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Robust evaluation of SCR for participating life insurances under Solvency II

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  • Hainaut, Donatien
  • Devolder, Pierre
  • Pelsser, Antoon

Abstract

This article proposes a robust framework to evaluate the solvency capital requirement (SCR) of a participating life insurance with death benefits. The preference for robustness arises from the ambiguity caused by the market incompleteness, model shortcomings and parameters misspecifications. To incorporate the uncertainty in the procedure of evaluation, we consider a set of potential equivalent pricing measures in the neighborhood of the real one. In this framework, closed form expressions for the net asset value (NAV) and for its moments are found. The SCR is next approximated by the Value at Risk of Gaussian or normal inverse Gaussian (NIG) random variables, approaching the NAV distribution and fitted by moments matching.

Suggested Citation

  • Hainaut, Donatien & Devolder, Pierre & Pelsser, Antoon, 2018. "Robust evaluation of SCR for participating life insurances under Solvency II," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 107-123.
    • Handle: RePEc:eee:insuma:v:79:y:2018:i:c:p:107-123
    DOI: 10.1016/j.insmatheco.2017.11.009
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    1. John H. Cochrane & Jesus Saa-Requejo, 2000. "Beyond Arbitrage: Good-Deal Asset Price Bounds in Incomplete Markets," Journal of Political Economy, University of Chicago Press, vol. 108(1), pages 79-119, February.
    2. Massimo Guidolin & Francesca Rinaldi, 2013. "Ambiguity in asset pricing and portfolio choice: a review of the literature," Theory and Decision, Springer, vol. 74(2), pages 183-217, February.
    3. Elisa Luciano & Luca Regis & Elena Vigna, 2017. "Single- and Cross-Generation Natural Hedging of Longevity and Financial Risk," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(3), pages 961-986, September.
    4. Maenhout, Pascal J., 2006. "Robust portfolio rules and detection-error probabilities for a mean-reverting risk premium," Journal of Economic Theory, Elsevier, vol. 128(1), pages 136-163, May.
    5. Deelstra, Griselda & Grasselli, Martino & Van Weverberg, Christopher, 2016. "The role of the dependence between mortality and interest rates when pricing Guaranteed Annuity Options," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 205-219.
    6. Tomas Björk & Irina Slinko, 2006. "Towards a General Theory of Good-Deal Bounds," Review of Finance, European Finance Association, vol. 10(2), pages 221-260.
    7. Hainaut, Donatien, 2016. "Impact of volatility clustering on equity indexed annuities," LIDAM Reprints ISBA 2016045, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Hainaut, Donatien, 2016. "Impact of volatility clustering on equity indexed annuities," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 367-381.
    9. Pascal J. Maenhout, 2004. "Robust Portfolio Rules and Asset Pricing," The Review of Financial Studies, Society for Financial Studies, vol. 17(4), pages 951-983.
    10. LUCIANO, Elisa & VIGNA, Elena, 2008. "Mortality risk via affine stochastic intensities: calibration and empirical relevance," MPRA Paper 59627, University Library of Munich, Germany.
    11. Catherine Donnelly, 2011. "Good-Deal Bounds in a Regime-Switching Diffusion Market," Applied Mathematical Finance, Taylor & Francis Journals, vol. 18(6), pages 491-515, May.
    12. Lars Peter Hansen & Thomas J Sargent, 2014. "A Quartet of Semigroups for Model Specification, Robustness, Prices of Risk, and Model Detection," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 4, pages 83-143, World Scientific Publishing Co. Pte. Ltd..
    13. Bauer, Daniel & Börger, Matthias & Ruß, Jochen, 2010. "On the pricing of longevity-linked securities," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 139-149, February.
    14. Lars Peter Hansen & Thomas J Sargent, 2014. "Robust Control and Model Uncertainty," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 5, pages 145-154, World Scientific Publishing Co. Pte. Ltd..
    15. 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.
    16. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    17. Anthony Floryszczak & Olivier Le Courtois & Mohamed Majri, 2016. "Inside the Solvency 2 Black Box : Net asset values and solvency capital requirements with a least-squares Monte-Carlo approach," Post-Print hal-02313445, HAL.
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    Cited by:

    1. Philippe ARTZNER & Karl-Theodor EISELE & Thorsten SCHMIDT, 2022. "Insurance-Finance Arbitrage," Working Papers of LaRGE Research Center 2022-09, Laboratoire de Recherche en Gestion et Economie (LaRGE), Université de Strasbourg.
    2. Flores, Eduardo & de Carvalho, João Vinicius França & Sampaio, Joelson Oliveira, 2021. "Impact of interest rates on the life insurance market development: Cross-country evidence," Research in International Business and Finance, Elsevier, vol. 58(C).
    3. Hainaut, Donatien & Devineau, Laurent, 2024. "Participating life insurances in an equity-Libor Market Model," LIDAM Discussion Papers ISBA 2024015, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Shuai Yang & Kenneth Q. Zhou, 2023. "On Risk Management of Mortality and Longevity Capital Requirement: A Predictive Simulation Approach," Risks, MDPI, vol. 11(12), pages 1-18, November.

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