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Constrained non-concave utility maximization: An application to life insurance contracts with guarantees

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  • Chen, An
  • Hieber, Peter
  • Nguyen, Thai

Abstract

We study a problem of non-concave utility maximization under a fair pricing constraint. The framework finds many applications in, for example, the optimal design of managerial compensation or equity-linked life insurance contracts. Deriving closed-form solutions, we observe that the fair pricing constraint will reduce the riskiness of the optimal strategies substantially. In an extensive numerical section, we analyze innovative retirement products that adapt the investment strategy of the premium pool according to the policyholder’s preferences, modeled as constant relative risk aversion (CRRA). Such products are a response to the loss of attractiveness of traditional life insurance contracts with guarantees that are negatively affected by increasing solvency requirements for return guarantees and a general decrease in interest rate levels. Taking into account that retirement products are usually tax-privileged, we find that fairly priced guarantee contracts that follow this optimal investment strategy lead to a higher expected utility level than asset investments.

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  • 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.
    • Handle: RePEc:eee:ejores:v:273:y:2019:i:3:p:1119-1135
    DOI: 10.1016/j.ejor.2018.09.002
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    Cited by:

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    2. Fangyuan Zhang, 2023. "Non-concave portfolio optimization with average value-at-risk," Mathematics and Financial Economics, Springer, volume 17, number 3, December.
    3. An Chen & Mitja Stadje & Fangyuan Zhang, 2020. "On the equivalence between Value-at-Risk- and Expected Shortfall-based risk measures in non-concave optimization," Papers 2002.02229, arXiv.org, revised Jun 2022.
    4. 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.
    5. Jennifer Alonso Garcia & Michael Sherris & Samuel Thirurajah & Jonathan Ziveyi, 2020. "Taxation and policyholder behavior: the case of guaranteed minimum accumulation benefits," ULB Institutional Repository 2013/307889, ULB -- Universite Libre de Bruxelles.
    6. Liu, Haibo & Tang, Qihe & Yuan, Zhongyi, 2021. "Indifference pricing of insurance-linked securities in a multi-period model," European Journal of Operational Research, Elsevier, vol. 289(2), pages 793-805.
    7. Chen, An & Nguyen, Thai & Rach, Manuel, 2021. "Optimal collective investment: The impact of sharing rules, management fees and guarantees," Journal of Banking & Finance, Elsevier, vol. 123(C).
    8. Chen, Chang-Chih & Chang, Chia-Chien & Sun, Edward W. & Yu, Min-Teh, 2022. "Optimal decision of dynamic wealth allocation with life insurance for mitigating health risk under market incompleteness," European Journal of Operational Research, Elsevier, vol. 300(2), pages 727-742.
    9. Dong, Yinghui & Zheng, Harry, 2020. "Optimal investment with S-shaped utility and trading and Value at Risk constraints: An application to defined contribution pension plan," European Journal of Operational Research, Elsevier, vol. 281(2), pages 341-356.
    10. Chen, An & Stadje, Mitja & Zhang, Fangyuan, 2024. "On the equivalence between Value-at-Risk- and Expected Shortfall-based risk measures in non-concave optimization," Insurance: Mathematics and Economics, Elsevier, vol. 117(C), pages 114-129.
    11. Hieber, Peter & Lucas, Nathalie, 2020. "Life-Care Tontines," LIDAM Discussion Papers ISBA 2020026, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    12. 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.
    13. 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.
    14. Christian Dehm & Thai Nguyen & Mitja Stadje, 2020. "Non-concave expected utility optimization with uncertain time horizon," Papers 2005.13831, arXiv.org, revised Oct 2021.
    15. Hanna, Vanessa & Hieber, Peter & Devolder, Pierre, 2021. "Mixed participating and unit-linked life insurance contracts: design, pricing and optimal strategy," LIDAM Discussion Papers ISBA 2021010, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    16. Bi, Xiuchun & Cui, Zhenyu & Fan, Jiacheng & Yuan, Lvning & Zhang, Shuguang, 2023. "Optimal investment problem under behavioral setting: A Lagrange duality perspective," Journal of Economic Dynamics and Control, Elsevier, vol. 156(C).
    17. Reichel, Lukas & Schmeiser, Hato & Schreiber, Florian, 2021. "Sometimes more, sometimes less: Prudence and the diversification of risky insurance coverage," European Journal of Operational Research, Elsevier, vol. 292(2), pages 770-783.

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