Computational results for a stopping rule problem on averages

G. L. Nemhauser and D. A. Pierce

Naval Research Logistics Quarterly, 1968, vol. 15, issue 4, 567-578

Abstract: Suppose x1, x2, … are independently distributed random variables with Pr (xi = 1) = Pr(xi = −1) = 1/2, and let sn = xi. The random variables are observed sequentially and after n observations, n = 1, 2, …, we can either stop and receive a return of sn/n or observe another random variable. Chow and Robbins [3] have shown that there exists a stopping rule that maximizes the expected return over all rules for which the probability of stopping is one. The optimum policy is characterized by a sequence of non‐decreasing integers kn, such that sn ≥ kn implies a stop. Calculations based upon lower bounds on kn developed by Chow and Robbins and upper bounds developed herein yield a substantial part of the optimal policy.

Date: 1968
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Persistent link: https://EconPapers.repec.org/RePEc:wly:navlog:v:15:y:1968:i:4:p:567-578

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