GRADUATE STUDENT SEMINAR, Viscosity solutions for McKean-Vlasov Control on a torus, Qinxin Yan

Viscosity solutions for McKean-Vlasov Control on a torus

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 Prof. H. Mete Soner from ORFE department.