On the time discretization of stochastic optimal control problems: the dynamic programming approach

Abstract : 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.
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https://hal.inria.fr/hal-01474285
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Joseph Frédéric Bonnans, Justina Gianatti, Francisco Silva. On the time discretization of stochastic optimal control problems: the dynamic programming approach. ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, In press. ⟨hal-01474285v2⟩

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