Systemic Risk and Stochastic Games with Delay by Jean-Pierre Fouque

Event Date: 

Monday, May 23, 2016 - 3:30pm to 5:00pm

Event Date Details: 

Refreshments served at 3:15 p.m. 

Event Location: 

  • South Hall 5607F

Jean-Pierre Fouque — PSTAT-UCSB 

Title: Systemic Risk and Stochastic Games with Delay

Abstract: 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.