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MODELING DEPENDENCE BETWEEN LOSS TRIANGLES WITH HIERARCHICAL ARCHIMEDEAN COPULAS

Published online by Cambridge University Press:  19 June 2015

Anas Abdallah ,
Jean-Philippe Boucher  and
Hélène Cossette
Anas Abdallah
Affiliation:
École d'Actuariat, Université Laval, Quebec City (Quebec) E-Mail: anas.abdallah.1@ulaval.ca
Jean-Philippe Boucher*
Affiliation:
Département de mathématiques, UQAM Montreal (Quebec)
Hélène Cossette
Affiliation:
École d'Actuariat, Université Laval, Quebec City (Quebec) E-Mail: helene.cossette@act.ulaval.ca
*
E-Mail: boucher.jean-philippe@uqam.ca
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Abstract

One of the most critical problems in property/casualty insurance is to determine an appropriate reserve for incurred but unpaid losses. These provisions generally comprise most of the liabilities of a non-life insurance company. The global provisions are often determined under an assumption of independence between the lines of business. Recently, Shi and Frees (2011) proposed to put dependence between lines of business with a copula that captures dependence between two cells of two different runoff triangles. In this paper, we propose to generalize this model in two steps. First, by using an idea proposed by Barnett and Zehnwirth (1998), we will suppose a dependence between all the observations that belong to the same calendar year (CY) for each line of business. Thereafter, we will then suppose another dependence structure that links the CYs of different lines of business. This model is done by using hierarchical Archimedean copulas. We show that the model provides more flexibility than existing models, and offers a better, more realistic and more intuitive interpretation of the dependence between the lines of business. For illustration, the model is applied to a dataset from a major US property-casualty insurer, where a bootstrap method is proposed to estimate the distribution of the reserve.

Keywords

Runoff trianglescopulahierarchical Archimedean copulamaximum likelihood estimationbootstrap
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 45 , Issue 3 , September 2015 , pp. 577 - 599
Copyright
Copyright © Astin Bulletin 2015 

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