Uniqueness of Clearing Payment Matrices in Financial Networks

Péter Csóka and P. Jean-Jacques Herings

No 2134, CERS-IE WORKING PAPERS from Institute of Economics, Centre for Economic and Regional Studies

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.

Keywords: Financial networks; systemic risk; bankruptcy rules; fixed points. (search for similar items in EconPapers)
JEL-codes: C71 G10 (search for similar items in EconPapers)
Pages: 32 pages
Date: 2021-09
New Economics Papers: this item is included in nep-isf and nep-net
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Citations: View citations in EconPapers (3)

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Working Paper: Uniqueness of Clearing Payment Matrices in Financial Networks (2021)
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