金融传染模型中的最优清算支付
Optimal Clearing Payments in a Financial Contagion Model
AI总结：
本文研究金融网络清算支付的唯一性条件，提出取消比例规则以降低级联违约损失，并通过凸优化求解最优清算支付。
摘要：
金融网络以相互义务的复杂结构为特征。这些义务通过一种称为清算的机制全部或部分（当发生违约时）得到履行，该机制确定一组支付，通过遵守有限责任、绝对优先权和比例性（按比例支付）等规则来结算债权。然而，在金融体系受到冲击的情况下，清算机制可能导致级联违约，并最终导致金融灾难。在本文中，我们首先研究艾森伯格和诺伊的按比例支付下的清算模型，并推导出清算支付唯一性的新的充分必要条件，该条件适用于任意拓扑结构的金融网络。然后，我们认为比例规则是导致级联违约的因素之一，并且如果取消该规则，整体系统损失可以减少。因此，所提出的方法将焦点从个体利益转移到整体系统利益，以控制和遏制级联失败的不利影响，并且我们表明，在这种设置下，清算支付可以通过求解适当的凸优化问题来计算。
英文摘要：
Financial networks are characterized by complex structures of mutual obligations. These obligations are fulfilled entirely or in part (when defaults occur) via a mechanism called clearing, which determines a set of payments that settle the claims by respecting rules such as limited liability, absolute priority, and proportionality (pro-rated payments). In the presence of shocks on the financial system, however, the clearing mechanism may lead to cascaded defaults and eventually to financial disaster. In this paper, we first study the clearing model under pro-rated payments of Eisenberg and Noe, and we derive novel necessary and sufficient conditions for the uniqueness of the clearing payments, valid for an arbitrary topology of the financial network. Then, we argue that the proportionality rule is one of the factors responsible for cascaded defaults, and that the overall system loss can be reduced if this rule is lifted. The proposed approach thus shifts the focus from the individual interest to the overall system's interest to control and contain adverse effects of cascaded failures, and we show that clearing payments in this setting can be computed by solving suitable convex optimization problems.
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