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The Solvency II square-root formula for systematic biometric risk

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  • Christiansen, Marcus C.
  • Denuit, Michel M.
  • Lazar, Dorina

Abstract

In this paper, we develop a model supporting the so-called square-root formula used in Solvency II to aggregate the modular life SCR. Describing the insurance policy by a Markov jump process, we can obtain expressions similar to the square-root formula in Solvency II by means of limited expansions around the best estimate. Numerical illustrations are given, based on German population data. Even if the square-root formula can be supported by theoretical considerations, it is shown that the QIS correlation matrix is highly questionable.

Suggested Citation

  • Christiansen, Marcus C. & Denuit, Michel M. & Lazar, Dorina, 2012. "The Solvency II square-root formula for systematic biometric risk," Insurance: Mathematics and Economics, Elsevier, vol. 50(2), pages 257-265.
    • Handle: RePEc:eee:insuma:v:50:y:2012:i:2:p:257-265
    DOI: 10.1016/j.insmatheco.2011.11.008
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    References listed on IDEAS

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    1. Christiansen, Marcus C., 2008. "A sensitivity analysis concept for life insurance with respect to a valuation basis of infinite dimension," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 680-690, April.
    2. Renshaw, A. E. & Haberman, S., 2000. "Modelling the recent time trends in UK permanent health insurance recovery, mortality and claim inception transition intensities," Insurance: Mathematics and Economics, Elsevier, vol. 27(3), pages 365-396, December.
    3. Hyndman, Rob J. & Shahid Ullah, Md., 2007. "Robust forecasting of mortality and fertility rates: A functional data approach," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4942-4956, June.
    4. Katja Hanewald, 2011. "Explaining Mortality Dynamics," North American Actuarial Journal, Taylor & Francis Journals, vol. 15(2), pages 290-314.
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    Cited by:

    1. Michael Heinrich & Thomas Schreck, 2017. "Effects of Solvency II on Portfolio Efficiency, The Case of Real Estate and Infrastructure Investments," LARES lares_2017_paper_8, Latin American Real Estate Society (LARES).
    2. Paulusch, Joachim & Schlütter, Sebastian, 2022. "Sensitivity-implied tail-correlation matrices," Journal of Banking & Finance, Elsevier, vol. 134(C).
    3. Eling, Martin & Pankoke, David, 2013. "Basis Risk, Procylicality, and Systemic Risk in the Solvency II Equity Risk Module," Working Papers on Finance 1306, University of St. Gallen, School of Finance.
    4. Boualem Djehiche & Björn Löfdahl, 2021. "Quantum Support Vector Regression for Disability Insurance," Risks, MDPI, vol. 9(12), pages 1-9, December.
    5. Marcus Christiansen, 2012. "Multistate models in health insurance," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 96(2), pages 155-186, June.
    6. Gatzert, Nadine & Martin, Michael, 2012. "Quantifying credit and market risk under Solvency II: Standard approach versus internal model," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 649-666.
    7. Djehiche, Boualem & Löfdahl, Björn, 2014. "Risk aggregation and stochastic claims reserving in disability insurance," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 100-108.
    8. 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.
    9. Andreas Niemeyer, 2015. "Safety Margins for Systematic Biometric and Financial Risk in a Semi-Markov Life Insurance Framework," Risks, MDPI, vol. 3(1), pages 1-26, January.
    10. Mezőfi, Balázs & Niedermayer, Andras & Niedermayer, Daniel & Süli, Balázs Márton, 2017. "Solvency II reporting: How to interpret funds’ aggregate solvency capital requirement figures," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 164-171.
    11. Christiansen, Marcus C. & Niemeyer, Andreas & Teigiszerová, Lucia, 2015. "Modeling and forecasting duration-dependent mortality rates," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 65-81.

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