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Optimal mean-reverting spread trading: nonlinear integral equation approach. (English) Zbl 1388.91145

Summary: 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 G. Peskir [J. Theor. Probab. 18, No. 3, 499–535 (2005; Zbl 1085.60033)] and derive the nonlinear integral equations of Volterra-type that uniquely characterize the boundaries associated with the optimal timing decisions in all three problems. These integral equations are used to numerically compute the optimal boundaries.

MSC:

91G80 Financial applications of other theories
60G40 Stopping times; optimal stopping problems; gambling theory
60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
45D05 Volterra integral equations

Citations:

Zbl 1085.60033
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References:

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