Modeling Financial System with Interbank Flows, Borrowing, and Investing

Abstract

In our model, private actors with interbank cash flows similar to, but nore general than (Carmona, Fouque, Sun, 2013) borrow from the outside economy at a certain interest rate, controlled by the central bank, and invest in risky assets. Each private actor aims to maximize its expected terminal logarithmic utility. The central bank, in turn, aims to control the overall economy by means of an exponential utility function. We solve all stochastic optimal control problems explicitly. We are able to recreate occasions such as liquidity trap. We study distribution of the number of defaults (net worth of a private actor going below a certain threshold).Comment: 27 pages, 29 figures. Keywords: systemic risk, stochastic control, principal-agent problem, stationary distribution, stochastic stability, Lyapunov functio