Systemic Risk and Interbank Lending

We propose a simple model of the banking system incorporating a game feature where the evolution of monetary reserve is modeled as a system of coupled Feller diffusions. The Markov Nash equilibrium generated through minimizing the linear quadratic cost subject to Cox-Ingersoll-Ross type processes creates liquidity and deposit rate. The adding liquidity leads to a flocking effect but the deposit rate diminishes the growth rate of the total monetary reserve causing a large number of bank defaults. In addition, the corresponding Mean Field Game and the infinite time horizon stochastic game with the discount factor are also discussed.