### Abstract

Original language | English |
---|---|

Pages (from-to) | 383-409 |

Journal | Mathematical Methods of Operations Research |

Volume | 87 |

Issue number | 3 |

DOIs | |

Publication status | Published - Jun 2018 |

### Keywords

- Mutual liability problems
- Bankruptcy
- Monetary interrelationships in financial crises

### Cite this

*Mathematical Methods of Operations Research*,

*87*(3), 383-409. https://doi.org/10.1007/s00186-017-0621-1

}

*Mathematical Methods of Operations Research*, vol. 87, no. 3, pp. 383-409. https://doi.org/10.1007/s00186-017-0621-1

**On solving mutual liability problems.** / Schaarsberg, Mirjam Groote; Reijnierse, Hans; Borm, Peter.

Research output: Contribution to journal › Article › Scientific › peer-review

TY - JOUR

T1 - On solving mutual liability problems

AU - Schaarsberg, Mirjam Groote

AU - Reijnierse, Hans

AU - Borm, Peter

PY - 2018/6

Y1 - 2018/6

N2 - This paper introduces mutual liability problems, as a generalization of bankruptcy problems, where every agent not only owns a certain amount of cash money, but also has outstanding claims and debts towards the other agents. Assuming that the agents want to cash their claims, we will analyze mutual liability rules which prescribe how the total available amount of cash should be allocated among the agents. We in particular focus on bilateral φ -transfer schemes, which are based on a bankruptcy rule φ . Although in general a φ -transfer scheme need not be unique, we show that the resulting φ -transfer allocation is. This leads to the definition of φ -based mutual liability rules. For so called hierarchical mutual liability problems an alternative characterization of φ -based mutual liability rules is provided. Moreover it is shown that the axiomatic characterization of the Talmud rule on the basis of consistency can be extended to the corresponding mutual liability rule.

AB - This paper introduces mutual liability problems, as a generalization of bankruptcy problems, where every agent not only owns a certain amount of cash money, but also has outstanding claims and debts towards the other agents. Assuming that the agents want to cash their claims, we will analyze mutual liability rules which prescribe how the total available amount of cash should be allocated among the agents. We in particular focus on bilateral φ -transfer schemes, which are based on a bankruptcy rule φ . Although in general a φ -transfer scheme need not be unique, we show that the resulting φ -transfer allocation is. This leads to the definition of φ -based mutual liability rules. For so called hierarchical mutual liability problems an alternative characterization of φ -based mutual liability rules is provided. Moreover it is shown that the axiomatic characterization of the Talmud rule on the basis of consistency can be extended to the corresponding mutual liability rule.

KW - Mutual liability problems

KW - Bankruptcy

KW - Monetary interrelationships in financial crises

U2 - 10.1007/s00186-017-0621-1

DO - 10.1007/s00186-017-0621-1

M3 - Article

VL - 87

SP - 383

EP - 409

JO - Mathematical Methods of Operations Research

JF - Mathematical Methods of Operations Research

SN - 1432-2994

IS - 3

ER -