A lending scheme for a system of interconnected banks with probabilistic constraints of failure

We derive a closed form solution for an optimal control problem related to an interbank lending schemes subject to terminal probability constraints on the failure of banks which are interconnectedthrough a financial network. The derived solution applies to a real banks network by obtaining ageneral solution when the aforementioned probability constraints are assumed for all the banks. We also present a direct method to compute the systemic relevance parameter for each bank within the network