Uniform value in Dynamic Programming

2008/03/19 by Jérôme Renault, Renault, Jérôme
Business, Management and Accounting · Economics, Econometrics and Finance · Mathematics · #Economic theories and models #FOS: Mathematics #Optimization and Control (math.OC) #Supply Chain and Inventory Management #math.OC

paper · pdf · doi:10.48550/arxiv.0803.2758

openalex publication_date 2008/03/19 · arxiv created 2009/04/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider dynamic programming problems with a large time horizon, and give sufficient conditions for the existence of the uniform value. As a consequence, we obtain an existence result when the state space is precompact, payoffs are uniformly continuous and the transition correspondence is non expansive. In the same spirit, we give an existence result for the limit value. We also apply our results to Markov decision processes and obtain a few generalizations of existing results.

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