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Computational results for a stopping rule problem on averages

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  • G. L. Nemhauser
  • D. A. Pierce

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.

Suggested Citation

  • G. L. Nemhauser & D. A. Pierce, 1968. "Computational results for a stopping rule problem on averages," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 15(4), pages 567-578, December.
    • Handle: RePEc:wly:navlog:v:15:y:1968:i:4:p:567-578
    DOI: 10.1002/nav.3800150409
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