Necessary and Sufficient Conditions for Risk-Sensitive Optimal Control with Delay

Abstract

In this paper, we consider risk-sensitive optimal control for stochastic differential delayed equations. We obtain necessary and sufficient conditions for optimality in terms of the coupled anticipated backward stochastic differential equations via the logarithmic transformation of the associated risk-neutral problem. As an application, we consider the risk-sensitive linear-quadratic optimal control with delay, for which we obtain an explicit optimal solution.