This was part of Distributed Solutions to Complex Societal Problems Reunion Workshop

Viscosity Solutions for McKean-Vlasov Control on a torus

Mete Soner, Princeton University

Tuesday, February 21, 2023

Abstract: We consider the viscosity solutions of the dynamic programming equations of a McKean Vlasov control defined using the intrinsic linear derivative.  We obtain a comparison result between the Lipschitz viscosity sub and super solutions under a structural assumption on the control set together with the given functions.  Proof follows the classical variable doubling argument of Crandall & Lions by using a novel smooth Fourier-Wasserstein metric that we construct.  The value function is also shown to be Lipschitz continuous with respect to this metric.   This is joint work with Qinxin Yan of Princeton University.