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.

中文翻译：

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具有故障概率约束的互连银行系统的贷款方案

我们针对与银行间借贷计划有关的最优控制问题，导出了一种封闭形式的解决方案，该计划受制于通过金融网络互连的银行倒闭的终端概率约束的终端概率约束。当为所有银行假设上述概率约束时，通过获得一般解决方案，导出的解决方案适用于真实银行网络。我们还提出了一种直接方法来计算网络内每个银行的系统相关性参数。