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Quickest drift change detection in Lévy-type force of mortality model. (English) Zbl 1427.60068

Summary: 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. The 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.

MSC:

60G40 Stopping times; optimal stopping problems; gambling theory
60G51 Processes with independent increments; Lévy processes
62L15 Optimal stopping in statistics
62P05 Applications of statistics to actuarial sciences and financial mathematics
62L10 Sequential statistical analysis
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References:

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