N. G. Medhin and Tianheng Wang. A Mean-Field Control Problem and Application to Inter-Bank Lending and Borrowing. Dynamic Systems and Applications 30 (2021) No.7, 1061-1089

https://doi.org/10.46719/dsa20213071

ABSTRACT.
An interacting stochastic system is studied and mean field problem is introduced as a limit of
large interacting system. Hamilton-Jacobi-Bellman Fokker-Planck equations are derived as necessary conditions
the optimal controls should satisfy. From an explicitly solvable problem, it is shown that the solution to the large
interacting system converges to the solution to the mean field problem. Moreover, we introduce impulse control
to the mean eld problem. Jump conditions of distribution and value function are discussed.

AMS (MOS) Subject Classication. 91A10, 91A13, 93E20.
Key Words and Phrases. Mean Field Games, Mean Field Optimal Control, Impulse Mean Field, HJB equation