金融系統性風險的回顧分析

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吳必成(Bi-Cheng Wu) 查詢紙本館藏

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統計研究所

論文名稱

金融系統性風險的回顧分析
(A Review and Analysis of Systemic Risk in Financial Systems)

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摘要(中)

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。

摘要(英)

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.

關鍵字(中)

★ 不動點
★ 清算向量
★ 違約序列

關鍵字(英)

★ fixed-point
★ clearing vectors
★ default sequence

論文目次

摘要 i
Abstract ii
誌謝 iii
1 Introduction of My Thesis 1
2 Paper Review 1
2.1 Backgroud . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2.2 Economic Framework . . . . . . . . . . . . . . . . . . . . . . .. . . . 2
2.3 The Properties of Clearing Vector . . . . . . . .. . . . . . . . . 6
2.3.1 The Existence of Clearing Payment Vectors . .. . . . . . 6 2.3.2 The Uniqueness of Clearing Payment Vectors .. . . . . 7 2.3.3 Some Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . 9
2.4 Charaterizing The clearing vector . . . . . . . . . . . . . . . . . 10 2.4.1 The Existence of Payment Vectors . . . . . . . . . . . . . . . 10 2.4.2 Sequence of Default . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.5 Some Other Properties . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3 A New Method of Proof 16
3.1 Completeness of A Closed Set in Rn . . . .. . . . . . . . . . . 16 3.1.1 Rn is Complete . . . . . . . . . . . . . . . . . . . . . .. . .. . . . . . . 16
3.1.2 Completeness of A Closed Subset . . . . . . . . . . . . . . . 17 3.2 Banach Fixed-point Theorem . . . . . . . . . . . . . . . . . . . . . 18
4 My view of this paper 20
References 20

參考文獻

[1] Larry Eisenberg and Thomas H Noe. Systemic risk in financial systems. Management Science, 47(2):236–249, 2001.
[2] Franklin Allen and Douglas Gale. Financial contagion. Journal of political economy, 108(1):1–33, 2000.
[3] Eberhard Zeidler. Nonlinear functional analysis vol. 1: Fixed-point theorems. 1986.
[4] Samuel Karlin. Mathematical methods and theory in games, programming, and economics / [by] Samuel Karlin. Pergamon Press London, 1959.
[5] Chi-fuHuangandRobertHLitzenberger. Foundationsforfinancialeconomics. NorthHolland, 1988.
[6] Darrell Duffie. Security markets: Stochastic models. 1988.

指導教授

孫立憲(Li-Hsien Sun)

審核日期

2018-10-11

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