Consider the problem where for two centred probabilities we look for the third probability that dominates the other two in the convex order while exhibiting the minimal variance. Although reminiscent of optimization in stochastic finance, this problem has emerged as a reformulation of an optimal design problem in structural mechanics. It also provides a new way of computing the first-order Zolotarev distance between two centred probabilities.
After expounding the links above, I will show how the optimal dominance problem can be tackled by a variant of the optimal transport problem with the extra martingale-like constraints. Finally, I will speak of its entropic regularization that facilitates a variation of the Sinkhorn algorithm.
This talk will discuss two joint works: the first one with Guy Bouchitté, and the second with Guillaume Carlier, Quentin Mérigot, and Filippo Santambrogio.
Maxime Laborde
