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Risk concentration of aggregated dependent risks: The second-order properties

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  • Tong, Bin
  • Wu, Chongfeng
  • Xu, Weidong

Abstract

Under the current regulatory guidelines for banks and insurance companies, the quantification of diversification benefits due to risk aggregation plays a prominent role. In this paper we establish second-order approximation of risk concentration associated with a random vector X:=(X1,X2,…,Xd) in terms of Value at Risk (VaR) within the methodological framework of second-order regular variation and the theory of Archimedean copula. Moreover, we find that the rate of convergence of the first-order approximation of risk concentration depends on the the interplay between the tail behavior of the marginal loss random variables and their dependence structure. Specifically, we find that the rate of convergence is determined by either the second-order parameter (ρ1) of Archimedean copula generator or the second-order parameter (ρ) of the tail margins, leading to either the so-called dependence dominated case or margin dominated case.

Suggested Citation

  • Tong, Bin & Wu, Chongfeng & Xu, Weidong, 2012. "Risk concentration of aggregated dependent risks: The second-order properties," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 139-149.
    • Handle: RePEc:eee:insuma:v:50:y:2012:i:1:p:139-149
    DOI: 10.1016/j.insmatheco.2011.11.002
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    Cited by:

    1. Bikramjit Das & Marie Kratz, 2017. "Diversification benefits under multivariate second order regular variation," Working Papers hal-01520655, HAL.
    2. Gilles Boevi Koumou & Georges Dionne, 2022. "Coherent Diversification Measures in Portfolio Theory: An Axiomatic Foundation," Risks, MDPI, vol. 10(11), pages 1-19, October.
    3. Mario Fortin & Marcelin Joanis & Philippe Kabore & Luc Savard, 2022. "Determination of Quebec's Quarterly Real GDP and Analysis of the Business Cycle, 1948–1980," Journal of Business Cycle Research, Springer;Centre for International Research on Economic Tendency Surveys (CIRET), vol. 18(3), pages 261-288, November.
    4. Das, Bikramjit & Kratz, Marie, 2017. "Diversification benefits under multivariate second order regular variation," ESSEC Working Papers WP1706, ESSEC Research Center, ESSEC Business School.

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    More about this item

    Keywords

    Aggregated risk; Risk concentration; Archimedean copula; Second-order regular variation; Dependence structure;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages

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