IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v490y2025ics0096300324006714.html
   My bibliography  Save this article

Optimal strategies for collective defined contribution plans when the stock and labor markets are co-integrated

Author

Listed:
  • Zhang, Jiannan
  • Chen, Ping
  • Jin, Zhuo
  • Li, Shuanming

Abstract

This paper investigates a collective defined contribution (CDC) pension fund scheme in continuous time, where members' contributions are fixed in advance, and benefit payments depend on the final salary rate. We take account of the co-integration between labor income and the stock market by letting the difference between logs of labor and dividends follow a mean-reverting process. Further, labor income is also a product of aggregate labor income and member's idiosyncratic shocks whose constant growth rate is unknown. It can be modeled by a continuous-time two-state hidden Markov chain. Further, the pension fund can be invested in the financial market consisting of one risky asset and one risk-free asset to enhance profits. After using Hamilton-Jacobi-Bellman (HJB) equations, the closed-form solutions for the optimal asset allocation and the benefit payment policies are obtained to maximize the social welfare and the terminal surplus wealth. Numerical examples are also conducted to illustrate the sensitivity of parameters on the optimal strategies.

Suggested Citation

  • Zhang, Jiannan & Chen, Ping & Jin, Zhuo & Li, Shuanming, 2025. "Optimal strategies for collective defined contribution plans when the stock and labor markets are co-integrated," Applied Mathematics and Computation, Elsevier, vol. 490(C).
  • Handle: RePEc:eee:apmaco:v:490:y:2025:i:c:s0096300324006714
    DOI: 10.1016/j.amc.2024.129210
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300324006714
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.amc.2024.129210?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Luca Benzoni & Pierre Collin‐Dufresne & Robert S. Goldstein, 2007. "Portfolio Choice over the Life‐Cycle when the Stock and Labor Markets Are Cointegrated," Journal of Finance, American Finance Association, vol. 62(5), pages 2123-2167, October.
    2. 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.
    3. Gao, Jianwei, 2009. "Optimal portfolios for DC pension plans under a CEV model," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 479-490, June.
    4. Annamaria Lusardi & Olivia S Mitchelli, 2007. "Financial Literacy and Retirement Preparedness: Evidence and Implications for Financial Education," Business Economics, Palgrave Macmillan;National Association for Business Economics, vol. 42(1), pages 35-44, January.
    5. John Y. Campbell & João F. Cocco & Francisco J. Gomes & Pascal J. Maenhout, 2001. "Investing Retirement Wealth: A Life-Cycle Model," NBER Chapters, in: Risk Aspects of Investment-Based Social Security Reform, pages 439-482, National Bureau of Economic Research, Inc.
    6. Gollier, Christian, 2008. "Intergenerational risk-sharing and risk-taking of a pension fund," Journal of Public Economics, Elsevier, vol. 92(5-6), pages 1463-1485, June.
    7. Annamaria Lusardi & Olivia Mitchell, 2006. "Financial Literacy and Retirement Preparedness: Evidence and Implications for Financial Education Programs," Working Papers wp144, University of Michigan, Michigan Retirement Research Center.
    8. Baxter, Marianne & Jermann, Urban J, 1997. "The International Diversification Puzzle Is Worse Than You Think," American Economic Review, American Economic Association, vol. 87(1), pages 170-180, March.
    9. Zhang, Aihua & Korn, Ralf & Ewald, Christian-Oliver, 2007. "Optimal management and inflation protection for defined contribution pension plans," MPRA Paper 3300, University Library of Munich, Germany.
    10. He, Lin & Liang, Zongxia & Yuan, Fengyi, 2020. "Optimal DB-PAYGO pension management towards a habitual contribution rate," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 125-141.
    11. Wang, Neng, 2009. "Optimal consumption and asset allocation with unknown income growth," Journal of Monetary Economics, Elsevier, vol. 56(4), pages 524-534, May.
    12. 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.
    13. Haberman, Steven & Sung, Joo-Ho, 1994. "Dynamic approaches to pension funding," Insurance: Mathematics and Economics, Elsevier, vol. 15(2-3), pages 151-162, December.
    14. Cui, Jiajia & Jong, Frank De & Ponds, Eduard, 2011. "Intergenerational risk sharing within funded pension schemes," Journal of Pension Economics and Finance, Cambridge University Press, vol. 10(1), pages 1-29, January.
    15. Wang, Suxin & Lu, Yi & Sanders, Barbara, 2018. "Optimal investment strategies and intergenerational risk sharing for target benefit pension plans," Insurance: Mathematics and Economics, Elsevier, vol. 80(C), pages 1-14.
    16. Josa-Fombellida, Ricardo & Rincon-Zapatero, Juan Pablo, 2004. "Optimal risk management in defined benefit stochastic pension funds," Insurance: Mathematics and Economics, Elsevier, vol. 34(3), pages 489-503, June.
