We consider a modelwhen 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 .
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) .
R
We consider a modelwhen private banks
In our model, private actors
R
as in
similar to, but nore general than
R
bank
actor
R
size of financial system. A default occurs when the net worth of a bank goes below a certain threshold. We solve
economy by means of an exponential utility function. We solve all
R
, and consider systemic risk by studying probability of a certain
explicitly. We are able to recreate occasions such as liquidity trap. We study distribution of the
R
over fixed finite time horizon
(net worth of a private actor going below a certain threshold)