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

  • Laurent Devineau

    ()

    (SAF - Laboratoire de Sciences Actuarielle et Financière - Université Claude Bernard - Lyon I : EA2429, R&D, Milliman, Paris - Milliman)

  • Stéphane Loisel

    ()

    (SAF - Laboratoire de Sciences Actuarielle et Financière - Université Claude Bernard - Lyon I : EA2429)

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.

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Paper provided by HAL in its series Post-Print with number hal-00403662.

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Date of creation: Dec 2009
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Publication status: Published, Bulletin Français d'Actuariat, 2009, 9, 18, 107-145
Handle: RePEc:hal:journl:hal-00403662
Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00403662/en/
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  1. 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.
  2. Joshua V. Rosenberg & Til Schuermann, 2004. "A general approach to integrated risk management with skewed, fat-tailed risks," Staff Reports 185, Federal Reserve Bank of New York.
  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.
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