Contents 1. Introduction
This paper is one in a series of papers studying linear-quadratic (LQ) control problems. In view of applications, LQ problems are useful tools in numerous areas, especially in modern engineering and applied mathematics. Recently, stochastic system in LQ problems became more complex and interesting, which provided us more realistic models in practices. Among various cases, some researchers paid much attention on delay systems, in which, the state depended not only on current time but also past time. For example, Chen and Wu [1] studied a LQ problem with delay, in that system, the state depended on past time but not the control; and in the further work, Chen, Wu and Yu [2] studied more general case with delay, they gave the feedback form of optimal control by the corresponding stochastic Riccati equation. Moreover, some researchers also focused on jump diffusion processes, such as Tang and Wu [7], they were concerned with the linear stochastic system with Lévy processes; and Zhu [8] investigated asymptotic stability in the pth moment for stochastic differential equations with Lévy processes. Except for the above reserch, Li and Wu [4] obtained the maximum principle for anticipated recursive stochastic optimal control problem with delay and Lévy processes. However, to our best knowledge, there are few work study stochastic LQ problem with delay and Lévy processes.
