The issue of making a decision several times and thereby earning a reward is the focus of this chapter. It considers the problem of multiply stopping a general one-dimensional diffusion process with fairly general reward functions at each decision time. A key aspect of the problem is the requirement that succeeding decisions be delayed by at least the length of time of a refraction period following a preceding decision. Using a conditioning argument, the multiple-stopping problem can be solved using an iterative set of single-stopping problems for which several solution approaches are known. The refraction period adds an interesting twist to the problem. A tractable solution method is developed for those processes whose distributions are known. This work is motivated by the recent paper [Carmona and Dayanik (Math Oper Res 32:446–460, 2008)].
CITATION STYLE
Stockbridge, R. H., & Zhu, C. (2012). A direct approach to the solution of optimal multiple-stopping problems. In Systems and Control: Foundations and Applications (pp. 283–299). Birkhauser. https://doi.org/10.1007/978-0-8176-8337-5_17
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