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On the Existence of Recursive Utility

Asen Kochov

No 12091, CESifo Working Paper Series from CESifo

Abstract: Recursive utility functions are often defined implicitly, as the solution of a functional equation known as the Koopmans recursion. As conditions for a unique solution can be demanding, a recent literature has tackled the problem of multiplicity, advocating that one focus attention on either the least or greatest solution, which possess a number of attractive properties. While a least solution can be shown to exist, I show that in the most general formulation of the problem, a greatest solution need not. The goal of the paper is to provide a sufficient condition for the existence of a greatest solution, which I term the weakly contractive property and which generalizes the usual contractive property sufficient for uniqueness.

Keywords: recursive utility; greatest and lowest fixed point; contractions (search for similar items in EconPapers)
JEL-codes: C6 D9 (search for similar items in EconPapers)
Date: 2025
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