Speaker: Dr. Domynikas Norgilas from the University of Michigan (invited by Adriana Ocejo Monge)
Title: The Monge-Kantorovich mass transport with supermartingale constraints.
Abstract: Given two measures μ,ν on R with μ(R) ≤ ν(R), and such that μ is smaller than ν in positive convex-decreasing order (i.e., μ ≤pcd ν), there exists a two-period supermartingale S = (S₁,S₂) that transports μ to ν. For each such supermartingale, S₁ ~ μ, but there are many possible choices for the law of S₂. In this talk we study two canonical choices (the minimal and the maximal measures) with respect to convex-decreasing order. We show how these measures give rise to the so-called supermartingale shadow couplings of S₁ and S₂.