Continuity of the martingale optimal transport problem on the real line
Johannes Wiesel
Abstract
We show continuity of the martingale optimal transport optimisation problem as a functional of its marginals. This is achieved via an estimate on the projection in the nested/causal Wasserstein distance of an arbitrary coupling on to the set of martingale couplings with the same marginals. As a corollary we obtain an independent proof of sufficiency of the monotonicity principle established in Beiglböck and Juillet (Ann. Probab. 44 (2016) 42–106) for cost functions of polynomial growth.
Topics & Concepts
MathematicsCorollaryMartingale (probability theory)Monotonic functionReal lineApplied mathematicsLocal martingaleMathematical optimizationDiscrete mathematicsPure mathematicsMathematical economicsMathematical analysisGeometric Analysis and Curvature FlowsPoint processes and geometric inequalitiesMarkov Chains and Monte Carlo Methods