IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v80y2018icp1-14.html
   My bibliography  Save this article

Optimal investment strategies and intergenerational risk sharing for target benefit pension plans

Author

Listed:
  • Wang, Suxin
  • Lu, Yi
  • Sanders, Barbara

Abstract

In this paper, we consider a stochastic model for a target benefit pension fund in continuous time, where the plan members’ contributions are set in advance while the pension payments depend on the financial situation of the plan, with risk sharing between different generations. The pension fund is invested in both a risk-free asset and a risky asset. In particular, stochastic salary rates and the correlation between salary movements and financial market fluctuations are considered. Using the stochastic optimal control approach, we derive closed-form solutions for optimal investment strategies as well as optimal benefit payment adjustments, which minimize the combination of benefit risk (in terms of deviating from the target) and intergenerational transfers. Numerical analysis is presented to illustrate the sensitivity of the optimal strategies to parameters of the financial market and salary rates. We also consider how the optimal benefit changes with respect to different target levels.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:80:y:2018:i:c:p:1-14
    DOI: 10.1016/j.insmatheco.2018.02.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668717302718
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.insmatheco.2018.02.003?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. Coen Teulings & Casper Vries, 2006. "Generational Accounting, Solidarity and Pension Losses," De Economist, Springer, vol. 154(1), pages 63-83, March.
    2. 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.
    3. Chang, S. C. & Tzeng, Larry Y. & Miao, Jerry C. Y., 2003. "Pension funding incorporating downside risks," Insurance: Mathematics and Economics, Elsevier, vol. 32(2), pages 217-228, April.
    4. 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.
    5. Chen, Damiaan H. J. & Beetsma, Roel M. W. J. & Ponds, Eduard H. M. & Romp, Ward E., 2016. "Intergenerational risk-sharing through funded pensions and public debt," Journal of Pension Economics and Finance, Cambridge University Press, vol. 15(2), pages 127-159, April.
    6. He, Lin & Liang, Zongxia, 2013. "Optimal dynamic asset allocation strategy for ELA scheme of DC pension plan during the distribution phase," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 404-410.
    7. Lans Bovenberg & Roel Mehlkopf, 2014. "Optimal Design of Funded Pension Schemes," Annual Review of Economics, Annual Reviews, vol. 6(1), pages 445-474, August.
    8. 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.
    9. Beetsma, Roel M.W.J. & Romp, Ward E. & Vos, Siert J., 2012. "Voluntary participation and intergenerational risk sharing in a funded pension system," European Economic Review, Elsevier, vol. 56(6), pages 1310-1324.
    10. Dickson,David C. M. & Hardy,Mary R. & Waters,Howard R., 2013. "Actuarial Mathematics for Life Contingent Risks," Cambridge Books, Cambridge University Press, number 9781107044074, October.
    11. Haberman, Steven & Sung, Joo-Ho, 1994. "Dynamic approaches to pension funding," Insurance: Mathematics and Economics, Elsevier, vol. 15(2-3), pages 151-162, December.
    12. Piggott, John & Woodland, Alan (ed.), 2016. "Handbook of the Economics of Population Aging," Handbook of the Economics of Population Aging, Elsevier, edition 1, volume 1, number 1.
    13. Dickson,David C. M. & Hardy,Mary R. & Waters,Howard R., 2013. "Solutions Manual for Actuarial Mathematics for Life Contingent Risks," Cambridge Books, Cambridge University Press, number 9781107620261, February.
    14. Ed Westerhout, 2011. "Intergenerational Risk Sharing in Time-Consistent Funded Pension Schemes," CPB Discussion Paper 176, CPB Netherlands Bureau for Economic Policy Analysis.
    15. 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.
    16. Mitchell, Olivia S. & Shea, Richard C. (ed.), 2016. "Reimagining Pensions: The Next 40 Years," OUP Catalogue, Oxford University Press, number 9780198755449.
    17. 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.
    18. 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.
    19. Bovenberg, A.L. & Koijen, R.S.J. & Nijman, T.E. & Teulings, C.N., 2007. "Saving and investing over the life cycle and the role of collective pension funds," Other publications TiSEM 6eab1341-eda5-4f21-8c06-8, Tilburg University, School of Economics and Management.
    20. Josa-Fombellida, Ricardo & Rincon-Zapatero, Juan Pablo, 2001. "Minimization of risks in pension funding by means of contributions and portfolio selection," Insurance: Mathematics and Economics, Elsevier, vol. 29(1), pages 35-45, August.
    21. 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.
    22. Alicia H. Munnell & Steven A. Sass, 2013. "New Brunswick’s New Shared Risk Pension Plan," Issues in Brief ibslp33, Center for Retirement Research.
    23. 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.
    24. Vigna, Elena & Haberman, Steven, 2001. "Optimal investment strategy for defined contribution pension schemes," Insurance: Mathematics and Economics, Elsevier, vol. 28(2), pages 233-262, April.
    25. Beetsma, R. & Romp, W., 2016. "Intergenerational Risk Sharing," Handbook of the Economics of Population Aging, in: Piggott, John & Woodland, Alan (ed.), Handbook of the Economics of Population Aging, edition 1, volume 1, chapter 0, pages 311-380, Elsevier.
    26. 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.
    27. 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.
    28. Battocchio, Paolo & Menoncin, Francesco, 2004. "Optimal pension management in a stochastic framework," Insurance: Mathematics and Economics, Elsevier, vol. 34(1), pages 79-95, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Xiaoyi Zhang, 2022. "Optimal DC Pension Management Under Inflation Risk With Jump Diffusion Price Index and Cost of Living Process," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 1253-1270, June.
    2. 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.
    3. 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.
    4. Lin He & Zongxia Liang & Zhaojie Ren & Yilun Song, 2023. "Optimal Mix Among PAYGO, EET and Individual Savings," Papers 2302.09218, arXiv.org.
    5. Yan, Tingjin & Park, Kyunghyun & Wong, Hoi Ying, 2022. "Irreversible reinsurance: A singular control approach," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 326-348.
    6. 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.
    7. Wujun Lv & Linlin Tian & Xiaoyi Zhang, 2023. "Optimal Defined Contribution Pension Management with Jump Diffusions and Common Shock Dependence," Mathematics, MDPI, vol. 11(13), pages 1-20, July.
    8. Bégin, Jean-François, 2020. "Levelling the playing field: A VIX-linked structure for funded pension schemes," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 58-78.
    9. 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.
    10. Wang, Suxin & Rong, Ximin & Zhao, Hui, 2019. "Optimal investment and benefit payment strategy under loss aversion for target benefit pension plans," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 205-218.
    11. Guglielmo D'Amico & Ada Lika & Filippo Petroni, 2019. "Risk Management of Pension Fund: A Model for Salary Evolution," IJFS, MDPI, vol. 7(3), pages 1-17, August.

