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Mean–variance efficiency of DC pension plan under stochastic interest rate and mean-reverting returns

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  • Guan, Guohui
  • Liang, Zongxia

Abstract

This paper studies the optimization problem of DC pension plan under mean–variance criterion. The financial market consists of cash, bond and stock. Similar to Guan and Liang (2014), we assume that the instantaneous interest rate is an affine process including the Cox–Ingersoll–Ross (CIR) model and Vasicek model. However, we assume that the expected return of the stock follows a completely different mean-reverting process, which can well display the bear and bull features of the market, and the market price of the stock index is the Ornstein–Uhlenbeck process. The pension manager thus has to undertake the risks of interest rate and market price of stock index. Besides, a special stochastic contribution rate is formulated. The goal of the pension manager is to maximize the expected terminal value and minimize the variance of terminal value. We will use the technique developed by Guan and Liang (2014) to tackle this problem and derive the closed-forms of efficient frontier and strategies. Numerical analysis is given in the end of this paper to show the economic behavior of the efficient frontier and strategies.

Suggested Citation

  • Guan, Guohui & Liang, Zongxia, 2015. "Mean–variance efficiency of DC pension plan under stochastic interest rate and mean-reverting returns," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 99-109.
    • Handle: RePEc:eee:insuma:v:61:y:2015:i:c:p:99-109
    DOI: 10.1016/j.insmatheco.2014.12.006
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    Cited by:

    1. Zhiping Chen & Liyuan Wang & Ping Chen & Haixiang Yao, 2019. "Continuous-Time Mean–Variance Optimization For Defined Contribution Pension Funds With Regime-Switching," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(06), pages 1-33, September.
    2. Wang, Pei & Shen, Yang & Zhang, Ling & Kang, Yuxin, 2021. "Equilibrium investment strategy for a DC pension plan with learning about stock return predictability," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 384-407.
    3. Walter Mudzimbabwe, 2020. "A time consistent derivative strategy," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 7(01), pages 1-25, March.
    4. Li, Yuying & Forsyth, Peter A., 2019. "A data-driven neural network approach to optimal asset allocation for target based defined contribution pension plans," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 189-204.
    5. Guan, Guohui & Liang, Zongxia & Xia, Yi, 2023. "Optimal management of DC pension fund under the relative performance ratio and VaR constraint," European Journal of Operational Research, Elsevier, vol. 305(2), pages 868-886.
    6. Guohui Guan, 2020. "Equilibrium and Precommitment Mean-Variance Portfolio Selection Problem with Partially Observed Price Index and Multiple Assets," Methodology and Computing in Applied Probability, Springer, vol. 22(1), pages 25-47, March.
    7. Liyuan Wang & Zhiping Chen, 2019. "Stochastic Game Theoretic Formulation for a Multi-Period DC Pension Plan with State-Dependent Risk Aversion," Mathematics, MDPI, vol. 7(1), pages 1-16, January.
    8. Bian, Lihua & Li, Zhongfei & Yao, Haixiang, 2018. "Pre-commitment and equilibrium investment strategies for the DC pension plan with regime switching and a return of premiums clause," Insurance: Mathematics and Economics, Elsevier, vol. 81(C), pages 78-94.
    9. Yao, Haixiang & Chen, Ping & Li, Xun, 2016. "Multi-period defined contribution pension funds investment management with regime-switching and mortality risk," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 103-113.
    10. Yang Wang & Xiao Xu & Jizhou Zhang, 2021. "Optimal Investment Strategy for DC Pension Plan with Stochastic Income and Inflation Risk under the Ornstein–Uhlenbeck Model," Mathematics, MDPI, vol. 9(15), pages 1-15, July.
    11. Wu, Huiling & Zeng, Yan, 2015. "Equilibrium investment strategy for defined-contribution pension schemes with generalized mean–variance criterion and mortality risk," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 396-408.
    12. Frank Bosserhoff & An Chen & Nils Sorensen & Mitja Stadje, 2021. "On the Investment Strategies in Occupational Pension Plans," Papers 2104.08956, arXiv.org.
    13. Ng, Kenneth Tsz Hin & Chong, Wing Fung, 2024. "Optimal investment in defined contribution pension schemes with forward utility preferences," Insurance: Mathematics and Economics, Elsevier, vol. 114(C), pages 192-211.
    14. Zeng, Yan & Li, Danping & Chen, Zheng & Yang, Zhou, 2018. "Ambiguity aversion and optimal derivative-based pension investment with stochastic income and volatility," Journal of Economic Dynamics and Control, Elsevier, vol. 88(C), pages 70-103.
    15. Yumo Zhang, 2022. "Dynamic optimal mean-variance portfolio selection with stochastic volatility and stochastic interest rate," Annals of Finance, Springer, vol. 18(4), pages 511-544, December.
    16. Guan, Guohui & Liang, Zongxia, 2019. "Robust optimal reinsurance and investment strategies for an AAI with multiple risks," Insurance: Mathematics and Economics, Elsevier, vol. 89(C), pages 63-78.
    17. Menoncin, Francesco & Vigna, Elena, 2017. "Mean–variance target-based optimisation for defined contribution pension schemes in a stochastic framework," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 172-184.
    18. Szymon Peszat & Dariusz Zawisza, 2020. "The investor problem based on the HJM model," Papers 2010.13915, arXiv.org, revised Dec 2021.
    19. Li, Danping & Rong, Ximin & Zhao, Hui, 2015. "Time-consistent reinsurance–investment strategy for a mean–variance insurer under stochastic interest rate model and inflation risk," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 28-44.
    20. Manli Ban & Hua He & Xiaoqing Liang, 2022. "Optimal Investment Strategy for DC Pension Schemes under Partial Information," Risks, MDPI, vol. 10(11), pages 1-20, November.
    21. Guan, Guohui & Liang, Zongxia, 2016. "A stochastic Nash equilibrium portfolio game between two DC pension funds," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 237-244.
    22. Liang, Zongxia & Zhao, Xiaoyang, 2016. "Optimal mean–variance efficiency of a family with life insurance under inflation risk," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 164-178.

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    More about this item

    Keywords

    IB13; IE12; IE13; IE43; Defined contribution pension plan; Stochastic interest rate; Mean-reverting returns; Stochastic market price of risk; Mean–variance efficiency; Stochastic dynamic programming;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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