Linear Quadratic Control Problem Of Stochastic System With Jumps

In this paper,we consider the linear quadratic control problem of stochastic system with jumps.The control system is a linear stochastic differential equation with jumps and the cost function is quadratic.We discuss the maximum principle,Riccati equation and dynamic programming principle of the linear quadratic control problem with jumps.Firstly,we use the maximum principle and dynamic programming principle to derive the Riccati equation associated with this problem,respectively.Then we combine the completion of squares technique to obtain a state feedback representation of the optimal control for the stochastic linear quadratic control problem with jumps via the Riccati equation.