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On the optimal design of insurance contracts with guarantees

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  • Branger, Nicole
  • Mahayni, Antje
  • Schneider, Judith C.

Abstract

The paper analyzes insurance contracts where the benefits of the insured depend on the performance of an investment strategy and which guarantee a certain interest rate on the contributions made by the insured. The insured has to decide simultaneously on the investment strategy and the guarantee scheme. For a CRRA insured and in a BS economy, the optimal combination is given by a constant mix strategy and the contribution guarantee scheme. In case the insured has a subsistence level, the CPPI strategy turns out to be optimal for arbitrary schemes. We illustrate our results by numerical examples and analyze the utility losses of a CRRA insured due to the use of a suboptimal combination of investment strategy and guarantee scheme.

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  • Branger, Nicole & Mahayni, Antje & Schneider, Judith C., 2010. "On the optimal design of insurance contracts with guarantees," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 485-492, June.
    • Handle: RePEc:eee:insuma:v:46:y:2010:i:3:p:485-492
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    Cited by:

    1. Dupret, Jean-Loup & Hainaut, Donatien, 2021. "Portfolio insurance under rough volatility and Volterra processes," LIDAM Discussion Papers ISBA 2021026, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Nielsen, J. Aase & Sandmann, Klaus & Schlögl, Erik, 2011. "Equity-linked pension schemes with guarantees," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 547-564.
    3. Mahayni, Antje & Schneider, Judith C., 2012. "Variable annuities and the option to seek risk: Why should you diversify?," Journal of Banking & Finance, Elsevier, vol. 36(9), pages 2417-2428.
    4. Daliana Luca & Hato Schmeiser & Florian Schreiber, 2023. "Investment guarantees in financial products: an analysis of consumer preferences," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 48(4), pages 906-940, October.
    5. Thai Nguyen & Mitja Stadje, 2018. "Optimal investment for participating insurance contracts under VaR-Regulation," Papers 1805.09068, arXiv.org, revised Jul 2019.
    6. Schmeiser, H. & Wagner, J., 2011. "A joint valuation of premium payment and surrender options in participating life insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 580-596.
    7. Alexander Bohnert, 2015. "The Impact of Guarantees on the Performance of Pension Saving Schemes: Insights from the Literature," Risks, MDPI, vol. 3(4), pages 1-28, November.
    8. Antje Mahayni & Oliver Lubos & Sascha Offermann, 2021. "Minimum return rate guarantees under default risk: optimal design of quantile guarantees," Review of Managerial Science, Springer, vol. 15(7), pages 1821-1848, October.
    9. Marcos Escobar-Anel & Andreas Lichtenstern & Rudi Zagst, 2020. "Behavioral portfolio insurance strategies," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 34(4), pages 353-399, December.
    10. Gatzert, Nadine, 2019. "An analysis of transaction costs in participating life insurance under mean–variance preferences," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 185-197.
    11. Chen, An & Hentschel, Felix & Klein, Jakob K., 2015. "A utility- and CPT-based comparison of life insurance contracts with guarantees," Journal of Banking & Finance, Elsevier, vol. 61(C), pages 327-339.
    12. Antje Mahayni & Judith C. Schneider, 2016. "Minimum return guarantees, investment caps, and investment flexibility," Review of Derivatives Research, Springer, vol. 19(2), pages 85-111, July.
    13. Chen, An & Hieber, Peter & Nguyen, Thai, 2019. "Constrained non-concave utility maximization: An application to life insurance contracts with guarantees," European Journal of Operational Research, Elsevier, vol. 273(3), pages 1119-1135.
    14. Tang, Chun-Hua, 2018. "Subjective value of the guarantees embedded in public cash-balance pension plans," Journal of Pension Economics and Finance, Cambridge University Press, vol. 17(2), pages 231-250, April.
    15. Guohui Guan & Lin He & Zongxia Liang & Litian Zhang, 2024. "Optimal VPPI strategy under Omega ratio with stochastic benchmark," Papers 2403.13388, arXiv.org.

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