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Optimal detection of a hidden target: The median rule


  • Peskir, Goran


We show that in the absence of any information about the ‘hidden’ target in terms of the observed sample path, and irrespectively of the distribution law of the observed process, the ‘median’ rule is optimal in both the space domain and the time domain. While the fact that the median rule minimises the spatial expectation can be seen as a direct extension of the well-known median characterisation dating back to Boscovich, the fact that this also holds for the temporal expectation seems to have stayed unnoticed until now. Building on this observation we derive new classes of median/quantile rules having a dynamic character.

Suggested Citation

  • Peskir, Goran, 2012. "Optimal detection of a hidden target: The median rule," Stochastic Processes and their Applications, Elsevier, vol. 122(5), pages 2249-2263.
  • Handle: RePEc:eee:spapps:v:122:y:2012:i:5:p:2249-2263
    DOI: 10.1016/

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    References listed on IDEAS

    1. Cohen, Albert, 2010. "Examples of optimal prediction in the infinite horizon case," Statistics & Probability Letters, Elsevier, vol. 80(11-12), pages 950-957, June.
    2. Jacques du Toit & Goran Peskir, 2009. "Selling a stock at the ultimate maximum," Papers 0908.1014,
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    Cited by:

    1. Gapeev, Pavel V. & Rodosthenous, Neofytos, 2016. "Perpetual American options in diffusion-type models with running maxima and drawdowns," Stochastic Processes and their Applications, Elsevier, vol. 126(7), pages 2038-2061.


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