On Stock Trading Via Feedback Control When Underlying Stock Returns Are Discontinuous

Trading rules based on feedback laws have recently attracted significant attention in the control community. One of the main results in this area states that the gain obtained by so-called simultaneously long short strategies has positive expectation for price processes governed by geometric Brownian motion. This technical note shows that this result extends to Merton's jump diffusion model. Particularly, we show that the expected total profit is invariant to the jumps and so still positive.