## Centralized clearing mechanisms: A programming approach

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)

doi: 10.22574/jmid.2022.12.002

### Abstract:

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.