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Target benefit pension with longevity risk and stochastic interest rate valuation

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  • Tao, Cheng
  • Rong, Ximin
  • Zhao, Hui

Abstract

This paper introduces a target benefit pension (TBP) model that integrates both longevity risk and stochastic interest rate valuation. The TBP benefit incorporates a fixed target benefit annuity and a dynamic adjustment term, determined through a stochastic control problem. To capture the dynamic nature of average remaining lifespan influenced by longevity risk, we combine a linear function with an Ornstein-Uhlenbeck (OU) process to model the evolving average remaining lifespan. We evaluate the expected discounted value of the target benefit annuity, taking into account stochastic interest rates and the dynamic average remaining lifespan. The pension fund trustee strategically invests in both risk-free and risky assets, framing a stochastic control problem with control variables that include asset allocation and the overall adjustment term. This paper advances pension theory by introducing a novel longevity risk model and enhancing the potential of TBP for intergenerational risk sharing.

Suggested Citation

  • Tao, Cheng & Rong, Ximin & Zhao, Hui, 2025. "Target benefit pension with longevity risk and stochastic interest rate valuation," Insurance: Mathematics and Economics, Elsevier, vol. 120(C), pages 285-301.
    • Handle: RePEc:eee:insuma:v:120:y:2025:i:c:p:285-301
    DOI: 10.1016/j.insmatheco.2024.12.003
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    References listed on IDEAS

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    1. Zhou, Hongjuan & Zhou, Kenneth Q. & Li, Xianping, 2022. "Stochastic mortality dynamics driven by mixed fractional Brownian motion," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 218-238.
    2. Rong, Ximin & Tao, Cheng & Zhao, Hui, 2023. "Target benefit pension plan with longevity risk and intergenerational equity – CORRIGENDUM," ASTIN Bulletin, Cambridge University Press, vol. 53(2), pages 488-488, May.
    3. John Hull & Alan White, 2001. "The General Hull–White Model and Supercalibration," Financial Analysts Journal, Taylor & Francis Journals, vol. 57(6), pages 34-43, November.
    4. Moore Mark A. & Boardman Anthony E. & Vining Aidan R., 2013. "More appropriate discounting: the rate of social time preference and the value of the social discount rate," Journal of Benefit-Cost Analysis, De Gruyter, vol. 4(1), pages 1-16, March.
    5. Zhu, Xiaobai & Hardy, Mary & Saunders, David, 2021. "Fair Transition From Defined Benefit To Target Benefit," ASTIN Bulletin, Cambridge University Press, vol. 51(3), pages 873-904, September.
    6. Perry, David & Stadje, Wolfgang, 2001. "Function space integration for annuities," Insurance: Mathematics and Economics, Elsevier, vol. 29(1), pages 73-82, August.
    7. Shripad Tuljapurkar, 2010. "The Final Inequality: Variance in Age at Death," NBER Chapters, in: Demography and the Economy, pages 209-221, National Bureau of Economic Research, Inc.
    8. Biffis, Enrico, 2005. "Affine processes for dynamic mortality and actuarial valuations," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 443-468, December.
    9. Beekman, John A. & Fuelling, Clinton P., 1990. "Interest and mortality randomness in some annuities," Insurance: Mathematics and Economics, Elsevier, vol. 9(2-3), pages 185-196, September.
    10. Wang, Suxin & Lu, Yi, 2019. "Optimal investment strategies and risk-sharing arrangements for a hybrid pension plan," Insurance: Mathematics and Economics, Elsevier, vol. 89(C), pages 46-62.
    11. Rong, Ximin & Tao, Cheng & Zhao, Hui, 2023. "Target benefit pension plan with longevity risk and intergenerational equity," ASTIN Bulletin, Cambridge University Press, vol. 53(1), pages 84-103, January.
    12. De Schepper, A. & De Vylder, F. & Goovaerts, M. & Kaas, R., 1992. "Interest randomness in annuities certain," Insurance: Mathematics and Economics, Elsevier, vol. 11(4), pages 271-281, December.
    13. Huang, Huaxiong & Milevsky, Moshe A. & Salisbury, Thomas S., 2012. "Optimal retirement consumption with a stochastic force of mortality," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 282-291.
    14. Wang, Suxin & Lu, Yi & Sanders, Barbara, 2018. "Optimal investment strategies and intergenerational risk sharing for target benefit pension plans," Insurance: Mathematics and Economics, Elsevier, vol. 80(C), pages 1-14.
    15. Vanneste, M. & Goovaerts, M. J. & De Schepper, A. & Dhaene, J., 1997. "A straightforward analytical calculation of the distribution of an annuity certain with stochastic interest rate," Insurance: Mathematics and Economics, Elsevier, vol. 20(1), pages 35-41, June.
    16. Wang, Ling & Wong, Hoi Ying, 2021. "Time-consistent longevity hedging with long-range dependence," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 25-41.
    17. De Schepper, A. & Goovaerts, M., 1992. "Some further results on annuities certain with random interest," Insurance: Mathematics and Economics, Elsevier, vol. 11(4), pages 283-290, December.
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