IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2407.11761.html
   My bibliography  Save this paper

Mean-Variance Optimization for Participating Life Insurance Contracts

Author

Listed:
  • Felix Fie{ss}inger
  • Mitja Stadje

Abstract

This paper studies the equity holders' mean-variance optimal portfolio choice problem for (non-)protected participating life insurance contracts. We derive explicit formulas for the optimal terminal wealth and the optimal strategy in the multi-dimensional Black-Scholes model, showing the existence of all necessary parameters. In incomplete markets, we state Hamilton-Jacobi-Bellman equations for the value function. Moreover, we provide a numerical analysis of the Black-Scholes market. The equity holders on average increase their investment into the risky asset in bad economic states and decrease their investment over time.

Suggested Citation

  • Felix Fie{ss}inger & Mitja Stadje, 2024. "Mean-Variance Optimization for Participating Life Insurance Contracts," Papers 2407.11761, arXiv.org.
    • Handle: RePEc:arx:papers:2407.11761
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2407.11761
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Lin, Hongcan & Saunders, David & Weng, Chengguo, 2017. "Optimal investment strategies for participating contracts," Insurance: Mathematics and Economics, Elsevier, vol. 73(C), pages 137-155.
    2. Chen, An & Nguyen, Thai & Stadje, Mitja, 2018. "Optimal investment under VaR-Regulation and Minimum Insurance," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 194-209.
    3. Kasper Larsen, 2005. "Optimal portfolio delegation when parties have different coefficients of risk aversion," Quantitative Finance, Taylor & Francis Journals, vol. 5(5), pages 503-512.
    4. Domenico Cuoco & Hua He & Sergei Isaenko, 2008. "Optimal Dynamic Trading Strategies with Risk Limits," Operations Research, INFORMS, vol. 56(2), pages 358-368, April.
    5. Yinghui Dong & Sang Wu & Wenxin Lv & Guojing Wang, 2020. "Optimal asset allocation for participating contracts under the VaR and PI constraint," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2020(2), pages 84-109, February.
    6. Lin He & Zongxia Liang & Yang Liu & Ming Ma, 2020. "Weighted utility optimization of the participating endowment contract," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2020(7), pages 577-613, August.
    7. Hato Schmeiser & Joël Wagner, 2015. "A Proposal on How the Regulator Should Set Minimum Interest Rate Guarantees in Participating Life Insurance Contracts," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 82(3), pages 659-686, September.
    8. Hui Mi & Zuo Quan Xu & Dongfang Yang, 2023. "Optimal Management of DC Pension Plan with Inflation Risk and Tail VaR Constraint," Papers 2309.01936, arXiv.org.
    9. Merton, Robert C., 1972. "An Analytic Derivation of the Efficient Portfolio Frontier," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 7(4), pages 1851-1872, September.
    10. Anna Rita Bacinello & Svein‐Arne Persson, 2002. "Design and Pricing of Equity‐Linked Life Insurance under Stochastic Interest Rates," Journal of Risk Finance, Emerald Group Publishing Limited, vol. 3(2), pages 6-21, January.
    11. Sang Wu & Yinghui Dong & Wenxin Lv & Guojing Wang, 2020. "Optimal asset allocation for participating contracts with mortality risk under minimum guarantee," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(14), pages 3481-3497, July.
    12. Hakansson, Nils H., 1971. "Capital Growth and the Mean-Variance Approach to Portfolio Selection," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 6(1), pages 517-557, January.
    13. Nadine Gatzert & Alexander Kling, 2007. "Analysis of Participating Life Insurance Contracts: A Unification Approach," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 74(3), pages 547-570, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Christian Dehm & Thai Nguyen & Mitja Stadje, 2020. "Non-concave expected utility optimization with uncertain time horizon," Papers 2005.13831, arXiv.org, revised Oct 2021.
    2. Thai Nguyen & Mitja Stadje, 2018. "Optimal investment for participating insurance contracts under VaR-Regulation," Papers 1805.09068, arXiv.org, revised Jul 2019.
    3. 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.
    4. Anne MacKay & Adriana Ocejo, 2022. "Portfolio Optimization With a Guaranteed Minimum Maturity Benefit and Risk-Adjusted Fees," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 1021-1049, June.
    5. Fu, Chenpeng & Lari-Lavassani, Ali & Li, Xun, 2010. "Dynamic mean-variance portfolio selection with borrowing constraint," European Journal of Operational Research, Elsevier, vol. 200(1), pages 312-319, January.
    6. Hui Mi & Zuo Quan Xu & Dongfang Yang, 2023. "Optimal Management of DC Pension Plan with Inflation Risk and Tail VaR Constraint," Papers 2309.01936, arXiv.org.
    7. L.J. Basson & Sune Ferreira-Schenk & Zandri Dickason-Koekemoer, 2022. "Fractal Dimension Option Hedging Strategy Implementation During Turbulent Market Conditions in Developing and Developed Countries," International Journal of Economics and Financial Issues, Econjournals, vol. 12(2), pages 84-95, March.
    8. 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.
    9. Fangyuan Zhang, 2023. "Non-concave portfolio optimization with average value-at-risk," Mathematics and Financial Economics, Springer, volume 17, number 3, December.
    10. Ankush Agarwal & Christian-Oliver Ewald & Yongjie Wang, 2023. "Hedging longevity risk in defined contribution pension schemes," Computational Management Science, Springer, vol. 20(1), pages 1-34, December.
    11. An Chen & Thai Nguyen & Mitja Stadje, 2018. "Risk management with multiple VaR constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 88(2), pages 297-337, October.
    12. Yuanyuan Zhang & Xiang Li & Sini Guo, 2018. "Portfolio selection problems with Markowitz’s mean–variance framework: a review of literature," Fuzzy Optimization and Decision Making, Springer, vol. 17(2), pages 125-158, June.
    13. Gordon J. Alexander & Alexandre M. Baptista, 2004. "A Comparison of VaR and CVaR Constraints on Portfolio Selection with the Mean-Variance Model," Management Science, INFORMS, vol. 50(9), pages 1261-1273, September.
    14. Muhinyuza, Stanislas & Bodnar, Taras & Lindholm, Mathias, 2020. "A test on the location of the tangency portfolio on the set of feasible portfolios," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    15. Malavasi, Matteo & Ortobelli Lozza, Sergio & Trück, Stefan, 2021. "Second order of stochastic dominance efficiency vs mean variance efficiency," European Journal of Operational Research, Elsevier, vol. 290(3), pages 1192-1206.
    16. Markowitz, Harry, 2014. "Mean–variance approximations to expected utility," European Journal of Operational Research, Elsevier, vol. 234(2), pages 346-355.
    17. Dong, Yinghui & Zheng, Harry, 2019. "Optimal investment of DC pension plan under short-selling constraints and portfolio insurance," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 47-59.
    18. Zhang, Nan & Jin, Zhuo & Li, Shuanming & Chen, Ping, 2016. "Optimal reinsurance under dynamic VaR constraint," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 232-243.
    19. Shuzhen Yang, 2019. "A varying terminal time mean-variance model," Papers 1909.13102, arXiv.org, revised Jan 2020.
    20. Alexander, Gordon J. & Baptista, Alexandre M. & Yan, Shu, 2012. "When more is less: Using multiple constraints to reduce tail risk," Journal of Banking & Finance, Elsevier, vol. 36(10), pages 2693-2716.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2407.11761. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.