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Quickest drift change detection in Lévy-type force of mortality model

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  • Krawiec, Michał
  • Palmowski, Zbigniew
  • Płociniczak, Łukasz

Abstract

In this paper, we give solution to the quickest drift change detection problem for a Lévy process consisting of both a continuous Gaussian part and a jump component. We consider here Bayesian framework with an exponential a priori distribution of the change point using an optimality criterion based on a probability of false alarm and an expected delay of the detection. Our approach is based on the optimal stopping theory and solving some boundary value problem. Paper is supplemented by an extensive numerical analysis related with the construction of the Generalized Shiryaev-Roberts statistics. In particular, we apply this method (after appropriate calibration) to analyse Polish life tables and to model the force of mortality in this population with a drift changing in time.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:338:y:2018:i:c:p:432-450
    DOI: 10.1016/j.amc.2018.06.038
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    References listed on IDEAS

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    1. Carter, Lawrence R. & Lee, Ronald D., 1992. "Modeling and forecasting US sex differentials in mortality," International Journal of Forecasting, Elsevier, vol. 8(3), pages 393-411, November.
    2. Aleksey S. Polunchenko & Alexander G. Tartakovsky, 2012. "State-of-the-Art in Sequential Change-Point Detection," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 649-684, September.
    3. 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.
    4. Savas Dayanik & Semih Onur Sezer, 2006. "Compound Poisson Disorder Problem," Mathematics of Operations Research, INFORMS, vol. 31(4), pages 649-672, November.
    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.
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    Cited by:

    1. Al Masry, Zeina & Rabehasaina, Landy & Verdier, Ghislain, 2022. "Change-level detection for Lévy subordinators," Stochastic Processes and their Applications, Elsevier, vol. 147(C), pages 423-455.

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