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Dependent risk models with Archimedean copulas: A computational strategy based on common mixtures and applications

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  • Cossette, Hélène
  • Marceau, Etienne
  • Mtalai, Itre
  • Veilleux, Déry

Abstract

In this paper, we investigate dependent risk models in which the dependence structure is defined by an Archimedean copula. Using such a structure with specific marginals, we derive explicit expressions for the pdf of the aggregated risk and other related quantities. The common mixture representation of Archimedean copulas is at the basis of a computational strategy proposed to find exact or approximated values of the distribution of the sum of risks in a general setup. Such results are then used to investigate risk models in regard to aggregation, capital allocation and ruin problems. An extension to nested Archimedean copulas is also discussed.

Suggested Citation

  • Cossette, Hélène & Marceau, Etienne & Mtalai, Itre & Veilleux, Déry, 2018. "Dependent risk models with Archimedean copulas: A computational strategy based on common mixtures and applications," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 53-71.
    • Handle: RePEc:eee:insuma:v:78:y:2018:i:c:p:53-71
    DOI: 10.1016/j.insmatheco.2017.11.002
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    References listed on IDEAS

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    Cited by:

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    2. Choe, Geon Ho & Choi, So Eun & Jang, Hyun Jin, 2020. "Assessment of time-varying systemic risk in credit default swap indices: Simultaneity and contagiousness," The North American Journal of Economics and Finance, Elsevier, vol. 54(C).
    3. Hengxin Cui & Ken Seng Tan & Fan Yang, 2024. "Portfolio credit risk with Archimedean copulas: asymptotic analysis and efficient simulation," Annals of Operations Research, Springer, vol. 332(1), pages 55-84, January.
    4. Cossette, Hélène & Marceau, Etienne & Mtalai, Itre, 2019. "Collective risk models with dependence," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 153-168.
    5. Jinghui Chen & Edward Furman & X. Sheldon Lin, 2025. "Static marginal expected shortfall: Systemic risk measurement under dependence uncertainty," Papers 2504.19953, arXiv.org, revised Nov 2025.
    6. Furman, Edward & Kye, Yisub & Su, Jianxi, 2021. "Multiplicative background risk models: Setting a course for the idiosyncratic risk factors distributed phase-type," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 153-167.
    7. Vadim Semenikhine & Edward Furman & Jianxi Su, 2018. "On a Multiplicative Multivariate Gamma Distribution with Applications in Insurance," Risks, MDPI, vol. 6(3), pages 1-20, August.

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