The disorder problem for purely jump Lévy processes with completely monotone jumps

We study the problem of detecting as quickly as possible the disorder time at which a purely jump Lévy process changes its probabilistic features. Assuming that its jumps are completely monotone, the monitored process is approximated by a sequence of hyperexponential processes. Then, the solution to the disorder problem for a hyperexponential process is used to approximate the one of the original problem. The efficiency of the proposed approximation scheme is investigated for some popular Lévy processes, such as the gamma, inverse Gaussian, variance-gamma and CGMY processes.