Advanced Search
MyIDEAS: Login to save this article or follow this journal

Copula based hierarchical risk aggregation through sample reordering


Author Info

  • Arbenz, Philipp
  • Hummel, Christoph
  • Mainik, Georg
Registered author(s):


    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.

    Download Info

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
    File URL:
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Bibliographic Info

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

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

    as in new window
    Handle: RePEc:eee:insuma:v:51:y:2012:i:1:p:122-133

    Contact details of provider:
    Web page:

    Related research

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

    Find related papers by JEL classification:


    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
    as in new window
    1. Jean-Philippe Bruneton, 2011. "Copula-based Hierarchical Aggregation of Correlated Risks. The behaviour of the diversification benefit in Gaussian and Lognormal Trees," Papers, 1111.1113,, 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, 0906.4853,, 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, 0708.2542,, revised Jun 2008.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as in new window

    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.


    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.


    Access and download statistics


    When requesting a correction, please mention this item's handle: RePEc:eee:insuma:v:51:y:2012:i:1:p:122-133. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.