  The takeoff point of this paper is to generalize the existing stock trading
results for a class of affine feedback controller to include consideration of a
stop-loss order. Using the geometric Brownian motion as the underlying stock
price model, our main result is to provide a closed-form expression for the
cumulative distribution function for the trading profit or loss. In addition,
we show that the affine feedback controller with stop-loss order indeed
generalizes the result without stop order in the sense of distribution
function. Some simulations and illustrative examples are also provided as
supporting evidence of the theory. Moreover, we provide some technical results
aimed at addressing the issues about survivability, cash-financing
considerations, long-only property, and lower bound of the expected gain or
loss.
