英文标题：
《Random Fixed Points, Limits and Systemic risk》
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作者：
Veeraruna Kavitha, Indrajit Saha, Sandeep Juneja
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最新提交年份：
2021
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英文摘要：
  We consider vector fixed point (FP) equations in large dimensional spaces involving random variables, and study their realization-wise solutions. We have an underlying directed random graph, that defines the connections between various components of the FP equations. Existence of an edge between nodes i, j implies the i th FP equation depends on the j th component. We consider a special case where any component of the FP equation depends upon an appropriate aggregate of that of the random neighbor components. We obtain finite dimensional limit FP equations (in a much smaller dimensional space), whose solutions approximate the solution of the random FP equations for almost all realizations, in the asymptotic limit (number of components increase). Our techniques are different from the traditional mean-field methods, which deal with stochastic FP equations in the space of distributions to describe the stationary distributions of the systems. In contrast our focus is on realization-wise FP solutions. We apply the results to study systemic risk in a large financial heterogeneous network with many small institutions and one big institution, and demonstrate some interesting phenomenon.
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中文摘要：
我们考虑了包含随机变量的大维空间中的向量不动点方程，并研究了它们的实现态解。我们有一个潜在的有向随机图，它定义了FP方程各个组成部分之间的联系。节点i，j之间的边的存在意味着第i个FP方程取决于第j个分量。我们考虑一种特殊情况，其中FP方程的任何分量取决于随机相邻分量的适当聚合。我们得到了有限维极限FP方程（在小得多的维空间中），其解在渐近极限（分量数量增加）下近似于几乎所有实现的随机FP方程的解。我们的方法不同于传统的平均场方法，它处理分布空间中的随机FP方程来描述系统的平稳分布。相反，我们的重点是实现明智的FP解决方案。我们将研究结果应用于由多个小型机构和一个大型机构组成的大型金融异构网络中的系统性风险，并展示了一些有趣的现象。
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分类信息：

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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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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