    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. 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.
    2. 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.
    3. Bégin, Jean-François, 2020. "Levelling the playing field: A VIX-linked structure for funded pension schemes," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 58-78.
    4. Alserda, G.A.G. & Steenbeek, O.W. & van der Lecq, S.G., 2017. "The Occurrence and Impact of Pension Fund Discontinuity," ERIM Report Series Research in Management ERS-2017-008-F&A, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    5. 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.
    6. Romp, Ward & Beetsma, Roel, 2020. "Sustainability of pension systems with voluntary participation," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 125-140.
    7. 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.
    8. 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.
    9. Boonen, Tim J. & De Waegenaere, Anja, 2017. "Intergenerational risk sharing in closing pension funds," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 20-30.
    10. Damiaan Chen & Roel Beetsma & Dirk Broeders, 2015. "Stability of participation in collective pension schemes: An option pricing approach," DNB Working Papers 484, Netherlands Central Bank, Research Department.
    11. Torsten Kleinow & Johannes M. Schumacher, 2017. "Financial fairness and conditional indexation," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2017(8), pages 651-669, September.
    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.
    13. Josa-Fombellida, Ricardo & López-Casado, Paula, 2023. "A defined benefit pension plan game with Brownian and Poisson jumps uncertainty," European Journal of Operational Research, Elsevier, vol. 310(3), pages 1294-1311.
    14. Josa-Fombellida, Ricardo & Rincón-Zapatero, Juan Pablo, 2012. "Stochastic pension funding when the benefit and the risky asset follow jump diffusion processes," European Journal of Operational Research, Elsevier, vol. 220(2), pages 404-413.
    15. Mehlkopf, R.J., 2011. "Risk sharing with the unborn," Other publications TiSEM fe8a8df6-455f-4624-af10-9, Tilburg University, School of Economics and Management.
    16. 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.
    17. Beetsma, R. & Romp, W., 2016. "Intergenerational Risk Sharing," Handbook of the Economics of Population Aging, in: Piggott, John & Woodland, Alan (ed.), Handbook of the Economics of Population Aging, edition 1, volume 1, chapter 0, pages 311-380, Elsevier.
    18. 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.
    19. He, Lin & Liang, Zongxia, 2013. "Optimal dynamic asset allocation strategy for ELA scheme of DC pension plan during the distribution phase," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 404-410.
    20. 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.

    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:insuma:v:80:y:2018:i:c:p:1-14. 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/inca/505554 .

    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.