, Benjamin

AU - Margheriti, William

AU - Pammer, Gudmund

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AB - While many questions in (robust) finance can be posed in the martingale optimal transport (MOT) framework, others require to consider also nonlinear cost functionals. Following the terminology of Gozlan, Roberto, Samson and Tetali (J. Funct. Anal. 273 (2017) 3327 3405) for classical optimal transport, this corresponds to weak martingale optimal transport (WMOT). In this article we establish stability of WMOT which is important since financial data can give only imprecise information on the underlying marginals. As application, we deduce the stability of the superreplication bound for VIX futures as well as the stability of the stretched Brownian motion and we derive a monotonicity principle for WMOT.

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JO - The Annals of Applied Probability

JF - The Annals of Applied Probability

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Stability of the weak martingale optimal transport problem

Abstract

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