英文标题：
《Financial Contagion in a Generalized Stochastic Block Model》
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作者：
Nils Detering, Thilo Meyer-Brandis, Konstantinos Panagiotou, Daniel
  Ritter
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最新提交年份：
2019
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英文摘要：
  One of the most defining features of the global financial network is its inherent complex and intertwined structure. From the perspective of systemic risk it is important to understand the influence of this network structure on default contagion. Using sparse random graphs to model the financial network, asymptotic methods turned out powerful to analytically describe the contagion process and to make statements about resilience. So far, however, they have been limited to so-called {\\em rank one} models in which informally the only network parameter is the degree sequence (see (Amini et. al. 2016) and (Detering et. al. 2019) for example) and the contagion process can be described by a one dimensional fix-point equation. These networks fail to account for a pronounced block structure such as core/periphery or a network composed of different connected blocks for different countries. We present a much more general model here, where we distinguish vertices (institutions) of different types and let edge probabilities and exposures depend on the types of both, the receiving and the sending vertex plus additional parameters. Our main result allows to compute explicitly the systemic damage caused by some initial local shock event, and we derive a complete characterisation of resilient respectively non-resilient financial systems. This is the first instance that default contagion is rigorously studied in a model outside the class of rank one models and several technical challenges arise. Moreover, in contrast to previous work, in which networks could be classified as resilient or non resilient, independent of the distribution of the shock, information about the shock becomes important in our model and a more refined resilience condition arises. Among other applications of our theory we derive resilience conditions for the global network based on subnetwork conditions only.
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中文摘要：
全球金融网络最具决定性的特征之一是其固有的复杂和交织的结构。从系统性风险的角度来看，了解这种网络结构对违约传染的影响很重要。使用稀疏随机图对金融网络进行建模，结果证明，渐近方法能够有效地分析描述传染过程，并说明弹性。然而，到目前为止，它们仅限于所谓的{\\em rank one}模型，其中非正式的唯一网络参数是度序列（参见（Amini et al.2016）和（Detering et al.2019），传染过程可以用一维定点方程来描述。这些网络无法解释明显的区块结构，如核心/外围或由不同国家的不同连接区块组成的网络。我们在这里提出了一个更为通用的模型，在该模型中，我们区分不同类型的顶点（机构），并让边缘概率和曝光取决于这两种类型，接收和发送顶点以及其他参数。我们的主要结果允许明确计算一些初始局部冲击事件造成的系统性损害，并且我们得出了弹性金融系统和非弹性金融系统的完整特征。这是第一次在一级模型之外的模型中严格研究违约传染，并出现了一些技术挑战。此外，与之前的工作不同，在之前的工作中，网络可分为弹性网络或非弹性网络，与冲击分布无关，有关冲击的信息在我们的模型中变得很重要，出现了更精确的弹性条件。在我们的理论的其他应用中，我们仅基于子网络条件推导出全球网络的弹性条件。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Risk Management        风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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