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The starting point of this paper is the so-called Robust Positive Expectation(RPE) Theorem, a result which appears in literature in the context ofSimultaneous Long-Short stock trading. This theorem states that using acombination of two specially-constructed linear feedback trading controllers,one long and one short, the expected value of the resulting gain-loss functionis guaranteed to be robustly positive with respect to a large class ofstochastic processes for the stock price. The main result of this paper is ageneralization of this theorem. Whereas previous work applies to a singlestock, in this paper, we consider a pair of stocks. To this end, we make twoassumptions on their expected returns. The first assumption involves pricecorrelation between the two stocks and the second involves a bounded non-zeromomentum condition. With known uncertainty bounds on the parameters associatedwith these assumptions, our new version of the RPE Theorem provides necessaryand sufficient conditions on the positive feedback parameter K of thecontroller under which robust positive expectation is assured. We alsodemonstrate that our result generalizes the one existing for the single-stockcase. Finally, it is noted that our results also can be interpreted in thecontext of pairs trading.

A Generalization of the Robust Positive Expectation Theorem for Stock Trading via Feedback Control