NATIONAL BUREAU OF ECONOMIC RESEARCH
NATIONAL BUREAU OF ECONOMIC RESEARCH
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John Stachurski

Research School of Economics
HW Arndt Building 25A
College of Business and Economics
The Australian National University
ACT 2601 Australia

E-Mail: john.stachurski@anu.edu.au
Institutional Affiliation: Australian National University

NBER Working Papers and Publications

December 2017Necessary and Sufficient Conditions for Existence and Uniqueness of Recursive Utilities
with Jaroslav Borovička: w24162
We study existence, uniqueness and stability of solutions for a class of discrete time recursive utilities models. By combining two streams of the recent literature on recursive preferences - one that analyzes principal eigenvalues of valuation operators and another that exploits the theory of monotone concave operators - we obtain conditions that are both necessary and sufficient for existence and uniqueness. We also show that the natural iterative algorithm is convergent if and only if a solution exists. Consumption processes are allowed to be nonstationary.
 
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