Expectations and martingales in metric spaces

Abstract

We develop a theory of martingales with values in metric spaces of nonpositive curvature. Our main results state existence of (continuous-time) martingales with given terminal data X T . These processes will be constructed via time discretization. The notion of discrete-time martingale is based on the concept of iterated conditional barycenters. Moreover, in more specific cases we present martingale characterizations.