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 . We also show a direct method to compute the systemic relevance of any node within the financial networkitself. Such a parameter being the fundamental one in deciding the accepted probability of failure, hence modifying the final optimal strategy adopted by a financial supervisor aiming at controlling the system .
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 interconnected through a financial network. The derived solution applies to a real banks network by obtaining a general 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 .
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of interbank lending
problem related to an interbank lending schemes
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banks which are interconnected through a financial network. The derived solution applies to a real banks network by obtaining
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bank. The solution can be applied to a network of banks providing a
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the
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in the system
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show
present
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of any node within the financial networkitself. Such a parameter being the fundamental one in deciding the accepted probability of failure, hence modifying the final optimal strategy adopted by a financial supervisor aiming at controlling the system
parameter for each bank within the network