金融网络中的连续违约
Sequential Defaulting in Financial Networks
摘要：
我们考虑金融网络，银行通过债务或信用违约互换等合同联系在一起。我们研究这些系统中的清算问题：我们想知道哪些银行最终违约，这些违约银行可以履行其债务的多少部分。我们在一个顺序模型中分析了这些网络，其中银行一次宣布一个违约，系统以一步一步的方式演变。我们首先考虑这些系统的可逆模型，其中银行可以从违约中恢复。我们发现，在这个模型中的稳定时间可以在很大程度上依赖于公告的顺序。然而，我们也表明，有系统的任何选择的顺序，该过程持续了一个指数的步骤之前，最终稳定。我们还表明，找到最小（或最大）的银行数量的顺序最终在违约是一个NP-困难的问题。此外，我们证明了在某些情况下，违约早期可以是一个有利的策略，银行，并在一般情况下，找到最佳的违约公告的时间是NP困难的。最后，我们讨论了如何改变这个设置的一些属性影响的过程的稳定时间，然后使用这些技术来设计一个单调的系统模型，它确保每个网络最终稳定。
英文摘要：
We consider financial networks, where banks are connected by contracts such as debts or credit default swaps. We study the clearing problem in these systems: we want to know which banks end up in a default, and what portion of their liabilities can these defaulting banks fulfill. We analyze these networks in a sequential model where banks announce their default one at a time, and the system evolves in a step-by-step manner. We first consider the reversible model of these systems, where banks may return from a default. We show that the stabilization time in this model can heavily depend on the ordering of announcements. However, we also show that there are systems where for any choice of ordering, the process lasts for an exponential number of steps before an eventual stabilization. We also show that finding the ordering with the smallest (or largest) number of banks ending up in default is an NP-hard problem. Furthermore, we prove that defaulting early can be an advantageous strategy for banks in some cases, and in general, finding the best time for a default announcement is NP-hard. Finally, we discuss how changing some properties of this setting affects the stabilization time of the process, and then use these techniques to devise a monotone model of the systems, which ensures that every network stabilizes eventually.
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