One Kind of Fully Coupled Linear Quadratic Stochastic Control Problem with Random Jumps

One kind of fully coupled linear quadratic stochastic control problem with random jumps is studied. The explicit form of the optimal control is obtained. The optimal control can be proved to be unique. One kind of generalized Riccati equation system is introduced and its solvability is discussed. The linear feedback regulator for the optimal control problem with random jumps is given by the solution of the generalized Riccati equation system.