Systemic risk and stochastic games with delay
Jean-Pierre Fouque | University of California at Santa Barbara
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.
Contact at the MS2Discovery Research Institute: Joe Campolieti, Roman Makarov, Roderick Melnik (Hosts of the speaker, Tecton 7: Mathematical Models in Finance)
Refreshments will be provided
May 11, 2017
4-5pm | Location: LH1009
The MS2Discovery Seminar Series:
Wilfrid Laurier University, 75 University Avenue West, Waterloo
This event is hosted by the MS2Discovery Interdisciplinary Research Institute | Waterloo