Mathematical modeling and analysis of insolvency contagion in an interbank network

In 2001, Eisenberg and Noe introduced a concept called “clearing payment vector” to handle the central clearing procedure of an interbank network. In this paper, we explore several conditions on the uniqueness of the clearing payment vector. It is shown that the clearing payment vector is, in general, not unique, but rather the net value of a bank is. Then, we show that the net value of the bank continuously depends on operating cash flows and so does the clearing payment vector under the condition that ensures the uniqueness of the clearing payment vector.