One of the most characteristic features of the global financial network is its inherently 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 to be powerful for the purpose of analytically describing the contagion process and making statements about resilience. So far, however, such methods have been limited to so-called rank-one models in which, informally speaking, the only parameter for the skeleton of the network is the degree sequence and the contagion process can be described by a one-dimensional fixed-point equation. Such networks fail to account for the possibility of 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 one to compute explicitly the systemic damage caused by some initial local shock event, and we derive a complete characterization of resilient and nonresilient 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. In contrast to previous work, in which networks could be classified as resilient or nonresilient independently 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.

中文翻译：

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随机块模型中的财务传染

全球金融网络最典型的特征之一是其固有的复杂和相互交织的结构。从系统性风险的角度来看，了解这种网络结构对违约蔓延的影响非常重要。使用稀疏随机图对金融网络进行建模，渐近方法被证明是强大的，用于分析描述传染过程和做出关于弹性的陈述。然而，到目前为止，这些方法仅限于所谓的 rank-one 模型，其中，通俗地说，网络骨架的唯一参数是度数序列，并且传染过程可以用一维固定的点方程。这样的网络无法解释明显的区块结构（例如核心/外围）或由不同国家的不同连接区块组成的网络的可能性。我们在这里提出了一个更通用的模型，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接收和发送顶点的类型，以及其他参数。我们的主要结果允许人们明确计算由某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和非弹性金融系统的完整特征。这是在一级模型类别之外的模型中严格研究默认传染的第一个实例，并且出现了一些技术挑战。与以往的工作相比，在这种情况下，网络可以独立于冲击的分布分为弹性或非弹性，关于冲击的信息在我们的模型中变得很重要，并且出现了更精细的弹性条件。在我们理论的其他应用中，我们仅根据子网条件推导出全球网络的弹性条件。