EconPapers    
Economics at your fingertips  
 

Collective risk models with dependence

Hélène Cossette, Etienne Marceau and Itre Mtalai

Insurance: Mathematics and Economics, 2019, vol. 87, issue C, 153-168

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 risk models 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 (search for similar items in EconPapers)
JEL-codes: C60 C63 C69 (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: Track citations by RSS feed

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167668718302099
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:87:y:2019:i:c:p:153-168

DOI: 10.1016/j.insmatheco.2019.04.008

Access Statistics for this article

Insurance: Mathematics and Economics is currently edited by R. Kaas, Hansjoerg Albrecher, M. J. Goovaerts and E. S. W. Shiu

More articles in Insurance: Mathematics and Economics from Elsevier
Bibliographic data for series maintained by Haili He ().

 
Page updated 2020-05-02
Handle: RePEc:eee:insuma:v:87:y:2019:i:c:p:153-168