Compound Poisson Disorder Problem

Abstract

In the compound Poisson disorder problem, arrival rate and/or jump distribution of some compound Poisson process changes suddenly at some unknown and unobservable time. The problem is to detect the change (or disorder) time as quickly as possible. A sudden regime shift may require some countermeasures be taken promptly, and a quickest detection rule can help with those efforts. We describe complete solution of the compound Poisson disorder problem with several standard Bayesian risk measures. Solution methods are feasible for numerical implementation and are illustrated by examples.