IDEAS home Printed from https://ideas.repec.org/p/hal/wpaper/hal-00848492.html
   My bibliography  Save this paper

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
    as

    Download full text from publisher

    File URL: https://hal.science/hal-00848492v2/document
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Ajne, Björn, 1994. "Additivity of Chain-Ladder Projections," ASTIN Bulletin, Cambridge University Press, vol. 24(2), pages 311-318, November.
    3. 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.
    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)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Klaus Schmidt, 2012. "Loss prediction based on run-off triangles," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 96(2), pages 265-310, June.
    2. Kris Peremans & Stefan Van Aelst & Tim Verdonck, 2018. "A Robust General Multivariate Chain Ladder Method," Risks, MDPI, vol. 6(4), pages 1-18, September.
    3. Zhang, Yanwei, 2010. "A general multivariate chain ladder model," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 588-599, June.
    4. Portugal, Luís & Pantelous, Athanasios A. & Verrall, Richard, 2021. "Univariate and multivariate claims reserving with Generalized Link Ratios," Insurance: Mathematics and Economics, Elsevier, vol. 97(C), pages 57-67.
    5. Peng Shi, 2017. "A Multivariate Analysis of Intercompany Loss Triangles," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(2), pages 717-737, June.
    6. Ioannis Badounas & Georgios Pitselis, 2020. "Loss Reserving Estimation With Correlated Run-Off Triangles in a Quantile Longitudinal Model," Risks, MDPI, vol. 8(1), pages 1-26, February.
    7. Hahn, Lukas, 2017. "Multi-year non-life insurance risk of dependent lines of business in the multivariate additive loss reserving model," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 71-81.
    8. Avanzi, Benjamin & Taylor, Greg & Vu, Phuong Anh & Wong, Bernard, 2020. "A multivariate evolutionary generalised linear model framework with adaptive estimation for claims reserving," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 50-71.
    9. 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.
    10. Himchan Jeong & Dipak Dey, 2020. "Application of a Vine Copula for Multi-Line Insurance Reserving," Risks, MDPI, vol. 8(4), pages 1-23, October.
    11. Morne Joubert & Tanja Verster & Helgard Raubenheimer & Willem D. Schutte, 2021. "Adapting the Default Weighted Survival Analysis Modelling Approach to Model IFRS 9 LGD," Risks, MDPI, vol. 9(6), pages 1-17, June.
    12. Yanwei Zhang & Vanja Dukic, 2013. "Predicting Multivariate Insurance Loss Payments Under the Bayesian Copula Framework," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(4), pages 891-919, December.
    13. Heo, Wookjae & Lee, Jae Min & Park, Narang & Grable, John E., 2020. "Using Artificial Neural Network techniques to improve the description and prediction of household financial ratios," Journal of Behavioral and Experimental Finance, Elsevier, vol. 25(C).
    14. Douw Gerbrand Breed & Niel van Jaarsveld & Carsten Gerken & Tanja Verster & Helgard Raubenheimer, 2021. "Development of an Impairment Point in Time Probability of Default Model for Revolving Retail Credit Products: South African Case Study," Risks, MDPI, vol. 9(11), pages 1-22, November.
    15. Gareth W. Peters & Mario V. Wuthrich & Pavel V. Shevchenko, 2010. "Chain ladder method: Bayesian bootstrap versus classical bootstrap," Papers 1004.2548, arXiv.org.
    16. Avanzi, Benjamin & Taylor, Greg & Vu, Phuong Anh & Wong, Bernard, 2016. "Stochastic loss reserving with dependence: A flexible multivariate Tweedie approach," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 63-78.
    17. Peters, Gareth W. & Wüthrich, Mario V. & Shevchenko, Pavel V., 2010. "Chain ladder method: Bayesian bootstrap versus classical bootstrap," Insurance: Mathematics and Economics, Elsevier, vol. 47(1), pages 36-51, August.
    18. Benjamin Avanzi & Gregory Clive Taylor & Phuong Anh Vu & Bernard Wong, 2020. "A multivariate evolutionary generalised linear model framework with adaptive estimation for claims reserving," Papers 2004.06880, arXiv.org.
    19. Kathrin Kloberdanz & Klaus Schmidt, 2009. "Loss prediction in a linear model under a linear constraint," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 93(2), pages 205-220, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:wpaper:hal-00848492. See general information about how to correct material in RePEc.

    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 CitEc recognized a bibliographic reference but did not link an item in RePEc 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.