The Annals of Applied Probability

On approximative solutions of multistopping problems

Andreas Faller and Ludger Rüschendorf

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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.

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Ann. Appl. Probab., Volume 21, Number 5 (2011), 1965-1993.

First available in Project Euclid: 25 October 2011

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Zentralblatt MATH identifier

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 62L15: Optimal stopping [See also 60G40, 91A60]

Optimal multiple stopping best choice problem extreme values Poisson process


Faller, Andreas; Rüschendorf, Ludger. On approximative solutions of multistopping problems. Ann. Appl. Probab. 21 (2011), no. 5, 1965--1993. doi:10.1214/10-AAP747.

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