Optimal control of stochastic delay differential equations: Optimal feedback controls

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 HamiltonJacobi-Bellman equations. We show how to use the partial C1,alpha-regularity of the value function established in [16] 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 economic application of our results to stochastic optimal advertising problems. (c) 2024 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).