### Abstract

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

Pages (from-to) | 122-133 |

Journal | Journal of Mathematical Economics |

Volume | 72 |

DOIs | |

Publication status | Published - Oct 2017 |

### Fingerprint

### Keywords

- risk sharing
- fair division
- Perron-Frobenius theory
- eigenvector computation
- collectives

### Cite this

*Journal of Mathematical Economics*,

*72*, 122-133. https://doi.org/10.1016/j.jmateco.2017.07.008

}

*Journal of Mathematical Economics*, vol. 72, pp. 122-133. https://doi.org/10.1016/j.jmateco.2017.07.008

**The composite iteration algorithm for finding efficient and financially fair risk-sharing rules.** / Pazdera, Jaroslav; Schumacher, Hans; Werker, Bas.

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

TY - JOUR

T1 - The composite iteration algorithm for finding efficient and financially fair risk-sharing rules

AU - Pazdera, Jaroslav

AU - Schumacher, Hans

AU - Werker, Bas

PY - 2017/10

Y1 - 2017/10

N2 - We consider the problem of finding an efficient and fair ex-ante rule for division of an uncertain monetary outcome among a finite number of von Neumann–Morgenstern agents. Efficiency is understood here, as usual, in the sense of Pareto efficiency subject to the feasibility constraint. Fairness is defined as financial fairness with respect to a predetermined pricing functional. We show that efficient and financially fair allocation rules are in one-to-one correspondence with positive eigenvectors of a nonlinear homogeneous and monotone mapping associated to the risk sharing problem. We establish relevant properties of this mapping. On the basis of this, we obtain a proof of existence and uniqueness of solutions via nonlinear Perron–Frobenius theory, as well as a proof of global convergence of the natural iterative algorithm. We argue that this algorithm is computationally attractive, and discuss its rate of convergence.

AB - We consider the problem of finding an efficient and fair ex-ante rule for division of an uncertain monetary outcome among a finite number of von Neumann–Morgenstern agents. Efficiency is understood here, as usual, in the sense of Pareto efficiency subject to the feasibility constraint. Fairness is defined as financial fairness with respect to a predetermined pricing functional. We show that efficient and financially fair allocation rules are in one-to-one correspondence with positive eigenvectors of a nonlinear homogeneous and monotone mapping associated to the risk sharing problem. We establish relevant properties of this mapping. On the basis of this, we obtain a proof of existence and uniqueness of solutions via nonlinear Perron–Frobenius theory, as well as a proof of global convergence of the natural iterative algorithm. We argue that this algorithm is computationally attractive, and discuss its rate of convergence.

KW - risk sharing

KW - fair division

KW - Perron-Frobenius theory

KW - eigenvector computation

KW - collectives

U2 - 10.1016/j.jmateco.2017.07.008

DO - 10.1016/j.jmateco.2017.07.008

M3 - Article

VL - 72

SP - 122

EP - 133

JO - Journal of Mathematical Economics

JF - Journal of Mathematical Economics

SN - 0304-4068

ER -