Thresholding events of extreme in simultaneous monitoring of multiple risks

This article develops a threshold system for monitoring airline performance. This threshold system divides the sample space into regions with increasing levels of risk and allows instant assessments of risk level of any observed airline performance. Of particular concern is the performance with extreme risk. In this article, a multivariate extreme value theory approach is used to establish thresholds for signaling varying levels of extremeness in the context of simultaneous monitoring of multiple risk measures. The threshold system is justified in terms of multivariate extreme quantiles, and its sample estimator is shown to be consistent. This threshold system applies to general extreme risk management. Finally, a simulation and comparison study demonstrates the good performance of the proposed multivariate extreme quantile estimator. Supplemental materials providing technical details are available online.