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One-Year Volatility of Reserve Risk in a Multivariate Framework

Listed author(s):
  • Yannick Appert-Raullin


    (Group Risk Management, GIE AXA - GIE AXA)

  • Laurent Devineau


    (Recherche et Développement, Milliman Paris - Milliman, SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1)

  • Hinarii Pichevin


    (Recherche et Développement, Milliman Paris - Milliman)

  • Philippe Tann


    (Group Risk Management, GIE AXA - GIE AXA)

Registered author(s):

    The one-year prediction error (one-year MSEP) proposed by Merz and Wüthrich has become a market-standard approach for the assessment of reserve volatilities for Solvency II purposes. However, this approach is declined in a univariate framework. Moreover, Braun proposed a closed-formed expression of the prediction error of several run-off portfolios at the ultimate horizon by taking into account their dependency. This article proposes an analytical expression of the one-year MSEP obtained by generalizing the modeling developed by Braun to the one-year horizon with an approach similar to Merz and Wüthrich. A full mathematical demonstration of the formula has been provided in this paper. A case study is presented to assess the dependency between commercial and motor liabilities businesses based on data coming from a major international insurer.

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    Paper provided by HAL in its series Working Papers with number hal-00848492.

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    Date of creation: 30 Jul 2013
    Handle: RePEc:hal:wpaper:hal-00848492
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    1. Hess, Klaus Th. & Schmidt, Klaus D. & Zocher, Mathias, 2006. "Multivariate loss prediction in the multivariate additive model," Insurance: Mathematics and Economics, Elsevier, vol. 39(2), pages 185-191, October.
    2. Ajne, Björn, 1994. "Additivity of Chain-Ladder Projections," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 24(02), pages 311-318, November.
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