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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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    References listed on IDEAS

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    1. John Y. Campbell & Luis M. Viceira, 1999. "Consumption and Portfolio Decisions when Expected Returns are Time Varying," The Quarterly Journal of Economics, Oxford University Press, vol. 114(2), pages 433-495.
    2. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    3. Epstein, Larry G & Zin, Stanley E, 1989. "Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: A Theoretical Framework," Econometrica, Econometric Society, vol. 57(4), pages 937-969, July.
    4. Henderson, Vicky, 2005. "Explicit solutions to an optimal portfolio choice problem with stochastic income," Journal of Economic Dynamics and Control, Elsevier, vol. 29(7), pages 1237-1266, July.
    5. Paul A. Samuelson, 2011. "Lifetime Portfolio Selection by Dynamic Stochastic Programming," World Scientific Book Chapters,in: THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE, chapter 31, pages 465-472 World Scientific Publishing Co. Pte. Ltd..
    6. Hyeng Keun Koo, 1998. "Consumption and Portfolio Selection with Labor Income: A Continuous Time Approach," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 49-65.
    7. Kahl, Matthias & Liu, Jun & Longstaff, Francis A., 2003. "Paper millionaires: how valuable is stock to a stockholder who is restricted from selling it?," Journal of Financial Economics, Elsevier, vol. 67(3), pages 385-410, March.
    8. Cairns, Andrew J.G. & Blake, David & Dowd, Kevin, 2006. "Stochastic lifestyling: Optimal dynamic asset allocation for defined contribution pension plans," Journal of Economic Dynamics and Control, Elsevier, vol. 30(5), pages 843-877, May.
    9. Milton Friedman, 1957. "Introduction to "A Theory of the Consumption Function"," NBER Chapters,in: A Theory of the Consumption Function, pages 1-6 National Bureau of Economic Research, Inc.
    10. Svensson, Lars E. O. & Werner, Ingrid M., 1993. "Nontraded assets in incomplete markets : Pricing and portfolio choice," European Economic Review, Elsevier, vol. 37(5), pages 1149-1168, June.
    11. Stephen P. Zeldes, 1989. "Optimal Consumption with Stochastic Income: Deviations from Certainty Equivalence," The Quarterly Journal of Economics, Oxford University Press, vol. 104(2), pages 275-298.
    12. Joao F. Cocco, 2005. "Consumption and Portfolio Choice over the Life Cycle," Review of Financial Studies, Society for Financial Studies, vol. 18(2), pages 491-533.
    13. Milton Friedman, 1957. "A Theory of the Consumption Function," NBER Books, National Bureau of Economic Research, Inc, number frie57-1.
    14. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    15. Blake, David & Cairns, Andrew J. G. & Dowd, Kevin, 2003. "Pensionmetrics 2: stochastic pension plan design during the distribution phase," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 29-47, August.
    16. Blake, David & Cairns, Andrew J. G. & Dowd, Kevin, 2001. "Pensionmetrics: stochastic pension plan design and value-at-risk during the accumulation phase," Insurance: Mathematics and Economics, Elsevier, vol. 29(2), pages 187-215, October.
    17. Jun Liu, 2007. "Portfolio Selection in Stochastic Environments," Review of Financial Studies, Society for Financial Studies, vol. 20(1), pages 1-39, January.
    18. Kyoung Jin Choi & Gyoocheol Shim, 2006. "Disutility, Optimal Retirement, And Portfolio Selection," Mathematical Finance, Wiley Blackwell, vol. 16(2), pages 443-467.
    19. Ballotta, Laura & Haberman, Steven, 2003. "Valuation of guaranteed annuity conversion options," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 87-108, August.
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    Citations

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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. 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.
    7. repec:eee:insuma:v:75:y:2017:i:c:p:137-150 is not listed on IDEAS

    More about this item

    Keywords

    Defined-contribution pension; Lifecycle model; Stochastic income; Replacement ratio;

    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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