A Note on Uniqueness of Clearing Prices in Financial Systems

The Eisenberg and Noe (2001) model of the financial system is generalized to the case where default is solved by means of a bankruptcy rule. For regular financial networks a unique vector of clearing prices exists if only the bankruptcy rule is strongly monotonic. This shows uniqueness of the clearing prices on regular financial networks for the class of equal sacrifice rules by Young (1988), and many variations of the proportional rule as in Csóka and Herings (2018). This paper disentangles the role of network topology from the way defaults are solved