英文标题：
《Network effects in default clustering for large systems》
---
作者：
Konstantinos Spiliopoulos and Jia Yang
---
最新提交年份：
2020
---
英文摘要：
We consider a large collection of dynamically interacting components defined on a weighted directed graph determining the impact of default of one component to another one. We prove a law of large numbers for the empirical measure capturing the evolution of the different components in the pool and from this we extract important information for quantities such as the loss rate in the overall pool as well as the mean impact on a given component from system wide defaults. A singular value decomposition of the adjacency matrix of the graph allows to coarse-grain the system by focusing on the highest eigenvalues which also correspond to the components with the highest contagion impact on the pool. Numerical simulations demonstrate the theoretical findings.
---
中文摘要：
我们考虑一个在加权有向图上定义的动态交互组件的大集合，确定一个组件的默认值对另一个组件的影响。我们证明了一个大数定律，用于捕捉池中不同组成部分的演变的经验度量，并从中我们提取了数量的重要信息，如整个池中的损失率以及系统范围违约对给定组成部分的平均影响。图邻接矩阵的奇异值分解允许通过关注最高特征值来粗化系统，这些特征值也对应于对池具有最高传染影响的组件。数值模拟验证了理论结果。
---
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
--
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
--
一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
--

---
PDF下载：
-->