The Institute for Mathematical Behavioral Sciences Colloquium Series presents
“Mean Field Games and Systemic Risk”
with Jean-Pierre Fouque, Director, Center for Financial Mathematics and Actuarial Research, UC Santa Barbara
Thursday, October 23, 2014
Social Science Plaza A, Room 2112
Fouque proposes a simple model of inter-bank borrowing and lending where the evolution of the log-monetary reserves of N banks is described by a system of diffusion processes coupled through their drifts in such a way that stability of the system depends on the rate of inter-bank borrowing and lending. Systemic risk is characterized by a large number of banks reaching a default threshold by a given time horizon. Our model incorporates a game feature where each bank controls its rate of borrowing/lending to a central bank. The optimization reflects the desire of each bank to borrow from the central bank when its monetary reserve falls below a critical level or lend if it rises above this critical level which is chosen here as the average monetary reserve. Borrowing from or lending to the central bank is also subject to a quadratic cost at a rate which can be fixed by the regulator. He solves explicitly for Nash equilibria with finitely many players, and shows that in this model the central bank acts as a clearing house, adding liquidity to the system without affecting its systemic risk. He also studies the corresponding Mean Field Game in the limit of large number of banks in the presence of a common noise.
Joint work with R. Carmona and L.H Sun.
For further information, please contact Joanna Kerner, firstname.lastname@example.org or 949.824.8651.