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Lifetime investment and consumption using a defined-contribution pension scheme

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  • Emms, Paul

Abstract

During the accumulation phase of a defined-contribution pension scheme, a scheme member invests part of their stochastic income in a portfolio of a stock and a bond in order to build up sufficient funds for retirement. It is assumed that the remainder of their salary pre-retirement is consumed, an annuity is purchased at retirement, and the stock allocation and consumption pre-retirement maximise the total expected lifetime consumption using a CARA utility function. Perfect correlation between the scheme member's income and the stock price leads to analytical expressions for the controls for a general income model. If the correlation is imperfect then analytical controls are found for two particular stochastic income models.

Suggested Citation

  • Emms, Paul, 2012. "Lifetime investment and consumption using a defined-contribution pension scheme," Journal of Economic Dynamics and Control, Elsevier, vol. 36(9), pages 1303-1321.
    • Handle: RePEc:eee:dyncon:v:36:y:2012:i:9:p:1303-1321
    DOI: 10.1016/j.jedc.2012.01.012
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    Cited by:

    1. Blake, David & Wright, Douglas & Zhang, Yumeng, 2014. "Age-dependent investing: Optimal funding and investment strategies in defined contribution pension plans when members are rational life cycle financial planners," Journal of Economic Dynamics and Control, Elsevier, vol. 38(C), pages 105-124.
    2. 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.
    3. 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.
    4. Blake, David & Wright, Douglas & Zhang, Yumeng, 2013. "Target-driven investing: Optimal investment strategies in defined contribution pension plans under loss aversion," Journal of Economic Dynamics and Control, Elsevier, vol. 37(1), pages 195-209.
    5. Han, Nan-Wei & Hung, Mao-Wei, 2015. "The investment management for a downside-protected equity-linked annuity under interest rate risk," Finance Research Letters, Elsevier, vol. 13(C), pages 113-124.
    6. Guohui Guan & Zongxia Liang & Yi Xia, 2023. "Optimal management of DB pension fund under both underfunded and overfunded cases," Papers 2302.08731, arXiv.org.
    7. Wang, Peiguang & Wang, Zihui & Wang, Wenli, 2024. "Modeling mispricing risk of defined contribution pension plan with a mean–variance criteria," The North American Journal of Economics and Finance, Elsevier, vol. 74(C).
    8. Yao, Haixiang & Lai, Yongzeng & Ma, Qinghua & Jian, Minjie, 2014. "Asset allocation for a DC pension fund with stochastic income and mortality risk: A multi-period mean–variance framework," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 84-92.
    9. 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.
    10. Chen, Zheng & Li, Zhongfei & Zeng, Yan & Sun, Jingyun, 2017. "Asset allocation under loss aversion and minimum performance constraint in a DC pension plan with inflation risk," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 137-150.
    11. Pagnoncelli, Bernardo K. & Homem-de-Mello, Tito & Lagos, Guido & Castañeda, Pablo & García, Javier, 2024. "Solving constrained consumption–investment problems by decomposition algorithms," European Journal of Operational Research, Elsevier, vol. 319(1), pages 292-302.

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    More about this item

    Keywords

    Defined-contribution pension; Lifecycle model; Stochastic income; Replacement ratio;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making

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