Eisenberg 和 Noe (2001) 所提出的想法非常有用。許多文獻將他們的模型一般化。他們的貢獻不僅聚焦在經濟學上，還引入了許多重要的數學問題。最重要的是，他們對清算支付向量唯一性提出了充分條件。而本文的目的是對於金融網絡中清算支付向量唯一性，提出了必要和充分條件。

The ideas of Eisenberg and Noe (2001) are quite useful. Many researchers generalize their models. Their contributions focus on economics and introduce many critical mathematical problems. Most importantly, they proposed a sufficient condition for the uniqueness of the clearing payment vector. The purpose of this paper is to propose a necessary and sufficient condition for the uniqueness of clearing payment vectors in a financial network.

第一章 Introduction 1
第二章 Preliminary and Existence 3
第三章 Sufficient Conditions for Uniqueness of Clearing Payment Vectors 6
第四章 A Necessary and Sufficient Condition for Uniqueness of Clearing Payment Vectors 12
第五章 Final Remark 18
第六章 Appendix 20
第七章 References 23

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[2] Eisenberg L, Noe TH(2001) Systemic risk in financial systems. Management Sciences.47(2):236–249.

[3] Glasserman P,Young HP(2016) Contagion in Financial Networks. Journal of Economics Literature,54:779-831.

[4] Horn RA,Johnson CR(1985) Matrix Analysis,Cambridge University Press,Cambridge.