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Optimal control problem for hybrid pension plans under longevity risk for alpha-maxmin expected utility minimization

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  • Chen, Ya
  • Liu, Wei
  • Zhao, Zhen

Abstract

This paper investigates the problem of portfolio selection and adjustment of hybrid pension plans under longevity risk. The longevity risk is described by a time-varying mortality rate, which is an extension of Markham’s law. Suppose that the financial market assets consist of a risk-free asset, a stock, and a defaultable bond. Specifically, the stock price is described by a constant elasticity of variance (CEV) model. The objective is to minimize interim adjustments to contributions and benefits under an exponential loss function, as well as the loss of terminal wealth. It is difficult for investors to fully understand the market information, so there is uncertainty in the financial market. By applying robust control theory to formulate investors’ aversion to uncertainty, we obtain the α-robust optimal investment strategies and the adjustment strategies. Finally, numerical analysis is presented to discuss the influence of the model parameters on the α-robust optimal control strategies.

Suggested Citation

  • Chen, Ya & Liu, Wei & Zhao, Zhen, 2025. "Optimal control problem for hybrid pension plans under longevity risk for alpha-maxmin expected utility minimization," The North American Journal of Economics and Finance, Elsevier, vol. 75(PA).
    • Handle: RePEc:eee:ecofin:v:75:y:2025:i:pa:s1062940824002109
    DOI: 10.1016/j.najef.2024.102285
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    References listed on IDEAS

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    1. Li, Bin & Li, Danping & Xiong, Dewen, 2016. "Alpha-robust mean-variance reinsurance-investment strategy," Journal of Economic Dynamics and Control, Elsevier, vol. 70(C), pages 101-123.
    2. Coen Teulings & Casper Vries, 2006. "Generational Accounting, Solidarity and Pension Losses," De Economist, Springer, vol. 154(1), pages 63-83, March.
    3. Peter Bossaerts & Paolo Ghirardato & Serena Guarnaschelli & William R. Zame, 2010. "Ambiguity in Asset Markets: Theory and Experiment," The Review of Financial Studies, Society for Financial Studies, vol. 23(4), pages 1325-1359, April.
    4. He, Lin & Liang, Zongxia & Wang, Sheng, 2022. "Dynamic optimal adjustment policies of hybrid pension plans," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 46-68.
    5. Li, Danping & Rong, Ximin & Zhao, Hui & Yi, Bo, 2017. "Equilibrium investment strategy for DC pension plan with default risk and return of premiums clauses under CEV model," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 6-20.
    6. Zhilin Kang & Xun Li & Zhongfei Li & Shushang Zhu, 2019. "Data-driven robust mean-CVaR portfolio selection under distribution ambiguity," Quantitative Finance, Taylor & Francis Journals, vol. 19(1), pages 105-121, January.
    7. Wang, Suxin & Rong, Ximin & Zhao, Hui, 2019. "Optimal investment and benefit payment strategy under loss aversion for target benefit pension plans," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 205-218.
    8. M. A. Milevsky & S. D. Promislow & V. R. Young, 2006. "Killing the Law of Large Numbers: Mortality Risk Premiums and the Sharpe Ratio," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(4), pages 673-686, December.
    9. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    10. Massimo Marinacci, 2002. "Probabilistic Sophistication and Multiple Priors," Econometrica, Econometric Society, vol. 70(2), pages 755-764, March.
    11. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2005. "A Smooth Model of Decision Making under Ambiguity," Econometrica, Econometric Society, vol. 73(6), pages 1849-1892, November.
    12. Knell, Markus, 2018. "Increasing life expectancy and NDC pension systems," Journal of Pension Economics and Finance, Cambridge University Press, vol. 17(2), pages 170-199, April.
    13. Zhang, Liming & Li, Bin, 2021. "Optimal reinsurance under the α-maxmin mean-variance criterion," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 225-239.
    14. Baumann, Roger T. & Müller, Heinz H., 2008. "Pension funds as institutions for intertemporal risk transfer," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1000-1012, June.
    15. Wang, Pei & Li, Zhongfei, 2018. "Robust optimal investment strategy for an AAM of DC pension plans with stochastic interest rate and stochastic volatility," Insurance: Mathematics and Economics, Elsevier, vol. 80(C), pages 67-83.
    16. Zhao, Hui & Wang, Suxin, 2022. "Optimal investment and benefit adjustment problem for a target benefit pension plan with Cobb-Douglas utility and Epstein-Zin recursive utility," European Journal of Operational Research, Elsevier, vol. 301(3), pages 1166-1180.
    17. Cairns, Andrew J.G. & Blake, David & Dowd, Kevin, 2006. "Pricing Death: Frameworks for the Valuation and Securitization of Mortality Risk," ASTIN Bulletin, Cambridge University Press, vol. 36(1), pages 79-120, May.
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    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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