  The take-off point for this paper is the Simultaneous Long-Short (SLS)
control class, which is known to guarantee the so-called robust positive
expectation (RPE) property. That is, the expected cumulative trading gain-loss
function is guaranteed to be positive for a broad class of stock price
processes. This fact attracts many new extensions and ramifications to the SLS
theory. However, it is arguable that "systematic" way to select an optimal
decision variable that is robust in the RPE sense is still unresolved. To this
end, we propose a modified SLS control structure, which we call the {double
linear feedback control scheme}, that allows us to solve the issue above for
stock price processes involving independent returns. In this paper, we go
beyond the existing literature by not only deriving explicit expressions for
the expected value and variance of cumulative gain-loss function but also
proving various theoretical results regarding {robust positive expected growth}
and {monotonicity}. Subsequently, we propose a new {robust optimal gain
selection problem} that seeks a solution maximizing the expected trading
gain-loss subject to the prespecified standard deviation {and} RPE constraints.
Under some mild conditions, we show that the optimal solution exists and is
unique. Moreover, a simple graphical approach that allows one to systematically
determine the optimal solution is also proposed. Finally, some numerical and
empirical studies using historical price data are also provided to support our
theory.
