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One-Year Volatility of Reserve Risk in a Multivariate Framework

Author

Listed:
  • Yannick Appert-Raullin

    (Group Risk Management, GIE AXA - GIE AXA)

  • Laurent Devineau

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

  • Hinarii Pichevin

    (Recherche et Développement, Milliman Paris - Milliman France)

  • Philippe Tann

    (Group Risk Management, GIE AXA - GIE AXA)

Abstract

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.

Suggested Citation

  • Yannick Appert-Raullin & Laurent Devineau & Hinarii Pichevin & Philippe Tann, 2013. "One-Year Volatility of Reserve Risk in a Multivariate Framework," Working Papers hal-00848492, HAL.
    • Handle: RePEc:hal:wpaper:hal-00848492
    Note: View the original document on HAL open archive server: https://hal.science/hal-00848492v2
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    References listed on IDEAS

    as
    1. Ajne, Björn, 1994. "Additivity of Chain-Ladder Projections," ASTIN Bulletin, Cambridge University Press, vol. 24(2), pages 311-318, November.
    2. Greg Taylor & Gráinne McGuire, 2007. "A Synchronous Bootstrap to Account for Dependencies Between Lines of Business in the Estimation of Loss Reserve Prediction Error," North American Actuarial Journal, Taylor & Francis Journals, vol. 11(3), pages 70-88.
    3. Braun, Christian, 2004. "The Prediction Error of the Chain Ladder Method Applied to Correlated Run-off Triangles," ASTIN Bulletin, Cambridge University Press, vol. 34(2), pages 399-423, November.
    4. 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.
    Full references (including those not matched with items on IDEAS)

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