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While many questions in (robust) finance can be posed in the martingaleoptimal transport (MOT) framework, others require to consider also non-linearcost functionals. Following the terminology of Gozlan, Roberto, Samson andTetali this corresponds to weak martingale optimal transport (WMOT).  In this article we establish stability of WMOT which is important sincefinancial data can give only imprecise information on the underlying marginals.As application, we deduce the stability of the superreplication bound for VIXfutures as well as the stability of stretched Brownian motion and we derive amonotonicity principle for WMOT.

Stability of the Weak Martingale Optimal Transport Problem