IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v220y2012i2p404-413.html
   My bibliography  Save this article

Stochastic pension funding when the benefit and the risky asset follow jump diffusion processes

Author

Listed:
  • Josa-Fombellida, Ricardo
  • Rincón-Zapatero, Juan Pablo

Abstract

We study the asset allocation of defined benefit pension plans of the type designed and sponsored by firms with the aim of providing a lifetime pension to the employees at the age of retirement. Benefits are stochastic, combining Poisson jumps with Brownian uncertainty. The sponsor dynamically forms portfolios where the risky asset is also subjected to Poisson jumps and Brownian uncertainty, possibly correlated with the evolution of benefits. The objective is to assure future benefits, while controlling the contribution made to the fund reserves. The problem is solved analytically using dynamic programming techniques.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:220:y:2012:i:2:p:404-413
    DOI: 10.1016/j.ejor.2012.01.033
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221712000689
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2012.01.033?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. 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.
    2. Sennewald, Ken, 2007. "Controlled stochastic differential equations under Poisson uncertainty and with unbounded utility," Journal of Economic Dynamics and Control, Elsevier, vol. 31(4), pages 1106-1131, April.
    3. Berkelaar, Arjan & Kouwenberg, Roy, 2003. "Retirement saving with contribution payments and labor income as a benchmark for investments," Journal of Economic Dynamics and Control, Elsevier, vol. 27(6), pages 1069-1097, April.
    4. Haberman, Steven & Butt, Zoltan & Megaloudi, Chryssoula, 2000. "Contribution and solvency risk in a defined benefit pension scheme," Insurance: Mathematics and Economics, Elsevier, vol. 27(2), pages 237-259, October.
    5. Paolo Battocchio & Francesco Menoncin & Olivier Scaillet, 2007. "Optimal asset allocation for pension funds under mortality risk during the accumulation and decumulation phases," Annals of Operations Research, Springer, vol. 152(1), pages 141-165, July.
    6. Tomas Björk & Irina Slinko, 2006. "Towards a General Theory of Good-Deal Bounds," Review of Finance, European Finance Association, vol. 10(2), pages 221-260.
    7. M. Iqbal Owadally & Steven Haberman, 1999. "Pension Fund Dynamics and Gains/Losses Due to Random Rates of Investment Return," North American Actuarial Journal, Taylor & Francis Journals, vol. 3(3), pages 105-117.
    8. 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.
    9. Chang, Shih-Chieh, 1999. "Optimal pension funding through dynamic simulations: the case of Taiwan public employees retirement system," Insurance: Mathematics and Economics, Elsevier, vol. 24(3), pages 187-199, May.
    10. 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.
    11. Taylor, Greg, 2002. "Stochastic control of funding systems," Insurance: Mathematics and Economics, Elsevier, vol. 30(3), pages 323-350, June.
    12. Zvi Bodie & Jay O. Light & Randall Morck, 1987. "Funding and Asset Allocation in Corporate Pension Plans: An Empirical Investigation," NBER Chapters, in: Issues in Pension Economics, pages 15-48, National Bureau of Economic Research, Inc.
    13. Wu, Liuren, 2003. "Jumps and Dynamic Asset Allocation," Review of Quantitative Finance and Accounting, Springer, vol. 20(3), pages 207-243, May.
    14. 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.
    15. Josa-Fombellida, Ricardo & Rincon-Zapatero, Juan Pablo, 2008. "Mean-variance portfolio and contribution selection in stochastic pension funding," European Journal of Operational Research, Elsevier, vol. 187(1), pages 120-137, May.
    16. Cairns, Andrew, 2000. "Some Notes on the Dynamics and Optimal Control of Stochastic Pension Fund Models in Continuous Time," ASTIN Bulletin, Cambridge University Press, vol. 30(1), pages 19-55, May.
    17. Haberman, Steven & Sung, Joo-Ho, 2005. "Optimal pension funding dynamics over infinite control horizon when stochastic rates of return are stationary," Insurance: Mathematics and Economics, Elsevier, vol. 36(1), pages 103-116, February.
    18. Bodie, Zvi & Shoven, John B. & Wise, David A. (ed.), 1987. "Issues in Pension Economics," National Bureau of Economic Research Books, University of Chicago Press, edition 1, number 9780226062846, December.
    19. Haberman, Steven & Sung, Joo-Ho, 1994. "Dynamic approaches to pension funding," Insurance: Mathematics and Economics, Elsevier, vol. 15(2-3), pages 151-162, December.
    20. 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)

    Citations

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


    Cited by:

