Robert A. Becker, Juan Pablo Rincón-Zapatero, Recursive utility for Thompson aggregators: Uniqueness via concave operator theory and iterative approximations, Vol. 2025 (2025), Article ID 43, pp. 1-39

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DOI: 10.23952/cot.2025.43

Received May 26, 2024; Accepted October 28, 2024; Published online September 22, 2025

Abstract. An alternative proof of the uniqueness theorem for recursive utility specified by a Thompson aggregator is available by verifying the Koopmans operator is a $u_{0}$ –concave operator. The Koopmans operator’s unique fixed point is a recursive utility. Uniqueness holds only on the interior of the commodity space’s positive cone. Consideration of $r$ -concave operators also yields a unique fixed point. An a posteriori error bound relates the norm difference between successive approximations of the fixed point and the fixed point.

How to Cite this Article:
R.A. Becker, J.P. Rincón-Zapatero, Recursive utility for Thompson aggregators: Uniqueness via concave operator theory and iterative approximations, Commun. Optim. Theory 2025 (2025) 43.