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On the Moments of Aggregate Discounted Claims with Dependence Introduced by a FGM Copula

Published online by Cambridge University Press:  09 August 2013

Mathieu Bargès ,
Hélène Cossette ,
Stéphane Loisel  and
Étienne Marceau
Mathieu Bargès
Affiliation:
Université de Lyon, Université Claude Bernard Lyon 1, Institut de Science Financière et d'Assurances, 50 Avenue Tony Garnier, F-69007 Lyon, France et, École d'Actuariat, Université Laval, Québec, Canada
Hélène Cossette
Affiliation:
École d'Actuariat, Université Laval, Québec, Canada
Stéphane Loisel
Affiliation:
Université de Lyon, Université Claude Bernard Lyon 1, Institut de Science Financière et d'Assurances, 50 Avenue Tony Garnier, F-69007 Lyon, France
Étienne Marceau
Affiliation:
École d'Actuariat, Université Laval, Québec, Canada
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Abstract

In this paper, we investigate the computation of the moments of the compound Poisson sums with discounted claims when introducing dependence between the interclaim time and the subsequent claim size. The dependence structure between the two random variables is defined by a Farlie-Gumbel-Morgenstern copula. Assuming that the claim distribution has finite moments, we give expressions for the first and the second moments and then we obtain a general formula for any mth order moment. The results are illustrated with applications to premium calculation and approximations based on moment matching methods.

Keywords

Compound Poisson processDiscounted aggregate claimsMomentsConstant interest rate
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 41 , Issue 1 , May 2011 , pp. 215 - 238
Copyright
Copyright © International Actuarial Association 2011

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