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Target benefit pension plan with longevity risk and intergenerational equity

Published online by Cambridge University Press:  12 January 2023

Ximin Rong ,
Cheng Tao  and
Hui Zhao
Ximin Rong
Affiliation:
School of Mathematics, Tianjin University, Tianjin 300350, PR China Center for Applied Mathematics, Tianjin University, Tianjin 300072, PR China
Cheng Tao*
Affiliation:
School of Mathematics, Tianjin University, Tianjin 300350, PR China
Hui Zhao
Affiliation:
School of Mathematics, Tianjin University, Tianjin 300350, PR China
*
*Corresponding author. E-mail: taocheng@tju.edu.cn
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Abstract

We study a stochastic model for a target benefit pension plan suffering from rising longevity and falling fertility. Policies for postponing retirement are carried out to hedge the payment difficulties caused by the aging population. The plan members’ contributions are set in advance while the pension payments reflect intergenerational equity by a target payment level and intergenerational risk sharing by an adjustment. The pension fund is invested in both a risk-free asset and a risky asset. Applying the stochastic optimal control methods, we derive analytic solutions for optimal investment and benefit payment strategies which minimize the benefit risk. Besides, an optimal delayed retirement age which can hedge against the aging phenomenon under certain parameters is given. Therefore, it can provide a basis for quantifying the delay of retirement time.

Keywords

Target benefit planlongevity riskintergenerational risk sharingintergenerational equitypostponing retirement

Information

Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 53 , Issue 1 , January 2023 , pp. 84 - 103
Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The International Actuarial Association

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Footnotes

‡

This article has been updated since its original publication. A notice detailing this change can be found here: https://doi.org/10.1017/asb.2023.9

