Uniqueness of clearing payment matrices in financial networks

Arbeitspapier

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, whichguarantees the existence of a greatest and a least clearing payment. Multiplicity ofclearing 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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: KRTK-KTI Working Papers ; No. KRTK-KTI WP - 2021/34

Classification and Topics

• Classification: Wirtschaft ; Cooperative Games ; General Financial Markets: General (includes Measurement and Data)
• Subject: Financial networks ; systemic risk ; bankruptcy rules ; fixed points

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Csóka, Péter ; Herings, Peter Jean-Jacques
• Event: Veröffentlichung
• (who): Hungarian Academy of Sciences, Institute of Economics, Centre for Economic and Regional Studies
• (where): Budapest
• (when): 2021

Further information

• Handle: http://hdl.handle.net/10419/256905
• Last update: 10.03.2025, 11:43 AM CET