Volume 25, 2019
|Number of page(s)||30|
|Published online||25 October 2019|
On the time discretization of stochastic optimal control problems: The dynamic programming approach*,**,***
Centre de Mathématiques Appliquées, Ecole Polytechnique, INRIA-Saclay, CNRS, Université Paris-Saclay,
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: firstname.lastname@example.org
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.
The first and third authors thank the support from project iCODE : “Large-scale systems and Smart grids: distributed decision making” and from the Gaspar Monge Program for Optimization and Operation Research (PGMO).
© EDP Sciences, SMAI 2019
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