References

Alvarez, J.-A., Kallestrup-Lamb, M. and Kjærgaard, S. (2021) Linking retirement age to life expectancy does not lessen the demographic implications of unequal lifespans. Insurance: Mathematics and Economics, 99, 363–375.Google Scholar
Andersen, T.M. (2014) Intergenerational redistribution and risk sharing with changing longevity. Journal of Economics, 111(1), 1–27.CrossRefGoogle Scholar
Ayuso, M., Bravo, J.M. and Holzmann, R. (2017) Addressing longevity heterogeneity in pension scheme design. Journal of Finance and Economics, 6(1), 1–21.CrossRefGoogle Scholar
Baumann, R.T. and Müller, H.H. (2008) Pension funds as institutions for intertemporal risk transfer. Insurance: Mathematics and Economics, 42, 1000–1012.Google Scholar
Boon, L.-N., Brière, M. and Werker, B.J.M. (2022) Systematic longevity risk: To bear or insure? Journal of Pension Economics and Finance, 19, 409–441.CrossRefGoogle Scholar
Bovenberg, A.L., Mehlkopf, R. and Nijman, T. (2016) The promise of defined ambition plans: Lessons for the united states. In Reimagining Pensions: The Next 40 Years (eds. Mitchell, O. and Shea, R.), pp. 215–246. Oxford: Oxford University Press.CrossRefGoogle Scholar
Bravo, J.M. and De Freitas, N.E.M. (2018) Valuation of longevity-linked life annuities. Insurance: Mathematics and Economics, 78, 212–229.Google Scholar
Bruce, N. and Turnovsky, S.J. (2013) Demography and growth: A unified treatment of overlapping generations. Macroeconomic Dynamics, 17, 1605–1637.CrossRefGoogle Scholar
Chen, A. and Rach, M. (2021) Current developments in German pension schemes: What are the benefits of the new target pension? European Actuarial Journal, 11(1), 21–47.CrossRefGoogle Scholar
Chen, D.H., Beetsma, R.M., Broeders, D.W. and Pelsser, A.A. (2017) Sustainability of participation in collective pension schemes: An option pricing approach. Insurance: Mathematics and Economics, 74, 182–196.Google Scholar
Chen, L., Li, D., Wang, Y. and Zhu, X. (2022) The optimal cyclical design for a target benefit pension plan. Journal of Pension Economics and Finance, 1–20. https://doi.org/10.1017/S1474747222000099 CrossRefGoogle Scholar
Cia (2015) Report of the task force on target benefit plans. Accessible via: https: www.cia-ica.ca/docs/default-source/2015/215043e.pdf.Google Scholar
Coughlan, G.D., Khalaf-Allah, M., Ye, Y., Kumar, S., Cairns, A.J., Blake, D. and Dowd, K. (2011) Longevity hedging 101: A framework for longevity basis risk analysis and hedge effectiveness. North American Actuarial Journal, 15(2), 150–176.CrossRefGoogle Scholar
Cui, J., De Jong, F. and Ponds, E. (2011) Intergenerational risk sharing within funded pension schemes. Journal of Pension Economics and Finance, 10(01), 1–29.CrossRefGoogle Scholar
Danish Ministry of Economic Affairs and Interior (2017) Denmark’s Convergence Programme 2017. Technical report, Danish Government, Copenhagen.Google Scholar
Danish Ministry of Economic Affairs and Interior (2018) Denmark’s Convergence Programme 2018. Technical report, Danish Government, Copenhagen.Google Scholar
Denuit, M., Haberman, S. and Renshaw, A. (2011) Longevity-indexed life annuities. North American Actuarial Journal, 15, 97–111.CrossRefGoogle Scholar
Dybvig, P.H. (1995) Dusenberry’s racheting of consumption: Optimal dynamic consumption and investment given intolerance for any decline in standard of living. Review of Economic Studies, 62(2), 287–313.CrossRefGoogle Scholar
Fleming, W.H. and Soner, H.M. (2006) Controlled Markov Processes and Viscosity Solutions, Vol. 25. New York: Springer Science & Business Media.Google Scholar
Galasso, V. (2008) Postponing retirement: The political effect of aging. Journal of Public Economics, 92, 2157–2169.CrossRefGoogle Scholar
Gollier, C. (2008) Intergenerational risk-sharing and risk-taking of a pension fund. Journal of Public Economics, 92(5), 1463–1485.CrossRefGoogle Scholar
Gompertz, B. (1825) On the nature of the function expressive of the law of human mortality and on a new mode of determining the value of life contingencies. Philosophical Transactions of the Royal Society of London, 115, 513–583.Google Scholar
Heeringa, W. and Bovenberg, A.L. (2009) Stabilizing Pay-as-You-Go pension schemes in the face of rising longevity and falling fertility: An application to the Netherlands, Netspar Discussion Paper 08/2009-025.CrossRefGoogle Scholar
Holzmann, R., Alonso-García, J., Labit-Hardy, H. and Villegas, A.M. (2019) NDC schemes and heterogeneity in longevity: Proposals for redesign. World Bank.CrossRefGoogle Scholar
Khorasanee, Z.M. (2012) Risk-sharing and benefit smoothing in a hybrid pension plan. North American Actuarial Journal, 16, 449–461.CrossRefGoogle Scholar
Knell, M. (2018) Increasing life expectancy and NDC pension systems. Journal of Pension Economics and Finance, 17(2), 170–199.CrossRefGoogle Scholar
Kortleve, N. (2013) The ‘defined ambition’ pension plan: A dutch interpretation. Rotman International Journal of Pension Management, 6, 6–11.Google Scholar
Medford, A. (2017) Best-practice life expectancy: An extreme value approach. Demographic Research, 36, 989–1014.CrossRefGoogle Scholar
Milevsky, M.A. (2020). Calibrating Gompertz in reverse: What is your longevity-risk-adjusted global age? Insurance: Mathematics and Economics, 92, 147–161.Google ScholarPubMed
Munnell, A.H. and Sass, S.A. (2013) New Brunswick’s new shared risk pension plan. Center for Retirement Research at Boston College, Boston, (33).Google Scholar
Oeppen, J. and Vaupel, J.W. (2002) Broken limits to life expectancy. Science, 296(5570), 1029–1031.CrossRefGoogle ScholarPubMed
Pascariu, M.D., Canudas-Romo, V. and Vaupel, J.W. (2018) The double-gap life expectancy forecasting model. Insurance: Mathematics and Economics, 78, 339–350.Google Scholar
Pugh, C. and Yermo, J. (2008) Funding regulations and risk sharing. OECD working papers on insurance and private pensions, No. 17, OECD Publishing. https://doi.org/10.1787/241841441002.CrossRefGoogle Scholar
Turner, J.A. (2014) Hybrid pensions: Risk sharing arrangements for pension plan sponsors and participants. Society of Actuaries.Google Scholar
United Nations, Department of Economic and Social Affairs (2020) Government policies to address population ageing. Population facts No. 2020/1.Google Scholar
Villegas, A.M. and Haberman, S. (2014) On the modeling and forecasting of socioeconomic mortality differentials: An application to deprivation and mortality in England. North American Actuarial Journal, 18(1), 168–193.CrossRefGoogle Scholar
Wang, S. and Lu, Y. (2019) Optimal investment strategies and risk-sharing arrangements for a hybrid pension plan. Insurance: Mathematics and Economics, 89, 46–62.Google Scholar
Wang, S., Lu, Y. and Sanders, B. (2018) Optimal investment strategies and intergenerational risk sharing for target benefit pension plans. Insurance: Mathematics and Economics, 80, 1–14.Google Scholar
Wang, S., Rong, X. and Zhao, H. (2019) Optimal investment and benefit payment strategy under loss aversion for target benefit pension plans. Applied Mathematics and Computation, 346, 205–218.CrossRefGoogle Scholar
Zhu, X., Hardy, M. and Saunders, D. (2021) Fair transition from defined benefit to target benefit. ASTIN Bulletin: The Journal of the IAA, 51(3), 873–904.CrossRefGoogle Scholar