## 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.

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.

Original language | English |
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Pages (from-to) | 45-69 |

Journal | Journal of Mechanism and Institution Design |

Volume | 7 |

Issue number | 1 |

DOIs | |

Publication status | Published - Dec 2022 |

## Keywords

- systemic risk
- bankruptcy rules
- integer linear programming