We consider a model when private banks with interbank cash flows as in (Carmona, Fouque, Sun, 2013) borrow from the outside economy at a certain interest rate, controlled by the central bank, and invest in risky assets. The cash flow between private banks is also facilitated by the central bank. Each private bank aims to maximize its expected terminal logarithmic utility. The central bank, in turn, aims to control the overall size of financial system , and the rate of circulation between banks . A default occurs when the net worth of a bank goes below a certain threshold. We  consider systemic risk by studying probability of a certain number of defaults over fixed finite time horizon.
We consider a model when private banks with interbank cash flows as in (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 bank aims to maximize its expected terminal logarithmic utility. 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.
D
The cash flow between private banks is also facilitated by the central bank.
D
, and the rate of circulation between banks
A
solve stochastic optimal control problems, and