| Issue |
ESAIM: COCV
Volume 26, 2020
|
|
|---|---|---|
| Article Number | 22 | |
| Number of page(s) | 18 | |
| DOI | https://doi.org/10.1051/cocv/2019071 | |
| Published online | 25 February 2020 | |
Optimal control on graphs: existence, uniqueness, and long-term behavior*
Université Paris 1 Panthéon-Sorbonne, Centre d’Economie de la Sorbonne,
106, Boulevard de l’Hôpital,
75013
Paris, France.
** Corresponding author: olivier.gueant@univ-paris1.fr
Received:
4
July
2019
Accepted:
20
November
2019
The literature on continuous-time stochastic optimal control seldom deals with the case of discrete state spaces. In this paper, we provide a general framework for the optimal control of continuous-time Markov chains on finite graphs. In particular, we provide results on the long-term behavior of value functions and optimal controls, along with results on the associated ergodic Hamilton-Jacobi equation.
Mathematics Subject Classification: 05C81 / 34E05 / 49L20 / 90C40 / 93E20
Key words: Optimal control / graphs / asymptotic analysis / Ergodic Hamilton-Jacobi equation
© The authors. Published by EDP Sciences, SMAI 2020
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