Before revision:  The central bank, in turn, aims to control the overall size of financial system. A default occurs when the net worth of a bank goes below a certain threshold. We solve stochastic optimal control problems , and consider systemic risk by studying probability of a certain number of defaults over fixed finite time horizon .
After revision:  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 , and consider systemic risk by studying probability of a certain number of defaults over fixed finite time horizon .