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The standard Poisson disorder problem revisited

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  • Bayraktar, Erhan
  • Dayanik, Savas
  • Karatzas, Ioannis

Abstract

A change in the arrival rate of a Poisson process sometimes necessitates immediate action. If the change time is unobservable, then the design of online change detection procedures becomes important and is known as the Poisson disorder problem. Formulated and partially solved by Davis [Banach Center Publ., 1 (1976) 65-72], the standard Poisson problem addresses the tradeoff between false alarms and detection delay costs in the most useful way for applications. In this paper we solve the standard problem completely and describe efficient numerical methods to calculate the policy parameters.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:115:y:2005:i:9:p:1437-1450
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    Citations

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    Cited by:

    1. Buonaguidi, B., 2022. "The disorder problem for diffusion processes with the ϵ-linear and expected total miss criteria," Statistics & Probability Letters, Elsevier, vol. 189(C).
    2. Gapeev, Pavel V., 2020. "On the problems of sequential statistical inference for Wiener processes with delayed observations," LSE Research Online Documents on Economics 104072, London School of Economics and Political Science, LSE Library.
    3. S. Cawston & L. Vostrikova, 2010. "$F$-divergence minimal equivalent martingale measures and optimal portfolios for exponential Levy models with a change-point," Papers 1004.3525, arXiv.org, revised Jun 2011.
    4. Erhan Bayraktar & H. Poor, 2008. "Optimal time to change premiums," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 68(1), pages 125-158, August.
    5. Omar Besbes & Assaf Zeevi, 2011. "On the Minimax Complexity of Pricing in a Changing Environment," Operations Research, INFORMS, vol. 59(1), pages 66-79, February.
    6. Savas Dayanik & Semih O Sezer, 2023. "Model Misspecification in Discrete Time Bayesian Online Change Detection," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-27, March.
    7. Ali Devin Sezer & Çağrı Haksöz, 2012. "Optimal Decision Rules for Product Recalls," Mathematics of Operations Research, INFORMS, vol. 37(3), pages 399-418, August.
    8. Savas Dayanik, 2010. "Wiener Disorder Problem with Observations at Fixed Discrete Time Epochs," Mathematics of Operations Research, INFORMS, vol. 35(4), pages 756-785, November.
    9. Krawiec, Michał & Palmowski, Zbigniew & Płociniczak, Łukasz, 2018. "Quickest drift change detection in Lévy-type force of mortality model," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 432-450.
    10. Christensen, Sören & Irle, Albrecht, 2020. "The monotone case approach for the solution of certain multidimensional optimal stopping problems," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 1972-1993.
    11. 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.
    12. Pavel V. Gapeev, 2020. "On the problems of sequential statistical inference for Wiener processes with delayed observations," Statistical Papers, Springer, vol. 61(4), pages 1529-1544, August.
    13. Savas Dayanik & Semih Onur Sezer, 2006. "Compound Poisson Disorder Problem," Mathematics of Operations Research, INFORMS, vol. 31(4), pages 649-672, November.
    14. Pavel V. Gapeev, 2016. "Bayesian Switching Multiple Disorder Problems," Mathematics of Operations Research, INFORMS, vol. 41(3), pages 1108-1124, August.
    15. Ekström, Erik & Milazzo, Alessandro, 2024. "A detection problem with a monotone observation rate," Stochastic Processes and their Applications, Elsevier, vol. 172(C).
    16. 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.

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