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August, 1984 Approximations to Optimal Stopping Rules for Exponential Random Variables
Adam T. Martinsek
Ann. Probab. 12(3): 876-881 (August, 1984). DOI: 10.1214/aop/1176993236


For $X_1, X_2, \cdots$ i.i.d. with finite mean and $Y_n = \max(X_1, \cdots, X_n) - cn, c$ positive, a number of authors have considered the problem of determining an optimal stopping rule for the reward sequence $Y_n$. The optimal stopping rule can be given explicitly in this case; however, in general its use requires complete knowledge of the distribution of the $X_i$. This paper examines the problem of approximating the optimal expected reward when only partial information about the distribution is available. Specifically, if the $X_i$ are known to be exponentially distributed with unknown mean, stopping rules designed to approximate the optimal rule (which can be used only when the mean is known) are proposed. Under certain conditions the difference between the expected reward using the proposed stopping rules and the optimal expected reward vanishes as $c$ approaches zero.


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Adam T. Martinsek. "Approximations to Optimal Stopping Rules for Exponential Random Variables." Ann. Probab. 12 (3) 876 - 881, August, 1984.


Published: August, 1984
First available in Project Euclid: 19 April 2007

zbMATH: 0544.62076
MathSciNet: MR744242
Digital Object Identifier: 10.1214/aop/1176993236

Primary: 62L15
Secondary: 60G40

Keywords: last times , Optimal stopping , uniform integrability

Rights: Copyright © 1984 Institute of Mathematical Statistics


Vol.12 • No. 3 • August, 1984
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