Articlegreen2017

Stochastic Optimal Control with Delay in the Control II: Verification Theorem and Optimal Feedbacks

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28 citations0/0 files storedSIAM Journal on Control and Optimization

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Stochastic processes and financial applications Nonlinear Differential Equations Analysis Stability and Controllability of Differential Equations

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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References

2002Nonlinear Kolmogorov equations in infinite dimensional spaces: the backward stochastic differential equations approach and applications to optimal control 2009On Controlled Linear Diffusions with Delay in a Model of Optimal Advertising under Uncertainty with Memory Effects 2003When Are HJB-Equations in Stochastic Control of Delay Systems Finite Dimensional?1991Second-Order Hamilton–Jacobi Equations in Infinite Dimensions 2008Impulse control problem on finite horizon with execution delay 2017Stochastic Optimal Control with Delay in the Control I: Solving the HJB Equation through Partial Smoothing 2005Generalized Directional Gradients, Backward Stochastic Differential Equations and Mild Solutions of Semilinear Parabolic Equations 2008Stochastic Optimal Control Problems and Parabolic Equations in Banach Spaces

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