IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v301y2022i3p1166-1180.html
   My bibliography  Save this article

Optimal investment and benefit adjustment problem for a target benefit pension plan with Cobb-Douglas utility and Epstein-Zin recursive utility

Author

Listed:
  • Zhao, Hui
  • Wang, Suxin

Abstract

This paper studies an optimal investment and benefit adjustment problem for a target benefit pension plan. The pension sponsor can adjust the benefit level to guarantee the stable operation of the plan. The pension is allowed to invest in a risk-free bond and a stock. The weighted product of the benefit outgo and pension wealth is considered in the objective function, which is taken in the form of Cobb-Douglas utility. Thus the plan takes both the benefit level and terminal wealth of the pension into account and then the benefit payment are dependent on the financial situation of the plan. By applying dynamic programming approach, we establish the corresponding Hamilton-Jacobi-Bellman equation and derive the optimal investment-benefit strategy and the value function explicitly. The verification theorem is presented and proved. Furthermore, the recursive utility is considered as an extension and we find that the elasticity of intertemporal substitution has a positive effect on the optimal benefit level. Finally, numerical examples are given and demonstrate that this pension scheme is sustainable and can provide stable and consecutive incremental benefit payment for future generations.

Suggested Citation

  • Zhao, Hui & Wang, Suxin, 2022. "Optimal investment and benefit adjustment problem for a target benefit pension plan with Cobb-Douglas utility and Epstein-Zin recursive utility," European Journal of Operational Research, Elsevier, vol. 301(3), pages 1166-1180.
    • Handle: RePEc:eee:ejores:v:301:y:2022:i:3:p:1166-1180
    DOI: 10.1016/j.ejor.2021.11.033
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037722172100984X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2021.11.033?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. Haberman, Steven & Vigna, Elena, 2002. "Optimal investment strategies and risk measures in defined contribution pension schemes," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 35-69, August.
    2. Josa-Fombellida, Ricardo & Rincón-Zapatero, Juan Pablo, 2019. "Equilibrium strategies in a defined benefit pension plan game," European Journal of Operational Research, Elsevier, vol. 275(1), pages 374-386.
    3. Elena Vigna, 2014. "On efficiency of mean--variance based portfolio selection in defined contribution pension schemes," Quantitative Finance, Taylor & Francis Journals, vol. 14(2), pages 237-258, February.
    4. Josa-Fombellida, Ricardo & Rincón-Zapatero, Juan Pablo, 2010. "Optimal asset allocation for aggregated defined benefit pension funds with stochastic interest rates," European Journal of Operational Research, Elsevier, vol. 201(1), pages 211-221, February.
    5. George Chacko & Luis M. Viceira, 2005. "Dynamic Consumption and Portfolio Choice with Stochastic Volatility in Incomplete Markets," The Review of Financial Studies, Society for Financial Studies, vol. 18(4), pages 1369-1402.
    6. David M. Kreps & Evan L. Porteus, 2013. "Temporal von Neumann—Morgenstern and Induced Preferences," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 11, pages 181-206, World Scientific Publishing Co. Pte. Ltd..
    7. Larry G. Epstein & Stanley E. Zin, 2013. "Substitution, risk aversion and the temporal behavior of consumption and asset returns: A theoretical framework," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 12, pages 207-239, World Scientific Publishing Co. Pte. Ltd..
    8. 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.
    9. Colin Pugh & Juan Yermo, 2008. "Funding regulations and risk sharing," OECD Journal: Financial Market Trends, OECD Publishing, vol. 2008(1), pages 163-196.