    17. 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.
    18. Joao F. Cocco, 2005. "Consumption and Portfolio Choice over the Life Cycle," The Review of Financial Studies, Society for Financial Studies, vol. 18(2), pages 491-533.
    19. Guan, Guohui & Liang, Zongxia & Feng, Jian, 2018. "Time-consistent proportional reinsurance and investment strategies under ambiguous environment," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 122-133.
    20. Russell Gerrard & Steven Haberman & Elena Vigna, 2006. "The Management of Decumulation Risks in a Defined Contribution Pension Plan," North American Actuarial Journal, Taylor & Francis Journals, vol. 10(1), pages 84-110.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mehlkopf, R.J., 2011. "Risk sharing with the unborn," Other publications TiSEM fe8a8df6-455f-4624-af10-9, Tilburg University, School of Economics and Management.
    2. Ilja Boelaars & Roel Mehlkopf, 2018. "Optimal risk-sharing in pension funds when stock and labor markets are co-integrated," DNB Working Papers 595, Netherlands Central Bank, Research Department.
    3. Claudio Campanale, 2011. "Learning, Ambiguity and Life-Cycle Portfolio Allocation," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 14(2), pages 339-367, April.
    4. 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.
    5. Wang, Suxin & Lu, Yi & Sanders, Barbara, 2018. "Optimal investment strategies and intergenerational risk sharing for target benefit pension plans," Insurance: Mathematics and Economics, Elsevier, vol. 80(C), pages 1-14.
    6. Molenaar, R. & Ponds, E.H.M., 2011. "Risk Sharing and Individual Lifecycle Investing in Funded Collective Pensions," Other publications TiSEM b036a69d-317f-41c5-9581-f, Tilburg University, School of Economics and Management.
    7. Fabio C. Bagliano & Carolina Fugazza & Giovanna Nicodano, 2014. "Optimal Life-Cycle Portfolios for Heterogeneous Workers," Review of Finance, European Finance Association, vol. 18(6), pages 2283-2323.
    8. Timmermans, S. & Schumacher, J.M. & Ponds, E.H.M., 2011. "A Cohort-Specific Approach to Retirement Savings," Other publications TiSEM 9f3040ab-8dd3-4eeb-b45a-6, Tilburg University, School of Economics and Management.
    9. Le Blanc, Julia & Scholl, Almuth, 2017. "Optimal Savings For Retirement: The Role Of Individual Accounts," Macroeconomic Dynamics, Cambridge University Press, vol. 21(6), pages 1361-1388, September.
    10. Zvi Bodie & Jérôme Detemple & Marcel Rindisbacher, 2009. "Life-Cycle Finance and the Design of Pension Plans," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 249-286, November.
    11. Jacob A. Bikker & Dirk W. G. A. Broeders & David A. Hollanders & Eduard H. M. Ponds, 2012. "Pension Funds’ Asset Allocation and Participant Age: A Test of the Life-Cycle Model," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 79(3), pages 595-618, September.
    12. Fugazza, Carolina & Giofré, Maela & Nicodano, Giovanna, 2011. "International diversification and industry-related labor income risk," International Review of Economics & Finance, Elsevier, vol. 20(4), pages 764-783, October.
    13. He, Lin & Liang, Zongxia & Yuan, Fengyi, 2020. "Optimal DB-PAYGO pension management towards a habitual contribution rate," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 125-141.
    14. Thomas Post & Helmut Gründl & Joan T. Schmit & Anja Zimmer, 2014. "The Impact of Investment Behaviour for Individual Welfare," Economica, London School of Economics and Political Science, vol. 81(321), pages 15-47, January.
    15. Marcel Lever & Ilja Boelaars & Ryanne Cox & Roel Mehlkopf, 2015. "The allocation of financial risks during the life cycle in individual and collective DC pension contracts," CPB Discussion Paper 317, CPB Netherlands Bureau for Economic Policy Analysis.
    16. Josa-Fombellida, Ricardo & López-Casado, Paula & Rincón-Zapatero, Juan Pablo, 2018. "Portfolio optimization in a defined benefit pension plan where the risky assets are processes with constant elasticity of variance," Insurance: Mathematics and Economics, Elsevier, vol. 82(C), pages 73-86.
    17. Le Blanc, Julia & Scholl, Almuth, 2011. "Optimal savings for retirement: The role of individual accounts and disaster expectations," Discussion Paper Series 1: Economic Studies 2011,33, Deutsche Bundesbank.
    18. He, Lin & Liang, Zongxia & Wang, Sheng, 2022. "Dynamic optimal adjustment policies of hybrid pension plans," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 46-68.
    19. Seokkeun Ha & Frank J. Fabozzi, 2022. "A lifetime allocation with human capital: implications for target date fund," Journal of Asset Management, Palgrave Macmillan, vol. 23(5), pages 365-375, September.
    20. Marcel Lever & Ilja Boelaars & Ryanne Cox & Roel Mehlkopf, 2015. "The allocation of financial risks during the life cycle in individual and collective DC pension contracts," CPB Discussion Paper 317.rdf, CPB Netherlands Bureau for Economic Policy Analysis.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:490:y:2025:i:c:s0096300324006714. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.