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Optimal investment strategy for the DC plan with the return of premiums clauses in a mean–variance framework

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  • He, Lin
  • Liang, Zongxia

Abstract

In this paper, we study the optimal investment strategy in the DC pension plan during the accumulation phase. During the accumulation phase, a pension member contributes a predetermined amount of money as premiums and the management of the pension plan invests the premiums in equities and bonds to increase the value of the accumulation. In practice, most of the DC pension plans have return of premium clauses to protect the rights of the plan members who die during the accumulation phase. In the model, the members withdraw their premiums when they die and the difference between the premium and the accumulation (negative or positive) is distributed among the survival members. From the surviving members’ point of view, when they retire, they want to maximize the fund size and to minimize the volatility of the accumulation. We formalize the problem as a continuous-time mean–variance stochastic optimal control problem. The management of the pension plan chooses the optimal investment strategy, i.e., the proportions invested in equities and bonds, to maximize the mean–variance utility of the pension member at the time of retirement. Using the variational inequalities methods in Björk and Murgoci (2009), we transform the mean–variance stochastic control into Markovian time inconsistent stochastic control, then establish a verification theorem, which is similar to one of He and Liang (2008, 2009) and Zeng and Li (2011), to find the optimal strategy and the efficient frontier of the pension member. The differences of the optimal strategies between the Pension plans with and without the return of premium clauses are studied via the Monte Carlo methods. The impacts of the risk averse level on the optimal strategies is also explored by the numerical methods.

Suggested Citation

  • He, Lin & Liang, Zongxia, 2013. "Optimal investment strategy for the DC plan with the return of premiums clauses in a mean–variance framework," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 643-649.
  • Handle: RePEc:eee:insuma:v:53:y:2013:i:3:p:643-649
    DOI: 10.1016/j.insmatheco.2013.09.002
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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 & 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.
    3. 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.
    4. Liang, Zongxia & Ma, Ming, 2015. "Optimal dynamic asset allocation of pension fund in mortality and salary risks framework," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 151-161.
    5. repec:eee:insuma:v:79:y:2018:i:c:p:210-224 is not listed on IDEAS
    6. Liang, Zongxia & Sheng, Wenlong, 2016. "Valuing inflation-linked death benefits under a stochastic volatility framework," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 45-58.
    7. Calisto Guambe & Rodwell Kufakunesu & Gusti Van Zyl & Conrad Beyers, 2018. "Optimal asset allocation for a DC plan with partial information under inflation and mortality risks," Papers 1808.06337, arXiv.org, revised Aug 2018.
    8. repec:eee:insuma:v:76:y:2017:i:c:p:172-184 is not listed on IDEAS
    9. 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.
    10. repec:eee:dyncon:v:88:y:2018:i:c:p:70-103 is not listed on IDEAS
    11. 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.
    12. He, Lin & Liang, Zongxia, 2015. "Optimal assets allocation and benefit outgo policies of DC pension plan with compulsory conversion claims," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 227-234.

    More about this item

    Keywords

    DC pension plan; Markovian time inconsistent stochastic control; Mean–Variance stochastic control; Optimal asset allocation; Return of premiums clauses;

    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
    • G23 - Financial Economics - - Financial Institutions and Services - - - Non-bank Financial Institutions; Financial Instruments; Institutional Investors
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth
    • E22 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Investment; Capital; Intangible Capital; Capacity

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