Before revision: We derive a closed form solution for an optimal control of interbank lending subject to terminal probability constraints on the failure of  a bank. The solution can be applied to a network of banks providing a general solution when  aforementioned probability constraints are assumed for all the banks in the system .
After revision: We derive a closed form solution for an optimal control of interbank lending subject to terminal probability constraints on the failure of a general solution when aforementioned probability constraints are assumed for all the banks in the system .