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Pairs trading is a typical example of a convergence trading strategy. Investors buy relatively under-priced assets simultaneously, and sell relatively over-priced assets to exploit temporary mispricing. This study examines optimal pairs trading strategies under symmetric and non-symmetric trading constraints. Under the assumption that the price spread of a pair of correlated securities follows a mean-reverting Ornstein-Uhlenbeck(OU) process, analytical trading strategies are obtained under a mean-variance(MV) framework. Model estimation and empirical studies on trading strategies have been conducted using data on pairs of stocks and futures traded on China’s securities market. These results indicate that pairs trading strategies have fairly good performance.

We consider portfolio optimization problems with expected loss constraints under the physical measure P and the risk neutral measure Q, respectively. Using Merton's portfolio as a benchmark portfolio, the optimal terminal wealth of the Q-risk constraint problem can be easily replicated with the standard delta hedging strategy. Motivated by this, we consider the Q-strategy fulfilling the P-risk constraint and compare its solution with the true optimal solution of the P-risk constraint problem. We show the existence and uniqueness of the optimal solution to the Q-strategy fulfilling the P-risk constraint, and provide a tractable evaluation method. The Q-strategy fulfilling the P-risk constraint is not only easier to implement with standard forwards and puts on a benchmark portfolio than the P-risk constraint problem, but also easier to solve than either of the Q-or P-risk constraint problem. The numerical test shows that the difference of the values of the two strategies (the Q-strategy fulfilling the P-risk constraint and the optimal strategy solving the P-risk constraint problem) is reasonably small.