Centralized clearing mechanisms: A programming approach

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.