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Markowitz’s mean–variance defined contribution pension fund management under inflation: A continuous-time model

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  • Yao, Haixiang
  • Yang, Zhou
  • Chen, Ping

Abstract

In defined contribution (DC) pension schemes, the financial risk borne by the member occurs during the accumulation phase. To build up sufficient funds for retirement, scheme members invest their wealth in a portfolio of assets. This paper considers an optimal investment problem of a scheme member facing stochastic inflation under the Markowitz mean–variance criterion. Besides, we consider a more general market with multiple assets that can all be risky. By applying the Lagrange method and stochastic dynamic programming techniques, we derive the associated Hamilton–Jacobi–Bellman (HJB) equation, which can be converted into six correlated but relatively simple partial differential equations (PDEs). The explicit solutions for these six PDEs are derived by using the homogenization approach and the variable transformation technique. Then the closed-form expressions for the optimal strategy and the efficient frontier can be obtained through the Lagrange dual theory. In addition, we illustrate the results by some numerical examples.

Suggested Citation

  • Yao, Haixiang & Yang, Zhou & Chen, Ping, 2013. "Markowitz’s mean–variance defined contribution pension fund management under inflation: A continuous-time model," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 851-863.
  • Handle: RePEc:eee:insuma:v:53:y:2013:i:3:p:851-863
    DOI: 10.1016/j.insmatheco.2013.10.002
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. 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.
    2. Wu, Huiling & Zhang, Ling & Chen, Hua, 2015. "Nash equilibrium strategies for a defined contribution pension management," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 202-214.
    3. repec:eee:insuma:v:79:y:2018:i:c:p:210-224 is not listed on IDEAS
    4. repec:eee:insuma:v:76:y:2017:i:c:p:172-184 is not listed on IDEAS
    5. repec:gam:jrisks:v:6:y:2018:i:2:p:24-:d:137519 is not listed on IDEAS
    6. Xiaoxiao Zheng & Xin Zhang, 2014. "Optimal investment-reinsurance policy under a long-term perspective," Papers 1406.7604, arXiv.org.
    7. Guan, Guohui & Liang, Zongxia, 2016. "Optimal management of DC pension plan under loss aversion and Value-at-Risk constraints," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 224-237.
    8. 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.
    9. Sun, Jingyun & Li, Zhongfei & Zeng, Yan, 2016. "Precommitment and equilibrium investment strategies for defined contribution pension plans under a jump–diffusion model," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 158-172.
    10. Li, Shaoyu & Wei, Lijia & Xu, Zhiwei, 2017. "Dynamic asset allocation and consumption under inflation inequality: The impacts of inflation experiences and expectations," Economic Modelling, Elsevier, vol. 61(C), pages 113-125.
    11. 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.

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