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arXiv · 2309.05029

Optimal control of stochastic delay differential equations: Optimal feedback controls

Filippo de Feo·Andrzej Święch
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Abstract

In this manuscript, we study optimal control problems for stochastic delay differential equations using the dynamic programming approach in Hilbert spaces via viscosity solutions of the associated Hamilton-Jacobi-Bellman equations. We show how to use the partial $C^{1,\alpha}$-regularity of the value function established in \cite{defeo_federico_swiech} to obtain optimal feedback controls. The main result of the paper is a verification theorem which provides a sufficient condition for optimality using the value function. We then discuss its applicability to the construction of optimal feedback controls. We provide an application to stochastic optimal advertising problems.

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Filippo de Feo, Andrzej Święch. 2023-09-10. Optimal control of stochastic delay differential equations: Optimal feedback controls. https://arxiv.org/abs/2309.05029

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