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In this paper we give a solution to the quickest drift change detectionproblem for a multivariate L\'evy process consisting of both continuous(Gaussian) and jump components in the Bayesian approach. We do it for a general0-modified continuous prior distribution of the change point. Classically, ourcriterion of optimality is based on a probability of false alarm and anexpected delay of the detection, which is then reformulated in terms of aposterior probability of the change point. We find a generator of the posteriorprobability, which in case of general prior distribution is inhomogeneous intime. The main solving technique uses the optimal stopping theory and is basedon solving a certain free-boundary problem. We also construct a GenerelizedShiryaev-Roberts statistic, which can be used for applications. The paper issupplemented by two examples, one of which is further used to analyze Polishlife tables (after proper calibration) and detect the drift change in thecorrelated force of mortality of men and women jointly.

Multivariate L\'evy-type drift change detection and mortality modeling