We consider a stochastic optimal control problem governed by a stochastic differential equation with delay in the control. Using an existence and uniqueness result of a sufficiently regular mild solution of the associated Hamilton--Jacobi--Bellman equation (see the companion paper [F. Gozzi and F. Masiero, SIAM J. Control Optim., 55 (2017), pp. 2981--3012]), we solve the control problem by proving a verification theorem and the existence of optimal feedback controls
Gozzi, F., Masiero, F. (2017). Stochastic Optimal Control with Delay in the Control II: Verification Theorem and Optimal Feedbacks. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 55(5), 3013-3038 [10.1137/16M1073637].
Stochastic Optimal Control with Delay in the Control II: Verification Theorem and Optimal Feedbacks
Masiero, F.
2017
Abstract
We consider a stochastic optimal control problem governed by a stochastic differential equation with delay in the control. Using an existence and uniqueness result of a sufficiently regular mild solution of the associated Hamilton--Jacobi--Bellman equation (see the companion paper [F. Gozzi and F. Masiero, SIAM J. Control Optim., 55 (2017), pp. 2981--3012]), we solve the control problem by proving a verification theorem and the existence of optimal feedback controls
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