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Prediction in a Poisson cluster model

Part of: Stochastic processes Special processes

Published online by Cambridge University Press:  14 July 2016

Muneya Matsui  and
Thomas Mikosch
Muneya Matsui*
Affiliation:
Keio University
Thomas Mikosch*
Affiliation:
University of Copenhagen
*
∗Current address: Mathematical Engineering No.4 Laboratory, Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan.
∗∗Postal address: Department of Mathematics, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark. Email address: [email protected]
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Abstract

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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.

Keywords

Poisson cluster modelpredictionconditional expectationclaims reservinginsuranceLévy processshot noise

MSC classification

Secondary: 60K30: Applications (congestion, allocation, storage, traffic, etc.) 60G25: Prediction theory 60G55: Point processes
Type
Research Article
Information
Journal of Applied Probability , Volume 47 , Issue 2 , June 2010 , pp. 350 - 366
Copyright
Copyright © Applied Probability Trust 2010 

Footnotes

Research supported by a JSPS Research Fellowship for Young scientists.

Research partly supported by the danish Reasearch Council (FNU) grants 272-06-0442 and 09-072331

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