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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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    3. 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.
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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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