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On the Calculation of the Solvency Capital Requirement Based on Nested Simulations


  • Bauer, Daniel
  • Reuss, Andreas
  • Singer, Daniela


Within the European Union, risk-based funding requirements for insurance companies are currently being revised as part of the Solvency II project. However, many life insurers struggle with the implementation, which to a large extent appears to be due to a lack of know-how regarding both, stochastic modeling and efficient techniques for the numerical implementation. The current paper addresses these problems by providing a mathematical framework for the derivation of the required risk capital and by reviewing different alternatives for the numerical implementation based on nested simulations. In particular, we seek to provide guidance for practitioners by illustrating and comparing the different techniques based on numerical experiments.

Suggested Citation

  • Bauer, Daniel & Reuss, Andreas & Singer, Daniela, 2012. "On the Calculation of the Solvency Capital Requirement Based on Nested Simulations," ASTIN Bulletin, Cambridge University Press, vol. 42(2), pages 453-499, November.
  • Handle: RePEc:cup:astinb:v:42:y:2012:i:02:p:453-499_00

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    Cited by:

    1. Michael Ludkovski & James Risk, 2017. "Sequential Design and Spatial Modeling for Portfolio Tail Risk Measurement," Papers 1710.05204,, revised May 2018.
    2. Seyed Amir Hejazi & Kenneth R. Jackson & Guojun Gan, 2017. "A Spatial Interpolation Framework for Efficient Valuation of Large Portfolios of Variable Annuities," Papers 1701.04134,
    3. Andreas Reuß & Jochen Ruß & Jochen Wieland, 2016. "Participating Life Insurance Products with Alternative Guarantees: Reconciling Policyholders’ and Insurers’ Interests," Risks, MDPI, Open Access Journal, vol. 4(2), pages 1-18, May.
    4. Xu, Wei & Chen, Yuehuan & Coleman, Conrad & Coleman, Thomas F., 2018. "Moment matching machine learning methods for risk management of large variable annuity portfolios," Journal of Economic Dynamics and Control, Elsevier, vol. 87(C), pages 1-20.
    5. Elia Berdin & Helmut Gründl, 2015. "The Effects of a Low Interest Rate Environment on Life Insurers," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 40(3), pages 385-415, July.
    6. Patrick Cheridito & John Ery & Mario V. Wüthrich, 2020. "Assessing Asset-Liability Risk with Neural Networks," Risks, MDPI, Open Access Journal, vol. 8(1), pages 1-17, February.
    7. Lin, X. Sheldon & Yang, Shuai, 2020. "Fast and efficient nested simulation for large variable annuity portfolios: A surrogate modeling approach," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 85-103.
    8. Risk, J. & Ludkovski, M., 2016. "Statistical emulators for pricing and hedging longevity risk products," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 45-60.
    9. repec:gam:jrisks:v:4:y:2016:i:2:p:11:d:69437 is not listed on IDEAS
    10. Boonen, Tim J. & Guillen, Montserrat & Santolino, Miguel, 2019. "Forecasting compositional risk allocations," Insurance: Mathematics and Economics, Elsevier, vol. 84(C), pages 79-86.
    11. Laurent Devineau & Pierre-Edouard Arrouy & Paul Bonnefoy & Alexandre Boumezoued, 2017. "Fast calibration of the Libor Market Model with Stochastic Volatility and Displaced Diffusion," Working Papers hal-01521491, HAL.
    12. Jing Liu & Huan Zhang, 2017. "Asymptotic Estimates for the One-Year Ruin Probability under Risky Investments," Risks, MDPI, Open Access Journal, vol. 5(2), pages 1-11, May.
    13. Gan, Guojun & Lin, X. Sheldon, 2015. "Valuation of large variable annuity portfolios under nested simulation: A functional data approach," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 138-150.
    14. Anne-Sophie Krah & Zoran Nikolić & Ralf Korn, 2020. "Machine Learning in Least-Squares Monte Carlo Proxy Modeling of Life Insurance Companies," Risks, MDPI, Open Access Journal, vol. 8(1), pages 1-79, February.
    15. James Risk & Michael Ludkovski, 2015. "Statistical Emulators for Pricing and Hedging Longevity Risk Products," Papers 1508.00310,, revised Sep 2015.
    16. Anne-Sophie Krah & Zoran Nikoli'c & Ralf Korn, 2019. "Machine Learning in Least-Squares Monte Carlo Proxy Modeling of Life Insurance Companies," Papers 1909.02182,
    17. Floryszczak, Anthony & Le Courtois, Olivier & Majri, Mohamed, 2016. "Inside the Solvency 2 Black Box: Net Asset Values and Solvency Capital Requirements with a least-squares Monte-Carlo approach," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 15-26.

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