  We study several optimal stopping problems that arise from trading a
mean-reverting price spread over a finite horizon. Modeling the spread by the
Ornstein-Uhlenbeck process, we analyze three different trading strategies: (i)
the long-short strategy; (ii) the short-long strategy, and (iii) the chooser
strategy, i.e. the trader can enter into the spread by taking either long or
short position. In each of these cases, we solve an optimal double stopping
problem to determine the optimal timing for starting and subsequently closing
the position. We utilize the local time-space calculus of Peskir (2005a) and
derive the nonlinear integral equations of Volterra-type that uniquely char-
acterize the boundaries associated with the optimal timing decisions in all
three problems. These integral equations are used to numerically compute the
optimal boundaries.
