Bertram’s pairs trading strategy with bounded risk

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 maximization expected profit per unit time. This model is generalized to form where riskiness profit, measured by its per-time-unit volatility, controlled (e.g. in case existence limits on strategies imposed regulatory bodies). The resulting need not convex. In spite this undesirable fact, it demonstrated that still efficiently solvable. addition, parameters are never known exactly and imprecisely estimated from observed finite sample investigated (recalling critical practice). It shown how imprecision affects quantification loss caused imprecise estimate compared theoretical trader knowing exactly. main results focus geometric optimization-theoretic viewpoint risk-bounded statistical estimates.