In this talk, we introduce pairs trading under a geometric Brownian motion. Pairs trading is about simultaneously trading a pair of stocks. A pairs trade is triggered when their prices diverge and consists of a short position of the strong stock and a long position of the weak one. Pairs trading bets on the reversal of their price strengths. Here, we study the optimal pairs-trading problem under general GBMs with cutting losses, the objective is to trade the pairs over time to maximize an overall return with a fixed transaction cost. Trading with cutting losses is important in practice to limit risk exposure due to unexpected events. In control theory, this is associated with a hard state constraint which is difficult to deal with. In the talk, the optimal policy is characterized by threshold curves obtained by solving the associated HJB equations. We provide sufficient conditions that guarantee the optimality of our trading rules. A numerical example is also provided to illustrate how to implement the results in practice.(This talk based on the joint paper in Automatica 115,2020 with Dr. Ruyi Liu and Prof. Qing Zhang)