We propose a model of inter-bank lending and
borrowing which takes into account clearing debt
obligations. The evolution of log-monetary reserves
of N banks is described by coupled diffusions driven
by controls with delay in their drifts. Banks are
minimizing their finite-horizon objective functions
which take into account a quadratic cost for lending
or borrowing and a linear incentive to borrow if the
reserve is low or lend if the reserve is high
relative to the average capitalization of the
system. As such, our problem is a linear-quadratic
stochastic game with delay between N players. A
unique open-loop Nash equilibrium is obtained using
a system of fully coupled forward and advanced
backward stochastic differential equations. We then
describe how the delay affects liquidity and
systemic risk characterized by a large number of
defaults. We also derive a close-loop Nash
equilibrium using an HJB approach to this stochastic
game with delay and we analyze its mean field limit.
Joint work with R. Carmona, M. Mousavi and L.H. Sun.
Jean-Pierre Fouque held positions at the CNRS and at the Ecole Polytechique in
France, before joining North Carolina State University in 1998 where he started the
Masters of Financial Mathematics.
Since 2006, he is Professor in the department of Statistics and Applied Probability at University of California
Santa Barbara and Director of the Center for Financial Mathematics and Actuarial Research (CFMAR).
His research is in the domain of random media with applications ranging from wave propagation phenomena to financial
mathematics. He published over ninety research articles and co-authored three books:
"Derivatives in Financial Markets with Stochastic Volatility" (Cambridge University Press, 2000),
"Wave Propagation and Time Reversal in Randomly Layered Media" (Springer, 2007),
and "Multiscale Stochastic Volatility for Equity, Interest-Rate and Credit
Derivatives" (Cambridge University Press, 2011).
He co-edited the "Handbook on Systemic Risk" (CUP, 2013), and he was a member
of the Advisory Committee of the U.S. Office
of Financial Research (2012-2015).
He is Editor-in-Chief of the SIAM Journal on Financial Mathematics.
Jean-Pierre Fouque is a Fellow of the Institute of Mathematical Statistics
since 2009 and a SIAM Fellow since 2011.