We consider a Poisson cluster model, motivated by insurance applications. At each claim arrival time, modeled by the point of a homogeneous Poisson process, we start a cluster process which represents the number or amount of payments triggered by the arrival of a claim in a portfolio. The cluster process is a Lévy or truncated compound Poisson process. Given the observations of the process over a finite interval, we consider the expected value of the number and amount of payments in a future time interval. We also give bounds for the error encountered in this prediction procedure.
