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Finite Horizon Sequential Detection with Exponential Penalty for the Delay

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  • Bruno Buonaguidi

    (Università Cattolica)

Abstract

The problem of the sequential detection of a change in the drift of a one-dimensional Brownian motion is considered under the assumptions that the detection must eventually occur within a finite horizon and the detection delay is exponentially penalized. Our results extend those obtained by Beibel for the infinite horizon sequential detection with exponential penalty (Ann Stat 28:1696–1701, 2000) and by Gapeev and Peskir for the finite horizon sequential detection with linear penalty (Stoch Process Appl 116:1770–1791, 2006).

Suggested Citation

  • Bruno Buonaguidi, 2023. "Finite Horizon Sequential Detection with Exponential Penalty for the Delay," Journal of Optimization Theory and Applications, Springer, vol. 198(1), pages 224-238, July.
    • Handle: RePEc:spr:joptap:v:198:y:2023:i:1:d:10.1007_s10957-023-02239-8
    DOI: 10.1007/s10957-023-02239-8
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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.
    2. Savas Dayanik & Semih Onur Sezer, 2006. "Compound Poisson Disorder Problem," Mathematics of Operations Research, INFORMS, vol. 31(4), pages 649-672, November.
    3. Goran Peskir, 2005. "A Change-of-Variable Formula with Local Time on Curves," Journal of Theoretical Probability, Springer, vol. 18(3), pages 499-535, July.
    4. Erhan Bayraktar & Savas Dayanik, 2006. "Poisson Disorder Problem with Exponential Penalty for Delay," Mathematics of Operations Research, INFORMS, vol. 31(2), pages 217-233, May.
    5. Gapeev, Pavel V., 2005. "The disorder problem for compound Poisson processes with exponential jumps," LSE Research Online Documents on Economics 3219, London School of Economics and Political Science, LSE Library.
    6. Stefan Gerhold, 2010. "The Hartman-Watson Distribution revisited: Asymptotics for Pricing Asian Options," Papers 1011.4830, arXiv.org, revised May 2011.
    7. Gapeev, P.V. & Peskir, G., 2006. "The Wiener disorder problem with finite horizon," Stochastic Processes and their Applications, Elsevier, vol. 116(12), pages 1770-1791, December.
    8. Goran Peskir, 2005. "On The American Option Problem," Mathematical Finance, Wiley Blackwell, vol. 15(1), pages 169-181, January.
    9. Goran Peskir, 2005. "The Russian option: Finite horizon," Finance and Stochastics, Springer, vol. 9(2), pages 251-267, April.
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