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One-Year Change Methodologies for Fixed-Sum Insurance Contracts

Author

Listed:
  • Michel Dacorogna

    (Prime Re Solutions, 6340 Zug, Switzerland)

  • Alessandro Ferriero

    (Department of Mathematics, UAM, Campus de Cantoblanco, 28049 Madrid, Spain
    SCOR, General Guisan-Quai 26, 8022 Zurich, Switzerland)

  • David Krief

    (LPSM, Université Paris Diderot, 75013 Paris, France)

Abstract

We study the dynamics of the one-year change in P&C insurance reserves estimation by analyzing the process that leads to the ultimate risk in the case of “fixed-sum” insurance contracts. The random variable ultimately is supposed to follow a binomial distribution. We compute explicitly various quantities of interest, in particular the Solvency Capital Requirement for one year change and the Risk Margin, using the characteristics of the underlying model. We then compare them with the same figures calculated with existing risk estimation methods. In particular, our study shows that standard methods (Merz–Wüthrich) can lead to materially incorrect results if the assumptions are not fulfilled. This is due to a multiplicative error assumption behind the standard methods, whereas our example has an additive error propagation as often happens in practice.

Suggested Citation

  • Michel Dacorogna & Alessandro Ferriero & David Krief, 2018. "One-Year Change Methodologies for Fixed-Sum Insurance Contracts," Risks, MDPI, vol. 6(3), pages 1-29, July.
    • Handle: RePEc:gam:jrisks:v:6:y:2018:i:3:p:75-:d:160853
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    References listed on IDEAS

    as
    1. Busse, Marc & Müller, Ulrich & Dacorogna, Michel, 2010. "Robust Estimation of Reserve Risk," ASTIN Bulletin, Cambridge University Press, vol. 40(2), pages 453-489, November.
    2. Mack, Thomas, 2008. "Correction Note to “The Prediction Error of Bornhuetter/Ferguson” By T. Mack," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 38(02), pages 669-669, November.
    3. Ferriero, A., 2016. "Solvency capital estimation, reserving cycle and ultimate risk," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 162-168.
    4. Mack, Thomas, 2008. "The Prediction Error of Bornhuetter/Ferguson," ASTIN Bulletin, Cambridge University Press, vol. 38(1), pages 87-103, May.
    5. Mack, Thomas, 1993. "Distribution-free Calculation of the Standard Error of Chain Ladder Reserve Estimates," ASTIN Bulletin, Cambridge University Press, vol. 23(2), pages 213-225, November.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Carnevale Giulio Ercole & Clemente Gian Paolo, 2020. "A Bayesian Internal Model for Reserve Risk: An Extension of the Correlated Chain Ladder," Risks, MDPI, vol. 8(4), pages 1-20, November.
    2. Michel Dacorogna, 2023. "How to Gain Confidence in the Results of Internal Risk Models? Approaches and Techniques for Validation," Risks, MDPI, vol. 11(5), pages 1-20, May.

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