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A Nonhomogeneous Poisson Hidden Markov Model for Claim Counts

Published online by Cambridge University Press:  09 August 2013

Yi Lu  and
Leilei Zeng
Yi Lu
Affiliation:
Department of Statistics & Actuarial Science, Simon Fraser University, 8888 University Drive Burnaby, BC, CanadaV5A 1S6, Fax: 1.778.782.4368, E-Mail: yilu@sfu.ca
Leilei Zeng
Affiliation:
Department of Statistics & Actuarial Science, University of Waterloo, 200 University Avenue West Waterloo, Ontario, CanadaN2L 3G1, Fax: 1.519.746.1875, E-Mail: lzeng@math.uwaterloo.ca
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Abstract

We propose a nonhomogeneous Poisson hidden Markov model for a time series ofclaim counts that accounts for both seasonal variations and random fluctuations in the claims intensity. It assumes that the parameters of the intensity function for the nonhomogeneous Poisson distribution vary according to an (unobserved) underlying Markov chain. This can apply to natural phenomena that evolve in a seasonal environment. For example, hurricanes that are subject to random fluctuations (El Niño-La Niña cycles) affect insurance claims. The Expectation-Maximization (EM) algorithm is used to calculate the maximum likelihood estimators for the parameters of this dynamic Poisson hidden Markov model. Statistical applications of this model to Atlantic hurricanes and tropical storms data are discussed.

Keywords

Poisson hidden Markov modelNonhomogeneous Poisson processSeasonalityIntensity functionHurricanes and tropical stormsMaximum likelihood estimationEM algorithm
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 42 , Issue 1 , May 2012 , pp. 181 - 202
Copyright
Copyright © International Actuarial Association 2012

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