Necessary and Sufficient Conditions for Existence and Uniqueness of Recursive Utilities
Economics
2019-04-24 v4 Optimization and Control
Abstract
We study existence, uniqueness and computability 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 of solutions. We also show that the natural iterative algorithm is convergent if and only if a solution exists. Consumption processes are allowed to be nonstationary.
Keywords
Cite
@article{arxiv.1710.06526,
title = {Necessary and Sufficient Conditions for Existence and Uniqueness of Recursive Utilities},
author = {Jaroslav Borovicka and John Stachurski},
journal= {arXiv preprint arXiv:1710.06526},
year = {2019}
}