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We derive a closed form solution for an optimal control problem related to aninterbank lending schemes subject to terminal probability constraints on thefailure of banks which are interconnected through a financial network. Thederived solution applies to a real banks network by obtaining a generalsolution when the aforementioned probability constraints are assumed for allthe banks. We also present a direct method to compute the systemic relevanceparameter for each bank within the network.

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