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On the lifetime and one-year views of reserve risk, with application to IFRS 17 and Solvency II risk margins

Author

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  • England, P.D.
  • Verrall, R.J.
  • Wüthrich, M.V.

Abstract

This paper brings together analytic and simulation-based approaches to reserve risk in general (P&C) insurance, applied to the traditional actuarial view of risk over the lifetime of the liabilities and to the one-year view of Solvency II. It also connects the lifetime and one-year views of risk. The framework of the model in Mack (1993) is used throughout, although the results have wider applicability.

Suggested Citation

  • England, P.D. & Verrall, R.J. & Wüthrich, M.V., 2019. "On the lifetime and one-year views of reserve risk, with application to IFRS 17 and Solvency II risk margins," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 74-88.
    • Handle: RePEc:eee:insuma:v:85:y:2019:i:c:p:74-88
    DOI: 10.1016/j.insmatheco.2018.12.002
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    References listed on IDEAS

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    1. Verrall, R. J., 1991. "On the estimation of reserves from loglinear models," Insurance: Mathematics and Economics, Elsevier, vol. 10(1), pages 75-80, March.
    2. repec:eme:jrfpps:v:14:y:2013:i:2:p:353-377 is not listed on IDEAS
    3. Mack, Thomas, 1999. "The Standard Error of Chain Ladder Reserve Estimates: Recursive Calculation and Inclusion of a Tail Factor," ASTIN Bulletin, Cambridge University Press, vol. 29(2), pages 361-366, November.
    4. Ohlsson, Esbjörn & Lauzeningks, Jan, 2009. "The one-year non-life insurance risk," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 203-208, October.
    5. England, P.D. & Verrall, R.J., 2002. "Stochastic Claims Reserving in General Insurance," British Actuarial Journal, Cambridge University Press, vol. 8(3), pages 443-518, August.
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    7. Mack, Thomas, 1991. "A Simple Parametric Model for Rating Automobile Insurance or Estimating IBNR Claims Reserves," ASTIN Bulletin, Cambridge University Press, vol. 21(1), pages 93-109, April.
    8. Renshaw, A.E. & Verrall, R.J., 1998. "A Stochastic Model Underlying the Chain-Ladder Technique," British Actuarial Journal, Cambridge University Press, vol. 4(4), pages 903-923, October.
    9. England, Peter, 2002. "Addendum to "Analytic and bootstrap estimates of prediction errors in claims reserving"," Insurance: Mathematics and Economics, Elsevier, vol. 31(3), pages 461-466, December.
    10. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    11. England, P. D. & Verrall, R. J., 2006. "Predictive Distributions of Outstanding Liabilities in General Insurance," Annals of Actuarial Science, Cambridge University Press, vol. 1(2), pages 221-270, September.
    12. Ashe, Frank, 1986. "An Essay at Measuring the Variance of Estimates of Outstanding Claim Payments," ASTIN Bulletin, Cambridge University Press, vol. 16(S1), pages 99-113, April.
    13. 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.
    14. Mario V. Wuthrich & Michael Merz, 2015. "Stochastic Claims Reserving Manual: Advances in Dynamic Modeling," Swiss Finance Institute Research Paper Series 15-34, Swiss Finance Institute.
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    16. Diers, Dorothea & Linde, Marc, 2013. "The multi-year non-life insurance risk in the additive loss reserving model," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 590-598.
    17. Dorothea Diers & Martin Eling & Christian Kraus & Marc Linde, 2013. "Multi-year non-life insurance risk," Journal of Risk Finance, Emerald Group Publishing, vol. 14(4), pages 353-377, August.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Eling, Martin & Jung, Kwangmin, 2020. "Risk aggregation in non-life insurance: Standard models vs. internal models," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 183-198.
    2. Yixing Zhao & Rogemar Mamon & Heng Xiong, 2021. "Claim reserving for insurance contracts in line with the International Financial Reporting Standards 17: a new paid-incurred chain approach to risk adjustments," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 7(1), pages 1-26, December.
    3. Jan Hájek, 2020. "Effect of tax deductibility on technical reserves recognized by Czech and Slovak insurance companies [Vliv daňové uznatelnosti na výši technických rezerv tvořených českými a slovenskými pojišťovnam," Český finanční a účetní časopis, Prague University of Economics and Business, vol. 2020(3-4), pages 25-37.
    4. Chen, An & Li, Hong & Schultze, Mark B., 2023. "Optimal longevity risk transfer under asymmetric information," Economic Modelling, Elsevier, vol. 120(C).
    5. Marcin Szatkowski, 2022. "Study of Actuarial Characteristics of One-Year and Ultimate Reserve Risk Distributions Based on Market Data," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 14(4), pages 225-262, December.
    6. Jorge Wilson Euphasio Junior & João Vinícius França Carvalho, 2022. "Resseguro e Capital de Solvência: Atenuantes da Probabilidade de Ruína de SeguradorasReinsurance and Solvency Capital: Mitigating Insurance Companies’ Ruin Probability," RAC - Revista de Administração Contemporânea (Journal of Contemporary Administration), ANPAD - Associação Nacional de Pós-Graduação e Pesquisa em Administração, vol. 26(1), pages 200191-2001.
    7. Marcin Szatkowski & Łukasz Delong, 2021. "One-Year and Ultimate Reserve Risk in Mack Chain Ladder Model," Risks, MDPI, vol. 9(9), pages 1-29, August.
    8. Jan Hájek, 2020. "Effect of tax deductibility on technical reserves recognized by Czech and Slovak insurance companies [Vliv daňové uznatelnosti na výši technických rezerv tvořených českými a slovenskými pojišťovnam," Český finanční a účetní časopis, Prague University of Economics and Business, vol. 2020(3-4).
    9. Anja Breuer & Yves Staudt, 2022. "Equalization Reserves for Reinsurance and Non-Life Undertakings in Switzerland," Risks, MDPI, vol. 10(3), pages 1-41, March.

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