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A detection problem with a monotone observation rate

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  • Ekström, Erik
  • Milazzo, Alessandro

Abstract

We study a quickest detection problem where the observation rate of the underlying process can be increased at any time for higher precision, but at an observation cost that grows linearly in the observation rate. This leads to a problem of combined control-and-stopping with incomplete information, with a two-dimensional sufficient statistic comprised of the current observation rate together with the conditional probability that disorder has already happened. The problem is shown to have a semi-explicit solution, where for some parameter values it is too costly to exert control at all, whereas for other parameter values the optimal strategy is to increase the observation rate in such a way that the sufficient statistic reflects at a certain boundary until the optimal stopping time. In both cases we fully characterise the optimal strategy with the help of appropriate smooth fit conditions.

Suggested Citation

  • Ekström, Erik & Milazzo, Alessandro, 2024. "A detection problem with a monotone observation rate," Stochastic Processes and their Applications, Elsevier, vol. 172(C).
    • Handle: RePEc:eee:spapps:v:172:y:2024:i:c:s0304414924000437
    DOI: 10.1016/j.spa.2024.104337
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    References listed on IDEAS

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    1. Bayraktar, Erhan & Dayanik, Savas & Karatzas, Ioannis, 2005. "The standard Poisson disorder problem revisited," Stochastic Processes and their Applications, Elsevier, vol. 115(9), pages 1437-1450, September.
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    3. Weijie Zhong, 2022. "Optimal Dynamic Information Acquisition," Econometrica, Econometric Society, vol. 90(4), pages 1537-1582, July.
    4. Tiziano De Angelis & Jhanvi Garg & Quan Zhou, 2022. "A quickest detection problem with false negatives," Papers 2210.01844, arXiv.org, revised Feb 2026.
    5. Savas Dayanik & Semih O. Sezer, 2016. "Sequential Sensor Installation for Wiener Disorder Detection," Mathematics of Operations Research, INFORMS, vol. 41(3), pages 827-850, August.
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    Cited by:

    1. Alessandro Milazzo, 2024. "On the Monotonicity of the Stopping Boundary for Time-Inhomogeneous Optimal Stopping Problems," Journal of Optimization Theory and Applications, Springer, vol. 203(1), pages 336-358, October.

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