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.
Cite this article
Jérôme Renault, Uniform value in dynamic programming. J. Eur. Math. Soc. 13 (2011), no. 2, pp. 309–330DOI 10.4171/JEMS/254