Geometry of Martingale Optimal Transport and the Cost of Robust Bounds

The paper studies the geometry of martingale optimal transport and shows that, for a large class of payoffs, the model-free price bound is attained on couplings supported on low-dimensional sets, giving both structural insight and a route to tractable computation of robust bounds. We read it as sharpening the MOT-bounds program from existence statements toward computable, geometrically characterized optima.

For the MOT problem sup over Q ∈ M(μ, ν) of E_Q[Φ], the optimizer's support is shown to concentrate on a set whose dimension is controlled by the structure of Φ, reducing the effective transport problem.

MOT bounds are usually criticized as wide and expensive; the dimension-reduction geometry attacks the expense and clarifies which model-free bounds are actually informative. It makes robust pricing more than a worst-case formality.

Improves the practicality of MOT as a sanity layer over event-window exotics — robust bounds become cheaper to compute and easier to interpret as binding versus slack.

The reduction depends on payoff structure and marginal regularity; for general path-dependent payoffs the low-dimensional characterization need not hold.