A class of infinite-horizon stochastic delay optimal control problems and a viscosity solution to the associated HJB equation

Abstract

In this paper, we investigate a class of infinite-horizon optimal control problems for stochastic differential equations with delays for which the associated second order Hamilton−Jacobi−Bellman (HJB) equation is a nonlinear partial differential equation with delays. We propose a new concept for the viscosity solution including timetand identify the value function of the optimal control problems as a unique viscosity solution to the associated second order HJB equation.