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Uniqueness of Clearing Payment Matrices in Financial Networks

Péter Csóka () and P. Jean-Jacques Herings ()

No 14, Research Memorandum from Maastricht University, Graduate School of Business and Economics (GSBE)

Abstract: 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, which guarantees the existence of a greatest and a least clearing payment. Multiplicity of clearing 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.

JEL-codes: C71 G10 (search for similar items in EconPapers)
Date: 2021-09-20
New Economics Papers: this item is included in nep-isf, nep-net and nep-ore
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Persistent link: https://EconPapers.repec.org/RePEc:unm:umagsb:2021014

DOI: 10.26481/umagsb.2021014

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