    10. Alicia H. Munnell & Steven A. Sass, 2013. "New Brunswick’s New Shared Risk Pension Plan," State and Local Pension Plans Briefs ibslp33, Center for Retirement Research.
    11. Farhi, Emmanuel & Panageas, Stavros, 2007. "Saving and investing for early retirement: A theoretical analysis," Journal of Financial Economics, Elsevier, vol. 83(1), pages 87-121, January.
    12. Zaki Khorasanee, 2012. "Risk-Sharing and Benefit Smoothing in A Hybrid Pension Plan," North American Actuarial Journal, Taylor & Francis Journals, vol. 16(4), pages 449-461.
    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. 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. Chen, Damiaan H.J. & Beetsma, Roel M.W.J. & Broeders, Dirk W.G.A. & Pelsser, Antoon A.J., 2017. "Sustainability of participation in collective pension schemes: An option pricing approach," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 182-196.
    16. Alicia H. Munnell & Steven A. Sass, 2013. "New Brunswick’s New Shared Risk Pension Plan," Issues in Brief ibslp33, Center for Retirement Research.
    17. Duffie, Darrel & Lions, Pierre-Louis, 1992. "PDE solutions of stochastic differential utility," Journal of Mathematical Economics, Elsevier, vol. 21(6), pages 577-606.
    18. Baumann, Roger T. & Müller, Heinz H., 2008. "Pension funds as institutions for intertemporal risk transfer," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1000-1012, June.
    19. Wang, Suxin & Lu, Yi, 2019. "Optimal investment strategies and risk-sharing arrangements for a hybrid pension plan," Insurance: Mathematics and Economics, Elsevier, vol. 89(C), pages 46-62.
    20. 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.
    21. 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.
    22. 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.
    23. Kraft, Holger & Weiss, Farina, 2019. "Consumption-portfolio choice with preferences for cash," Journal of Economic Dynamics and Control, Elsevier, vol. 98(C), pages 40-59.
    24. 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.
    25. Kraft, Holger & Seifried, Frank Thomas, 2014. "Stochastic differential utility as the continuous-time limit of recursive utility," Journal of Economic Theory, Elsevier, vol. 151(C), pages 528-550.
    26. Colin Pugh & Juan Yermo, 2008. "Funding Regulations and Risk Sharing," OECD Working Papers on Insurance and Private Pensions 17, OECD Publishing.
    27. Holger Kraft & Thomas Seiferling & Frank Thomas Seifried, 2017. "Optimal consumption and investment with Epstein–Zin recursive utility," Finance and Stochastics, Springer, vol. 21(1), pages 187-226, January.
    28. Duffie, Darrell & Epstein, Larry G, 1992. "Stochastic Differential Utility," Econometrica, Econometric Society, vol. 60(2), pages 353-394, March.
    29. Holger Kraft & Frank Seifried & Mogens Steffensen, 2013. "Consumption-portfolio optimization with recursive utility in incomplete markets," Finance and Stochastics, Springer, vol. 17(1), pages 161-196, January.
    30. Hao Xing, 2017. "Consumption–investment optimization with Epstein–Zin utility in incomplete markets," Finance and Stochastics, Springer, vol. 21(1), pages 227-262, January.
    31. Kreps, David M & Porteus, Evan L, 1978. "Temporal Resolution of Uncertainty and Dynamic Choice Theory," Econometrica, Econometric Society, vol. 46(1), pages 185-200, January.
    32. Duffie, Darrell & Epstein, Larry G, 1992. "Asset Pricing with Stochastic Differential Utility," The Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 411-436.
    33. Gerrard, Russell & Haberman, Steven & Vigna, Elena, 2004. "Optimal investment choices post-retirement in a defined contribution pension scheme," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 321-342, October.
    34. Steven Haberman & Elena Vigna, 2002. "Optimal investment strategies and risk measures in defined contribution pension schemes," ICER Working Papers - Applied Mathematics Series 09-2002, ICER - International Centre for Economic Research.
