A Generalization of Simultaneous Long–Short Stock Trading to PI Controllers

The main objective of this paper is to provide a generalization of the so-called Simultaneous Long–Short (SLS) stock-trading result in the feedback control literature. The significance of the SLS strategy is that it guarantees a “win” in expected value of profits. Whereas previous work involves use of static linear feedback to establish this robust positive expectation property of the gain–loss function, here we obtain the same result for the more general case of PI control. In this SLS setting, robustness is assured with respect to stock prices governed by a Geometric Brownian Motion whose drift and volatility parameters are unknown to the trader. This technical note also includes numerical simulations.