    1. Hainaut, Donatien, 2014. "Impulse control of pension fund contributions, in a regime switching economy," European Journal of Operational Research, Elsevier, vol. 239(3), pages 810-819.
    2. Di Giacinto, Marina & Federico, Salvatore & Gozzi, Fausto & Vigna, Elena, 2014. "Income drawdown option with minimum guarantee," European Journal of Operational Research, Elsevier, vol. 234(3), pages 610-624.
    3. 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.
    4. Le Courtois, Olivier & Menoncin, Francesco, 2015. "Portfolio optimisation with jumps: Illustration with a pension accumulation scheme," Journal of Banking & Finance, Elsevier, vol. 60(C), pages 127-137.
    5. 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.
    6. Guohui Guan & Zongxia Liang & Yi Xia, 2023. "Optimal management of DB pension fund under both underfunded and overfunded cases," Papers 2302.08731, arXiv.org.
    7. Castellano, Rosella & Cerqueti, Roy & Spinesi, Luca, 2016. "Sustainable management of fossil fuels: A dynamic stochastic optimization approach with jump-diffusion," European Journal of Operational Research, Elsevier, vol. 255(1), pages 288-297.
    8. Menoncin, Francesco & Vigna, Elena, 2017. "Mean–variance target-based optimisation for defined contribution pension schemes in a stochastic framework," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 172-184.
    9. 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.
    10. Lu, Lijue & Navas, Jorge, 2021. "Advertising and quality improving strategies in a supply chain when facing potential crises," European Journal of Operational Research, Elsevier, vol. 288(3), pages 839-851.
    11. Henrique Ferreira Morici & Elena Vigna, 2023. "Optimal additional voluntary contribution in DC pension schemes to manage inadequacy risk," Carlo Alberto Notebooks 699 JEL Classification: C, Collegio Carlo Alberto.
    12. Ayşegül İşcanog̃lu-Çekiç, 2016. "An Optimal Turkish Private Pension Plan with a Guarantee Feature," Risks, MDPI, vol. 4(3), pages 1-12, June.
    13. Guan, Guohui & Hu, Jiaqi & Liang, Zongxia, 2022. "Robust equilibrium strategies in a defined benefit pension plan game," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 193-217.
    14. Tan, Ken Seng & Weng, Chengguo & Zhang, Jinggong, 2022. "Optimal dynamic longevity hedge with basis risk," European Journal of Operational Research, Elsevier, vol. 297(1), pages 325-337.
    15. 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.
    16. Baltas, I. & Dopierala, L. & Kolodziejczyk, K. & Szczepański, M. & Weber, G.-W. & Yannacopoulos, A.N., 2022. "Optimal management of defined contribution pension funds under the effect of inflation, mortality and uncertainty," European Journal of Operational Research, Elsevier, vol. 298(3), pages 1162-1174.
    17. Francesco Menoncin & Elena Vigna, 2013. "Mean-variance target-based optimisation in DC plan with stochastic interest rate," Carlo Alberto Notebooks 337, Collegio Carlo Alberto.
    18. Guohui Guan & Jiaqi Hu & Zongxia Liang, 2021. "Robust equilibrium strategies in a defined benefit pension plan game," Papers 2103.09121, arXiv.org.

    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. Ayşegül İşcanog̃lu-Çekiç, 2016. "An Optimal Turkish Private Pension Plan with a Guarantee Feature," Risks, MDPI, vol. 4(3), pages 1-12, June.
    2. Josa-Fombellida, Ricardo & Navas, Jorge, 2020. "Time consistent pension funding in a defined benefit pension plan with non-constant discounting," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 142-153.
    3. 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.
    4. 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.
    5. 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.
    6. Hainaut, Donatien, 2014. "Impulse control of pension fund contributions, in a regime switching economy," European Journal of Operational Research, Elsevier, vol. 239(3), pages 810-819.
    7. 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.
    8. Josa-Fombellida, Ricardo & Rincon-Zapatero, Juan Pablo, 2008. "Mean-variance portfolio and contribution selection in stochastic pension funding," European Journal of Operational Research, Elsevier, vol. 187(1), pages 120-137, May.
    9. Maurer, Raimond & Mitchell, Olivia S. & Rogalla, Ralph, 2009. "Managing contribution and capital market risk in a funded public defined benefit plan: Impact of CVaR cost constraints," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 25-34, August.
    10. Samuel H. Cox & Yijia Lin & Ruilin Tian & Jifeng Yu, 2013. "Managing Capital Market and Longevity Risks in a Defined Benefit Pension Plan," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(3), pages 585-620, September.
    11. Delong, Lukasz & Gerrard, Russell & Haberman, Steven, 2008. "Mean-variance optimization problems for an accumulation phase in a defined benefit plan," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 107-118, February.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. Josa-Fombellida, