Systemic Risk and Stochastic Games with Delay

Understand

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 an $N$-player linear-quadratic stochastic differential game with delay.