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On the Existence of Recursive Utility

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  • Asen Kochov

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.

Suggested Citation

  • Asen Kochov, 2025. "On the Existence of Recursive Utility," CESifo Working Paper Series 12091, CESifo.
    • Handle: RePEc:ces:ceswps:_12091
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    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • D9 - Microeconomics - - Micro-Based Behavioral Economics

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