Prediction in a Poisson cluster model

Thomas Valentin Mikosch; Muneya Matsui

Prediction in a Poisson cluster model

Department of Mathematical Sciences

8 Citations (Scopus)

Abstract

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.

Original language	English
Journal	Journal of Applied Probability
Volume	47
Pages (from-to)	350-366
ISSN	0021-9002
Publication status	Published - Jun 2010

Cite this

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title = "Prediction in a Poisson cluster model",

abstract = "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 L{\'e}vy 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.",

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T1 - Prediction in a Poisson cluster model

AU - Mikosch, Thomas Valentin

AU - Matsui, Muneya

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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 -

Prediction in a Poisson cluster model

Abstract

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