The Annals of Probability

Approximations to Optimal Stopping Rules for Exponential Random Variables

Adam T. Martinsek

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Probab., Volume 12, Number 3 (1984), 876-881.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176993236

Digital Object Identifier
doi:10.1214/aop/1176993236

Mathematical Reviews number (MathSciNet)
MR744242

Zentralblatt MATH identifier
0544.62076

JSTOR
links.jstor.org

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

Keywords
Optimal stopping uniform integrability last times

Citation

Martinsek, Adam T. Approximations to Optimal Stopping Rules for Exponential Random Variables. Ann. Probab. 12 (1984), no. 3, 876--881. doi:10.1214/aop/1176993236. https://projecteuclid.org/euclid.aop/1176993236


Export citation