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. An open-loop Nash equilibrium is obtained using a system of fully coupled forward and advanced backward stochastic differential equations. In addition, we discuss the application of the coupled diffusions on credit risk under Merton setting.