    35. Ngwira, Bernard & Gerrard, Russell, 2007. "Stochastic pension fund control in the presence of Poisson jumps," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 283-292, March.
    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. Wang, Suxin & Lu, Yi, 2019. "Optimal investment strategies and risk-sharing arrangements for a hybrid pension plan," Insurance: Mathematics and Economics, Elsevier, vol. 89(C), pages 46-62.
    2. Shigeta, Yuki, 2022. "Quasi-hyperbolic discounting under recursive utility and consumption–investment decisions," Journal of Economic Theory, Elsevier, vol. 204(C).
    3. Shigeta, Yuki, 2020. "Gain/loss asymmetric stochastic differential utility," Journal of Economic Dynamics and Control, Elsevier, vol. 118(C).
    4. Kraft, Holger & Munk, Claus & Weiss, Farina, 2022. "Bequest motives in consumption-portfolio decisions with recursive utility," Journal of Banking & Finance, Elsevier, vol. 138(C).
    5. Zixin Feng & Dejian Tian, 2021. "Optimal consumption and portfolio selection with Epstein-Zin utility under general constraints," Papers 2111.09032, arXiv.org, revised May 2023.
    6. Chen, Xingjiang & Ruan, Xinfeng & Zhang, Wenjun, 2021. "Dynamic portfolio choice and information trading with recursive utility," Economic Modelling, Elsevier, vol. 98(C), pages 154-167.
    7. Fahrenwaldt, Matthias Albrecht & Jensen, Ninna Reitzel & Steffensen, Mogens, 2020. "Nonrecursive separation of risk and time preferences," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 95-108.
    8. Anis Matoussi & Hao Xing, 2016. "Convex duality for stochastic differential utility," Papers 1601.03562, arXiv.org.
    9. Dirk Becherer & Wilfried Kuissi-Kamdem & Olivier Menoukeu-Pamen, 2023. "Optimal consumption with labor income and borrowing constraints for recursive preferences," Working Papers hal-04017143, HAL.
    10. Aït-Sahalia, Yacine & Matthys, Felix, 2019. "Robust consumption and portfolio policies when asset prices can jump," Journal of Economic Theory, Elsevier, vol. 179(C), pages 1-56.
    11. Joshua Aurand & Yu-Jui Huang, 2019. "Epstein-Zin Utility Maximization on a Random Horizon," Papers 1903.08782, arXiv.org, revised May 2023.
    12. 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.
    13. 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.
    14. Yaroslav Melnyk & Johannes Muhle‐Karbe & Frank Thomas Seifried, 2020. "Lifetime investment and consumption with recursive preferences and small transaction costs," Mathematical Finance, Wiley Blackwell, vol. 30(3), pages 1135-1167, July.
    15. Dariusz Zawisza, 2020. "On the parabolic equation for portfolio problems," Papers 2003.13317, arXiv.org, revised Oct 2020.
    16. Matoussi, Anis & Xing, Hao, 2018. "Convex duality for Epstein-Zin stochastic differential utility," LSE Research Online Documents on Economics 82519, London School of Economics and Political Science, LSE Library.
    17. Knut K. Aase & Petter Bjerksund, 2021. "The Optimal Spending Rate versus the Expected Real Return of a Sovereign Wealth Fund," JRFM, MDPI, vol. 14(9), pages 1-36, September.
    18. Kabderian Dreyer, Johannes & Sharma, Vivek & Smith, William, 2023. "Warm-glow investment and the underperformance of green stocks," International Review of Economics & Finance, Elsevier, vol. 83(C), pages 546-570.
    19. Li, Hanwu & Riedel, Frank & Yang, Shuzhen, 2024. "Optimal consumption for recursive preferences with local substitution — the case of certainty," Journal of Mathematical Economics, Elsevier, vol. 110(C).
    20. Zixin Feng & Dejian Tian & Harry Zheng, 2024. "Consumption-investment optimization with Epstein-Zin utility in unbounded non-Markovian markets," Papers 2407.19995, arXiv.org.

    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:ejores:v:301:y:2022:i:3:p:1166-1180. 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: http://www.elsevier.com/locate/eor .

    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.