The Composite Iteration Algorithm for Finding Efficient and Financially Fair Risk-Sharing Rules

Journal of Mathematical Economics 72 (2017), 122-133

33 Pages Posted: 10 Feb 2014 Last revised: 18 May 2018

See all articles by Jaroslav Pazdera

Jaroslav Pazdera

Tilburg University - Center for Economic Research (CentER)

J. M. Schumacher

University of Amsterdam - Department of Quantitative Economics (KE)

Bas J. M. Werker

Tilburg University - Center for Economic Research (CentER)

Date Written: August 6, 2017

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.

Keywords: risk sharing, fair division, Perron-Frobenius theory, eigenvector computation, collectives

JEL Classification: D51, D52, D53, C62

Suggested Citation

Pazdera, Jaroslav and Schumacher, J.M. (Hans) and Werker, Bas J.M., The Composite Iteration Algorithm for Finding Efficient and Financially Fair Risk-Sharing Rules (August 6, 2017). Journal of Mathematical Economics 72 (2017), 122-133, Available at SSRN: https://ssrn.com/abstract=2393288 or http://dx.doi.org/10.2139/ssrn.2393288

Jaroslav Pazdera

Tilburg University - Center for Economic Research (CentER) ( email )

J.M. (Hans) Schumacher (Contact Author)

University of Amsterdam - Department of Quantitative Economics (KE) ( email )

Roetersstraat 11
Amsterdam, 1018 WB
Netherlands

Bas J.M. Werker

Tilburg University - Center for Economic Research (CentER) ( email )

Econometrics and Finance Group
5000 LE Tilburg
Netherlands

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