| Abstract: |
| We study the problem of trading a mean-reverting price spread over a finite horizon with transaction costs and an unbounded number of trades. Modeling the price spread by the Ornstein-Uhlenbeck process, we formulate a coupled optimal stopping problems to determine the optimal timing to switch positions. We analyze the corresponding free-boundary system for the value functions. Our solution approach involves deriving a system of Volterra-type integral equations that uniquely characterize the boundaries associated with the optimal timing decisions. These integral equations are used to numerically compute the optimal boundaries. Numerical examples are provided to illustrate the optimal trading boundaries and examine their sensitivity with respect to model parameters. |
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