Necessary and Sufficient Conditions for Existence and Uniqueness of\n Recursive Utilities

2017/10/17 by Jaroslav Borovička, John Stachurski, Borovicka, Jaroslav +1
Decision Sciences · Economics, Econometrics and Finance · #Auction Theory and Applications #Economic theories and models #FOS: Economics and business #FOS: Mathematics #Game Theory and Voting Systems #General Economics (econ.GN) #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.1710.06526

openalex publication_date 2017/10/17 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We study existence, uniqueness and computability of solutions for a class of\ndiscrete time recursive utilities models. By combining two streams of the\nrecent literature on recursive preferences---one that analyzes principal\neigenvalues of valuation operators and another that exploits the theory of\nmonotone concave operators---we obtain conditions that are both necessary and\nsufficient for existence and uniqueness of solutions. We also show that the\nnatural iterative algorithm is convergent if and only if a solution exists.\nConsumption processes are allowed to be nonstationary.\n

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