  The main purpose of this paper is to discuss detailed the stochastic LQ
control problem with random coefficients where the linear system is a
multidimensional stochastic differential equation driven by a multidimensional
Brownian motion and a Poisson random martingale measure. In the paper, we will
establish the connections of the multidimensional Backward stochastic Riccati
equation with jumps (BSRDEJ in short form) to the stochastic LQ problem and to
the associated Hamilton systems. By the connections, we show the optimal
control have the state feedback representation. Moreover, we will show the
existence and uniqueness result of the multidimensional BSRDEJ for the case
where the generator is bounded linear dependence with respect to the unknowns
martingale term.

Optimization and Control;Systems and Control