  Control of drawdown, that is, the control of the drops in wealth over time
from peaks to subsequent lows, is of great concern from a risk management
perspective. With this motivation in mind, the focal point of this paper is to
address the drawdown issue in a stock trading context. Although our analysis
can be carried out without reference to control theory, to make the work
accessible to this community, we use the language of feedback systems. The
takeoff point for the results to follow, which we call the Drawdown Modulation
Lemma, characterizes any investment which guarantees that the percentage
drawdown is no greater than a prespecified level with probability one. With the
aid of this lemma, we introduce a new scheme which we call the
drawdown-modulated feedback control. To illustrate the power of the theory, we
consider a drawdown-constrained version of the well-known Kelly Optimization
Problem which involves maximizing the expected logarithmic growth of the
trader's account value. As the drawdown parameter dmax in our new formulation
tends to one, we recover existing results as a special case. This new theory
leads to an optimal investment strategy whose application is illustrated via an
example with historical stock-price data.
