Abstract: A Bass martingale, in one dimension, is an increasing transformation of a Brownian motion with an arbitrary initial distribution. This definition extends to higher dimensions by using gradients of convex functions instead of increasing transformations. In parallel to the theory of optimal transport, one can ask whether a Bass martingale interpolating between given initial and terminal marginals exists (that is, under minimal assumptions on these marginals). A positive answer to this question is desirable, since arguably these objects provide the simplest way of transporting an initial marginal into a terminal marginal while preserving the martingale property. In this talk we discuss the existence of Bass martingales, their key properties, and their connection to convex potentials.
On the existence and structure of Bass martingales
01.03.2023 15:45 - 16:45
Organiser:
M. Beiglböck, N. Berestycki, L. Erdös, J. Maas, F. Toninelli, E. Schertzer
Location:
TU Wien, Sahulka Hörsaal EI 3 (Gußhausstraße 25-29)