Abstract
In this paper, we consider multistopping problems for finite discrete time sequences X1, …, Xn. m-stops are allowed and the aim is to maximize the expected value of the best of these m stops. The random variables are neither assumed to be independent not to be identically distributed. The basic assumption is convergence of a related imbedded point process to a continuous time Poisson process in the plane, which serves as a limiting model for the stopping problem. The optimal m-stopping curves for this limiting model are determined by differential equations of first order. A general approximation result is established which ensures convergence of the finite discrete time m-stopping problem to that in the limit model. This allows the construction of approximative solutions of the discrete time m-stopping problem. In detail, the case of i.i.d. sequences with discount and observation costs is discussed and explicit results are obtained.
Citation
Andreas Faller. Ludger Rüschendorf. "On approximative solutions of multistopping problems." Ann. Appl. Probab. 21 (5) 1965 - 1993, October 2011. https://doi.org/10.1214/10-AAP747
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