Necessary and Sufficient Conditions for Existence and Uniqueness of Recursive Utilities

Abstract

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.