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Risk aggregation in Solvency II: How to converge the approaches of the internal models and those of the standard formula?

Author

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  • Laurent Devineau

    () (SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon, R&D, Milliman, Paris - Milliman)

  • Stéphane Loisel

    () (SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

Abstract

Two approaches may be considered in order to determine the Solvency II economic capital: the use of a standard formula or the use of an internal model (global or partial). However, the results produced by these two methods are rarely similar, since the underlying hypothesis of marginal capital aggregation is not verified by the projection models used by companies. We demonstrate that the standard formula can be considered as a first order approximation of the result of the internal model. We therefore propose an alternative method of aggregation that enables to satisfactorily capture the diversity among the various risks that are considered, and to converge the internal models and the standard formula.

Suggested Citation

  • 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-00403662, HAL.
  • Handle: RePEc:hal:journl:hal-00403662
    Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00403662v2
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    File URL: https://hal.archives-ouvertes.fr/hal-00403662v2/document
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    References listed on IDEAS

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    1. Rosenberg, Joshua V. & Schuermann, Til, 2006. "A general approach to integrated risk management with skewed, fat-tailed risks," Journal of Financial Economics, Elsevier, vol. 79(3), pages 569-614, March.
    2. Biard, Romain & Lefèvre, Claude & Loisel, Stéphane, 2008. "Impact of correlation crises in risk theory: Asymptotics of finite-time ruin probabilities for heavy-tailed claim amounts when some independence and stationarity assumptions are relaxed," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 412-421, December.
    3. Wayne Fisher & Stéphane Loisel & Shaun Wang, 2008. "On some key research issues in Enterprise Risk Management related to economic capital and diversification effect at group level," Post-Print hal-00268841, HAL.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Julien Vedani & Fabien Ramaharobandro, 2013. "Continuous compliance: a proxy-based monitoring framework," Papers 1309.7222, arXiv.org, revised Dec 2013.
    2. Loisel, Stéphane & Milhaud, Xavier, 2011. "From deterministic to stochastic surrender risk models: Impact of correlation crises on economic capital," European Journal of Operational Research, Elsevier, vol. 214(2), pages 348-357, October.
    3. Julien Vedani & Laurent Devineau, 2012. "Solvency assessment within the ORSA framework: issues and quantitative methodologies," Working Papers hal-00744351, HAL.
    4. Julien Vedani & Fabien Ramaharobandro, 2013. "Continuous compliance: a proxy-based monitoring framework," Working Papers hal-00866531, HAL.
    5. Matthieu Chauvigny & Laurent Devineau & Stéphane Loisel & Véronique Maume-Deschamps, 2011. "Fast remote but not extreme quantiles with multiple factors. Applications to Solvency II and Enterprise Risk Management," Post-Print hal-00517766, HAL.
    6. Julien Vedani & Laurent Devineau, 2012. "Solvency assessment within the ORSA framework: issues and quantitative methodologies," Papers 1210.6000, arXiv.org, revised Oct 2012.
    7. repec:eee:insuma:v:76:y:2017:i:c:p:164-171 is not listed on IDEAS
    8. Asier Garayeta & J. Inaki De La Pena & Ivan Iturricastillo, 2014. "Pragmatic Solutions for Solvency Capital Requirements at Life Insurance Companies: The Case of Spain," International Journal of Business Administration, International Journal of Business Administration, Sciedu Press, vol. 5(4), pages 39-51, July.
    9. 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.

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