General mean-field stochastic linear quadratic control problem driven by L\'evy processes with random coefficients

Abstract

This paper studies a stochastic mean-field linear-quadratic optimal control problem with random coefficients. The state equation is a general linear stochastic differential equation with mean-field terms $\EE X(t)$ and $\EE u(t)$ of the state and the control processes and is driven by a Brownian motion and a Poisson random measure. By the coupled system of Riccati equations, an explicit expressions for the optimal state feedback control is obtained. As a by-product, the non-homogeneous stochastic linear-quadratic control problem with random coefficients and L\'evy driving noises is also studied.