Larry Eisenberg 和 Thomas H. Noe 2001 年發表了一篇論文：金融系統的系統性 風險。在我的論文裏，我將回顧這篇論文的主要内容，並給出一些改進。跟著 Larry Eisenberg 和 Thomas H. Noe 的思路，我們將先分析這篇論文的理論框架。首先我們會 介紹一下這篇論文的基本模型，然後我們分析證明清算向量 clearing vector 的存在唯一 性。原文作者利用的 latice 理論，通過 Tarski 的不動點定理完成證明。接下來我會給出 一個具體的矩陣形式的清算模型作爲案例，並利用此模型對金融違約風潮給出一個直觀 解釋。最後我們將對原論文關於 clearing vector 的存在唯一性的證法給出一個新的證明， 使用的是 Banach 的不動點定理，而不是原文中的 Tarski 的不動點定理。 ;Larry Eisenberg and Thomas H. Noe published a paper: Systemic Risk in Financial Systems in 2001. In my thesis, we take a review of their work and make some improvement. Following Larry Eisenberg and Thomas H. Noe’s step, we analyse the structure of their economic framework. First we introduce the basic framework of Larry Eisenberg and Thomas H. Noe’s model, then we prove the existence and uniqueness of the clearing vector about a financial system by a fixed-point theorem. Once the existence and uniqueness have been proved, we can specify this model by a matrix form example which can be proved to have a fixed-point too. Then we get a sequence of default, by which a financial system can be explained by an intuitive reasoning. We also use Banach fixed-point theorem rather than Tarski fixed-point theorem to give a new method to prove the existence and uniqueness of the clearing vector.
