Abstract: In the continuous time finance model the stock price valiatility is deemed the Brownian motion. However in teh real world as the significant information occurs, a discontinuous jump will occur in the stock price. This paper extends the classical stochastic LQ control to the jump-diffusion model. With the jump-diffusion stochastic Riccati equation introduced, the optimal feedback control can be obtained. With its application in hedging strategy and the Mean-Variance model, we obtain the optimal bedging strategy and the optimal portfolio strategy.

Key words: stochastic Linear-Quadric control, jump-diffusion process, hedging, portfolio