  Finding Bertram's optimal trading strategy for a pair of cointegrated assets
following the Ornstein-Uhlenbeck price difference process can be formulated as
an unconstrained convex optimization problem for maximization of expected
profit per unit of time. We generalize this model to the form where the
riskiness of profit, measured by its per-time-unit volatility, is controlled
(e.g. in case of existence of limits on riskiness of trading strategies imposed
by regulatory bodies). The resulting optimization problem need not be convex.
In spite of this undesirable fact, we demonstrate that it is still efficiently
solvable. We also investigate the problem critical for practice that parameters
of the price difference process are never known exactly and are imprecisely
estimated from an observed finite sample. We show how the imprecision affects
the optimal trading strategy and quantify the loss caused by the imprecise
estimate compared to a theoretical trader knowing the parameters exactly.
