Template-type: ReDif-Paper 1.0
Author-Name: Csóka, Péter
Author-Name: Herings, P. Jean-Jacques
Author-workplace-name: RS: GSBE Theme Data-Driven Decision-Making, RS: GSBE Theme Conflict & Cooperation, Microeconomics & Public Economics
Title: Uniqueness of Clearing Payment Matrices in Financial Networks
Abstract: We study bankruptcy problems in financial networks in the presence of general bankruptcy laws. The set of clearing payment matrices is shown to be a lattice, which guarantees the existence of a greatest and a least clearing payment. Multiplicity of clearing payment matrices is both a theoretical and a practical concern. We present a new condition for uniqueness that generalizes all the existing conditions proposed in the literature. Our condition depends on the decomposition of the financial network into strongly connected components. A strongly connected component which contains more than one agent is called a cycle and the involved agents are called cyclical agents. If there is a cycle without successors, then one of the agents in such a cycle should have a positive endowment. The division rule used by a cyclical agent with a positive endowment should be positive monotonic and the rule used by a cyclical agent with a zero endowment should be strictly monotonic. Since division rules involving priorities are not positive monotonic, uniqueness of the clearing payment matrix is a much bigger concern for such division rules than for proportional ones. We also show how uniqueness of clearing payment matrices is related to continuity of bankruptcy rules.
Classification-JEL: c71,g10
Series: GSBE Research Memoranda
Creation-Date: 20210920
Number: 014
File-URL: https://cris.maastrichtuniversity.nl/ws/files/72858255/RM21014.pdf
File-Format: application/pdf
File-Size: 640723
Handle: Repec:unm:umagsb:2021014
DOI: 10.26481/umagsb.2021014