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