Weak Solutions of Mean Field Game Master Equations

Speaker

Jianfeng Zhang

University of Southern California

Professor, Department of Mathematics

Description

In this talk, we consider master equations arising from mean field game problems under the Lasry-Lions monotonicity condition. Classical solutions of such equations typically require very strong technical conditions. Moreover, unlike the equations arising from mean-field control problems, the mean-field game master equations are non-local, and even classical solutions often do not satisfy the comparison principle, so the standard viscosity solution approach seems infeasible. We shall propose a new notion of weak solutions for such equations and establish its wellposedness. For the crucial regularity in terms of the measures, we construct a smooth mollifier for functions on Wasserstein space, which is new in the literature and is interesting in its own right. The talk is based on a joint work with Chenchen Mou.

Event Topic

Mathematical Finance, Stochastic Analysis, and Machine Learning