[GS_M_APP] Stability of Wasserstein projections in convex order via metric extrapolation
ABSTRACT
Optimal transport (OT) has been one of the most active research area in both pure and applied mathematical sciences. For its importance, there have been numerous variants and extOptimal transport (OT) has been one of the most active research area in both pure and applied mathematical sciences. For its importance, there have been numerous variants and extensions of it. One of them is "Martingale OT (MOT)", which is regarding OT with martingale constraint. This problem in particularly is studied for mathematical finance due to its relation to optional stopping. However, unlike classical OT, MOT does not always attain a solution. It is well known by Strassen that MOT has a solution if and only if two measures are in convex order, one of the most popular stochastic order in finance and economics. Recently, Gozlan and Juillet connect MOT with weak OT (WOT), and show that WOT value is the same as the projected distance onto "Convex order cone" with respect to a classical OT and related regularity. We prove the stability of Wasserstein projections in convex order based on metric extrapolation in Wasserstein space developed by Gallouët, Natale and Todeschi. In this talk, we provide MOT, its connection to mathematical finance briefly, and the sketch of the proof.
