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Copula based hierarchical risk aggregation through sample reordering

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

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    Bibliographic Info

    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 51 (2012)
    Issue (Month): 1 ()
    Pages: 122-133

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    Handle: RePEc:eee:insuma:v:51:y:2012:i:1:p:122-133

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    Web page: http://www.elsevier.com/locate/inca/505554

    Related research

    Keywords: IM12; IM22; IM43; IE43; IE46; Hierarchical risk aggregation; Copulas; High-dimensional dependence; Iman–Conover method;

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    References

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    1. Jean-Philippe Bruneton, 2011. "Copula-based Hierarchical Aggregation of Correlated Risks. The behaviour of the diversification benefit in Gaussian and Lognormal Trees," Papers, arXiv.org 1111.1113, arXiv.org, revised Nov 2011.
    2. Philip M. Lurie & Matthew S. Goldberg, 1998. "An Approximate Method for Sampling Correlated Random Variables from Partially-Specified Distributions," Management Science, INFORMS, INFORMS, vol. 44(2), pages 203-218, February.
    3. Christoph Hummel, 2009. "Shaping tail dependencies by nesting box copulas," Papers, arXiv.org 0906.4853, arXiv.org, revised Aug 2009.
    4. repec:sae:ecolab:v:16:y:2006:i:2:p:1-2 is not listed on IDEAS
    5. Bürgi, Roland & Dacorogna, Michel M & Iles, Roger, 2008. "Risk aggregation, dependence structure and diversification benefit," MPRA Paper 10054, University Library of Munich, Germany.
    6. Laurent Devineau & Stéphane Loisel, 2009. "Risk aggregation in Solvency II: How to converge the approaches of the internal models and those of the standard formula?," Post-Print, HAL hal-00403662, HAL.
    7. Paul Embrechts, 2009. "Copulas: A Personal View," Journal of Risk & Insurance, The American Risk and Insurance Association, The American Risk and Insurance Association, vol. 76(3), pages 639-650.
    8. Packham, Natalie & Schmidt, Wolfgang M., 2008. "Latin hypercube sampling with dependence and applications in finance," CPQF Working Paper Series, Frankfurt School of Finance and Management, Centre for Practical Quantitative Finance (CPQF) 15, Frankfurt School of Finance and Management, Centre for Practical Quantitative Finance (CPQF).
    9. Dirk Tasche, 2007. "Capital Allocation to Business Units and Sub-Portfolios: the Euler Principle," Papers, arXiv.org 0708.2542, arXiv.org, revised Jun 2008.
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    Cited by:
    1. Guillén, Montserrat & Sarabia, José María & Prieto, Faustino, 2013. "Simple risk measure calculations for sums of positive random variables," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 53(1), pages 273-280.
    2. Zaks, Yaniv & Tsanakas, Andreas, 2014. "Optimal capital allocation in a hierarchical corporate structure," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 56(C), pages 48-55.
    3. Embrechts, Paul & Puccetti, Giovanni & Rüschendorf, Ludger, 2013. "Model uncertainty and VaR aggregation," Journal of Banking & Finance, Elsevier, Elsevier, vol. 37(8), pages 2750-2764.

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