Stochastic Optimal Control with Delay in the Control II: Verification Theorem and Optimal Feedbacks
Abstract
We consider a stochastic optimal control problem governed by a stochastic differential equation with delay in the control. Using a result of existence and uniqueness of a sufficiently regular mild solution of the associated Hamilton-Jacobi-Bellman (HJB) equation, see the companion paper "Stochastic Optimal Control with Delay in the Control I: solving the HJB equation through partial smoothing ", we solve the control problem by proving a Verification Theorem and the existence of optimal feedback controls.
Cite
@article{arxiv.1607.06508,
title = {Stochastic Optimal Control with Delay in the Control II: Verification Theorem and Optimal Feedbacks},
author = {F. Gozzi and F. Masiero},
journal= {arXiv preprint arXiv:1607.06508},
year = {2021}
}
Comments
This is substantially the second part of the paper arXiv:1506.06013. We have submitted thsi new version where, towards the previous one, we notice that the current cost of the control problem cannot depend on the state. All the changes towards the published version are written in red color