Optimal pairs trading in theory and practice: A continuous-time approach with evidence from cross-market equities

This study derives a fully closed-form pairs trading strategy under a mean-reverting spread without imposing the restrictive assumption of a unit cointegrating vector. Modeling the spread as an Ornstein–Uhlenbeck process, we incorporate risk aversion directly into a utility-based framework and obtain analytic expressions for the optimal position sizes of each asset. The proposed strategy is applied to a broad cross-market equity sample spanning China, the United States, the United Kingdom, and major European markets, including France and Germany. After accounting for transaction costs, the strategy delivers robust and consistent profitability across regions. Notably, cross-listed pairs exhibit stronger and more persistent arbitrage opportunities than conventional cointegrated pairs within a single market, suggesting that informational and structural segmentation between markets generates exploitable mispricing. Overall, the framework provides a transparent and analytically tractable tool for implementing risk-adjusted statistical arbitrage in global equity markets.