TY - JOUR
T1 - Prediction in a Poisson cluster model
AU - Mikosch, Thomas Valentin
AU - Matsui, Muneya
PY - 2010/6
Y1 - 2010/6
N2 - 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.
AB - 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.
M3 - Journal article
SN - 0021-9002
VL - 47
SP - 350
EP - 366
JO - Journal of Applied Probability
JF - Journal of Applied Probability
ER -