英文标题：
《Mapping systemic risk: critical degree and failures distribution in
financial networks》
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作者：
Matteo Smerlak, Brady Stoll, Agam Gupta, James S. Magdanz
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最新提交年份：
2014
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英文摘要：
The 2008 financial crisis illustrated the need for a thorough, functional understanding of systemic risk in strongly interconnected financial structures. Dynamic processes on complex networks being intrinsically difficult, most recent studies of this problem have relied on numerical simulations. Here we report analytical results in a network model of interbank lending based on directly relevant financial parameters, such as interest rates and leverage ratios. Using a mean-field approach, we obtain a closed-form formula for the \"critical degree\", viz. the number of creditors per bank below which an individual shock can propagate throughout the network. We relate the failures distribution (probability that a single shock induces $F$ failures) to the degree distribution (probability that a bank has $k$ creditors), showing in particular that the former is fat-tailed whenever the latter is. Our criterion for the onset of contagion turns out to be isomorphic to the condition for cooperation to evolve on graphs and social networks, as recently formulated in evolutionary game theory. This remarkable connection supports recent calls for a methodological rapprochement between finance and ecology.
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中文摘要：
2008年的金融危机表明，需要对紧密相连的金融结构中的系统性风险进行全面、功能性的理解。复杂网络上的动态过程本质上是困难的，最近对这个问题的研究依赖于数值模拟。在这里，我们报告了基于直接相关金融参数（如利率和杠杆率）的银行间贷款网络模型的分析结果。利用平均场方法，我们得到了“临界度”的封闭形式公式，即。每家银行的债权人数量，低于该数量，个人冲击可以在整个网络中传播。我们将失败分布（一次冲击导致$F$失败的概率）与程度分布（一家银行拥有$k$债权人的概率）联系起来，特别表明，无论后者何时发生，前者都是厚尾的。我们关于传染开始的标准被证明与合作在图和社交网络上演化的条件是同构的，正如最近在进化博弈论中所阐述的那样。这种非凡的联系支持了最近关于在金融和生态之间建立方法论和解的呼吁。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：General Finance 一般财务
分类描述：Development of general quantitative methodologies with applications in finance
通用定量方法的发展及其在金融中的应用
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一级分类：Physics 物理学
二级分类：Physics and Society 物理学与社会
分类描述：Structure, dynamics and collective behavior of societies and groups (human or otherwise). Quantitative analysis of social networks and other complex networks. Physics and engineering of infrastructure and systems of broad societal impact (e.g., energy grids, transportation networks).
社会和团体（人类或其他）的结构、动态和集体行为。社会网络和其他复杂网络的定量分析。具有广泛社会影响的基础设施和系统（如能源网、运输网络）的物理和工程。
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