  While many questions in (robust) finance can be posed in the martingale
optimal transport (MOT) framework, others require to consider also non-linear
cost functionals. Following the terminology of Gozlan, Roberto, Samson and
Tetali 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 stretched Brownian motion and we derive a
monotonicity principle for WMOT.
