  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. This model is generalized 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, it is demonstrated that the problem is still
efficiently solvable. In addition, the problem that parameters of the price
difference process are never known exactly and are imprecisely estimated from
an observed finite sample is investigated (recalling that this problem is
critical for practice). It is shown how the imprecision affects the optimal
trading strategy by quantification of the loss caused by the imprecise estimate
compared to a theoretical trader knowing the parameters exactly. The main
results focus on the geometric and optimization-theoretic viewpoint of the
risk-bounded trading strategy and the imprecision resulting from the
statistical estimates.
