NATIONAL BUREAU OF ECONOMIC RESEARCH
NATIONAL BUREAU OF ECONOMIC RESEARCH

Necessary and Sufficient Conditions for Existence and Uniqueness of Recursive Utilities

Jaroslav Borovička, John Stachurski

NBER Working Paper No. 24162
Issued in December 2017
NBER Program(s):Asset Pricing

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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Document Object Identifier (DOI): 10.3386/w24162

 
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