The composite iteration algorithm for finding efficient and financially fair risk-sharing rules
Pazdera,Jaroslav Schumacher,Hans Werker,Bas J.M.
Pazdera,Jaroslav
Schumacher,Hans
Werker,Bas J.M.
Abstract
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.
Description
Date
2017-10
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Volume Title
Publisher
Research Projects
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Keywords
risk sharing, fair division, Perron-Frobenius theory, eigenvector computation, collectives
Citation
Pazdera, J, Schumacher, H & Werker, B J M 2017, 'The composite iteration algorithm for finding efficient and financially fair risk-sharing rules', Journal of Mathematical Economics, vol. 72, pp. 122-133. https://doi.org/10.1016/j.jmateco.2017.07.008