## 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.

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.

Original language | English |
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Publisher | Institute of Economics, Centre for Economic and Regional Studies |

Number of pages | 32 |

Publication status | Published - 2021 |

### Publication series

Series | KRTK-KTI Working Papers |
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Number | 34 |

Volume | 2021 |

## JEL classifications

- c71 - Cooperative Games
- g10 - General Financial Markets: General (includes Measurement and Data)

## Keywords

- financial networks
- systemic risk
- bankruptcy rules
- fixed points