Open Access
2012 Approximative solutions of best choice problems
Andreas Faller, Ludger Rüschendorf
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Electron. J. Probab. 17: 1-22 (2012). DOI: 10.1214/EJP.v17-2172


We consider the full information best choice problem from a sequence $X_1,\dots, X_n$ of independent random variables. Under the basic assumption of convergence of the corresponding imbedded point processes in the plane to a Poisson process we establish that the optimal choice problem can be approximated by the optimal choice problem in the limiting Poisson process. This allows to derive approximations to the optimal choice probability and also to determine approximatively optimal stopping times. An extension of this result to the best $m$-choice problem is also given.


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Andreas Faller. Ludger Rüschendorf. "Approximative solutions of best choice problems." Electron. J. Probab. 17 1 - 22, 2012.


Accepted: 17 July 2012; Published: 2012
First available in Project Euclid: 4 June 2016

zbMATH: 1252.60038
MathSciNet: MR2955046
Digital Object Identifier: 10.1214/EJP.v17-2172

Primary: 60G40
Secondary: 62L15

Keywords: best choice problem , Optimal stopping , Poisson process

Vol.17 • 2012
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