Multivariate Lévy-type drift change detection and mortality modeling

被引:0
作者
Michał Krawiec
Zbigniew Palmowski
机构
[1] University of Wrocław,Mathematical Insititute
[2] Wrocław University of Science and Technology,Faculty of Pure and Applied Mathematics
来源
European Actuarial Journal | 2024年 / 14卷
关键词
Lévy process; Multidimensional jump-diffusion; Quickest detection; Optimal stopping; Change of measure; Force of mortality; Longevity;
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学科分类号
摘要
In this paper we give a solution to the quickest drift change detection problem for a multivariate Lévy process consisting of both continuous (Gaussian) and jump components in the Bayesian approach. We do it for a general 0-modified continuous prior distribution of the change point as well as for a random post-change drift parameter. Classically, our criterion of optimality is based on a probability of false alarm and an expected delay of the detection, which is then reformulated in terms of a posterior probability of the change point. We find a generator of the posterior probability, which in case of general prior distribution is inhomogeneous in time. The main solving technique uses the optimal stopping theory and is based on solving a certain free-boundary problem. We also construct a Generelized Shiryaev-Roberts statistic, which can be used for applications. The paper is supplemented by two examples, one of which is further used to analyze Polish life tables (after proper calibration) and detect the drift change in the correlated force of mortality of men and women jointly.
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页码:175 / 203
页数:28
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