Unbounded Markov dynamic programming with weighted supremum norm Perov contractions

Alexis Akira Toda

Economic Theory Bulletin, 2024, vol. 12, issue 2, No 2, 156 pages

Abstract: Abstract This paper shows the usefulness of the Perov contraction theorem, which is a generalization of the classical Banach contraction theorem, for solving Markov dynamic programming problems. When the reward function is unbounded, combining an appropriate weighted supremum norm with the Perov contraction theorem yields a unique fixed point of the Bellman operator under weaker conditions than existing approaches. An application to the optimal savings problem shows that the average growth rate condition derived from the spectral radius of a certain nonnegative matrix is sufficient and almost necessary for obtaining a solution.

Keywords: Dynamic programming; Gelfand formula; Optimal savings; Perov contraction; Spectral radius; Weighted supremum norm (search for similar items in EconPapers)
JEL-codes: C61 C65 D14 E21 (search for similar items in EconPapers)
Date: 2024
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Working Paper: Unbounded Markov Dynamic Programming with Weighted Supremum Norm Perov Contractions (2023)
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DOI: 10.1007/s40505-024-00267-9

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