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Discrete-Time Risk Models Based on Time Series for Count Random Variables

Published online by Cambridge University Press:  09 August 2013

Hélène Cossette ,
Etienne Marceau  and
Véronique Maume-Deschamps
Hélène Cossette
Affiliation:
École d'Actuariat, Université Laval, Québec, Canada
Etienne Marceau
Affiliation:
École d'Actuariat, Université Laval, Québec, Canada
Véronique Maume-Deschamps
Affiliation:
Université de Lyon, Université Lyon 1, ISFA, Laboratoire SAF
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Abstract

In this paper, we consider various specifications of the general discrete-time risk model in which a serial dependence structure is introduced between the claim numbers for each period. We consider risk models based on compound distributions assuming several examples of discrete variate time series as specific temporal dependence structures: Poisson MA(1) process, Poisson AR(1) process, Markov Bernoulli process and Markov regime-switching process. In these models, we derive expressions for a function that allow us to find the Lundberg coefficient. Specific cases for which an explicit expression can be found for the Lundberg coefficient are also presented. Numerical examples are provided to illustrate different topics discussed in the paper.

Keywords

Discrete-time risk modelPoisson MA(1) processPoisson AR(1) processMarkov Bernoulli ProcessMarkovian EnvironmentLundberg Coefficient
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 40 , Issue 1 , May 2010 , pp. 123 - 150
Copyright
Copyright © International Actuarial Association 2010

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