Collective Risk Models with Dependence

31 Pages Posted: 27 Jan 2018 Last revised: 19 Jun 2018

See all articles by Hélène Cossette

Hélène Cossette

Université Laval - Faculté des Sciences et Génie

Etienne Marceau

Université Laval - Faculté des Sciences et Génie

Itre Mtalai

Laval University, Faculté des Sciences et Génie

Date Written: June 12, 2018

Abstract

In actuarial science, collective risk models, in which the aggregate claim amount of a portfolio is defined in terms of random sums, play a crucial role. In these models, it is common to assume that the number of claims and their amounts are independent, even if this might not always be the case. We consider collective risk models with different dependence structures. Due to the importance of such distributions in an actuarial setting, we first investigate a collective risk model with dependence involving the family of multivariate mixed Erlang distributions. Other models based on mixtures involving bivariate and multivariate copulas in a more general setting are then presented. These different structures allow to link the number of claims to each claim amount, and to quantify the aggregate claim loss. Then, we use Archimedean and hierarchical Archimedean copulas in collective risk models, to model the dependence between the claim number random variable and the claim amount random variables involved in the random sum. Such dependence structures allow us to derive a computational methodology for the assessment of the aggregate claim amount. While being very flexible, this methodology is easy to implement, and can easily fit more complicated hierarchical structures.

Keywords: Random sums; collective risk models; dependence; copulas; Archimedean copulas; hierarchical Archimedean copulas; mixed Erlang distributions

JEL Classification: C60; C63; C02; G22

Suggested Citation

Cossette, Hélène and Marceau, Etienne and Mtalai, Itre, Collective Risk Models with Dependence (June 12, 2018). Available at SSRN: https://ssrn.com/abstract=3104912 or http://dx.doi.org/10.2139/ssrn.3104912

Hélène Cossette

Université Laval - Faculté des Sciences et Génie ( email )

1033, Pavillon Alexandre-Vachon
Cite Universitaire, Quebec G1K 7P4
Canada
418-656-2603 (Phone)

Etienne Marceau (Contact Author)

Université Laval - Faculté des Sciences et Génie ( email )

1033, Pavillon Alexandre-Vachon
Cite Universitaire, Quebec G1K 7P4
Canada
418-656-2013 (Phone)

Itre Mtalai

Laval University, Faculté des Sciences et Génie ( email )

1033, Pavillon Alexandre-Vachon
Québec, G1K 7P4
Canada
418-656-2131 (3639) (Phone)

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