Quickest drift change detection in L\'evy-type force of mortality model

TL;DR

This paper develops an optimal Bayesian method for quickest detection of drift changes in a Le9vy process with Gaussian and jump components, applying it to mortality data and constructing the Generalized Shiryaev-Roberts statistic.

Contribution

It introduces a novel approach combining boundary value problems and optimal stopping theory for drift change detection in complex Le9vy processes, with practical mortality modeling applications.

Findings

Effective detection method for drift changes in Le9vy processes.

Application to Polish mortality data demonstrating practical utility.

Construction of the Generalized Shiryaev-Roberts statistic for this context.

Abstract

In this paper we give solution to the quickest drift change detection problem for a L\'evy 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.