Issue |
ESAIM: COCV
Volume 25, 2019
|
|
---|---|---|
Article Number | 63 | |
Number of page(s) | 30 | |
DOI | https://doi.org/10.1051/cocv/2018045 | |
Published online | 25 October 2019 |
On the time discretization of stochastic optimal control problems: The dynamic programming approach*,**,***
1
Centre de Mathématiques Appliquées, Ecole Polytechnique, INRIA-Saclay, CNRS, Université Paris-Saclay,
91128
Palaiseau, France.
2
CIFASIS - Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas - CONICET - UNR,
S2000EZP
Rosario, Argentina.
3
Institut de recherche XLIM-DMI, UMR-CNRS 7252, Faculté des sciences et techniques, Université de Limoges,
87060
Limoges, France.
**** Corresponding author: frederic.bonnans@inria.fr
Received:
19
April
2017
Accepted:
14
August
2018
In this work, we consider the time discretization of stochastic optimal control problems. Under general assumptions on the data, we prove the convergence of the value functions associated with the discrete time problems to the value function of the original problem. Moreover, we prove that any sequence of optimal solutions of discrete problems is minimizing for the continuous one. As a consequence of the Dynamic Programming Principle for the discrete problems, the minimizing sequence can be taken in discrete time feedback form.
Mathematics Subject Classification: 93E20 / 49L20 / 90C15 / 93C55
Key words: Stochastic Control / Discrete Time Systems / Dynamic Programming Principle / Value Function / Feedback Control
The first and second author thank the Laboratoire de Finance des Marchés de l’Energie for its support.
© EDP Sciences, SMAI 2019
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.