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.
Funding Statement
MB acknowledges support from FWF through grant no. Y00782. WM acknowledges support from the “Chaire Risques Financiers”, Fondation du Risque. GP acknowledges support from the Austrian Science Fund (FWF) through grant number W1245.
Citation
Mathias Beiglböck. Benjamin Jourdain. William Margheriti. Gudmund Pammer. "Stability of the weak martingale optimal transport problem." Ann. Appl. Probab. 33 (6B) 5382 - 5412, December 2023. https://doi.org/10.1214/23-AAP1950
Information
