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
Date Written: August 6, 2017
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: Suggested Citation