On performance limits of feedback control-based stock trading strategies

On Performance Limits of Feedback Control-Based Stock Trading Strategies B. Ross Barmish Abstract-The starting point for this paper is the control theoretic paradigm for stock trading developed in [1]. Within this framework, a so-called idealized market is characterized by continuous trading and smooth stock price variations. Subsequently, a feedback controller processes the stock price history p(t) to determine the current level of investment I(t). In this idealized setting, we show that that feedback control laws exist which guarantee a profit for all admissible price variations. This first result is only viewed as a benchmark because the controller which achieves this trading profit relies on price signal differentiation which is undesirable. Subsequently, the paper concentrates on more practical differentiator-free controller dynamics. For the simple case of a static linear feedback on the cumulative trading profit or loss g(t), surprisingly, it turns out that a profit is still guaranteed. The final part of the paper involves numerical simulation using historical price; we study the extent to which the idealized market results carry over to real markets.