UC Berkeley

This thesis studies a class of mean field games (MFG) with singular controls of bounded velocity. By relaxing absolute continuity of control processes, it generalizes the MFG framework of Lasry and Lions \cite{LL2007} and Huang, Malham e, and Caines \cite{HMC2006}. It provides a unique solution to the MFG with singular controls of bounded velocity and its explicit optimal control policy establishes an \epsilon-Nash equilibrium of the corresponding stochastic differential N player game with singular controls.

It also includes MFGs on an infinite time horizon. Our method to approach MFGs with singular controls is from bounded velocity processes, and we analyse the relationship between singular controls with finite variation processes and singular controls with bounded velocity.

Finally, it illustrates particular MFGs with explicit solutions in a systemic risk model originally formulated by Carmona, Fouque, and Sun \cite{CFS2013} in a regular control setting and an optimal partially reversible investment problem with N players originally formulated by Guo and Pham \cite{GP2005} in a single player setting.