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Copula based hierarchical risk aggregation through sample reordering

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  • Arbenz, Philipp
  • Hummel, Christoph
  • Mainik, Georg

Abstract

For high-dimensional risk aggregation purposes, most popular copula classes are too restrictive in terms of attainable dependence structures. These limitations aggravate with increasing dimension. We study a hierarchical risk aggregation method which is flexible in high dimensions. With this method it suffices to specify a low dimensional copula for each aggregation step in the hierarchy. Copulas and margins of arbitrary kind can be combined. We give an algorithm for numerical approximation which introduces dependence between originally independent marginal samples through reordering.

Suggested Citation

  • Arbenz, Philipp & Hummel, Christoph & Mainik, Georg, 2012. "Copula based hierarchical risk aggregation through sample reordering," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 122-133.
    • Handle: RePEc:eee:insuma:v:51:y:2012:i:1:p:122-133
    DOI: 10.1016/j.insmatheco.2012.03.009
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    References listed on IDEAS

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    Cited by:

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    12. Souhaib Ben Taieb & James W. Taylor & Rob J. Hyndman, 2017. "Coherent Probabilistic Forecasts for Hierarchical Time Series," Monash Econometrics and Business Statistics Working Papers 3/17, Monash University, Department of Econometrics and Business Statistics.
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    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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