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Spectral Conditions for Existence and Uniqueness of Recursive Utilities

Research paper by Jaroslav Borovicka, John Stachurski

Indexed on: 17 Oct '17Published on: 17 Oct '17Published in: arXiv - Quantitative Finance - Economics



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.