Mean Field Games with Singular Controls of Bounded Velocity

Xin Guo, Joon Seok Lee

Published 2017-03-13Version 1

This paper studies a class of mean field games (MFGs) with singular controls of bounded velocity. By relaxing the absolute continuity of the control process, it generalizes the MFG framework of Lasry and Lions [36] and Huang, Malham\'e, and Caines [29]. It provides a unique solution to the MFG with explicit optimal control policies and establishes the $\epsilon$-Nash equilibrium of the corresponding $N$-player game. Finally, it analyzes a particular MFG with explicit solutions in a systemic risk model originally formulated by Carmona, Fouque, and Sun [17] in a regular control setting.