  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).
