DOI link to open access article:
Centralized clearing mechanisms: A programming approach
Péter Csóka, P. Jean-Jacques Herings
Journal of Mechanism and Institution Design
Volume 7, issue 1, pages 45-69 (December 2022)
We consider financial networks where agents are linked to each other by financial contracts. A centralized clearing mechanism collects the initial endowments, the liabilities and the division rules of the agents and determines the payments to be made. A division rule specifies how the assets of the agents should be rationed. Since payments made depend on payments received, we are looking for solutions to a system of equations. The set of solutions is known to have a lattice structure, leading to the existence of a least and a greatest clearing payment matrix. Previous research has shown how decentralized clearing selects the least clearing payment matrix. We present a centralized approach towards clearing in order to select the greatest clearing payment matrix. To do so, we formulate the determination of the greatest clearing payment matrix as a programming problem. When agents use proportional division rules, this programming problem corresponds to a linear programming problem. We show that for other common division rules, it can be written as an integer linear programming problem.
Keywords: Systemic risk, bankruptcy rules, integer linear programming.
JEL Classification Numbers: C71, G10.