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The secretary problem for a random walk

Author

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  • Hlynka, M.
  • Sheahan, J. N.

Abstract

The secretary problem for a random walk is described. A particle has equal probabilities of moving j steps up or j steps down. The optimal strategy of picking the maximum height in n steps without the opportunity of recall is found. The best strategy is shown to be exactly the same as the naive strategy of choosing the first element of the sequence. The theory is extended to symmetric continuous distributions.

Suggested Citation

  • Hlynka, M. & Sheahan, J. N., 1988. "The secretary problem for a random walk," Stochastic Processes and their Applications, Elsevier, vol. 28(2), pages 317-325, June.
    • Handle: RePEc:eee:spapps:v:28:y:1988:i:2:p:317-325
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    Cited by:

    1. Chun, Young Hak, 1997. "Rank-based selection strategies for the random walk process," European Journal of Operational Research, Elsevier, vol. 96(2), pages 417-427, January.
    2. Hak Chun, Young, 1996. "Selecting the best choice in the weighted secretary problem," European Journal of Operational Research, Elsevier, vol. 92(1), pages 135-147, July.
    3. Pieter C. Allaart, 2009. "A general "bang-bang" principle for predicting the maximum of a random walk," Papers 0910.0545, arXiv.org.

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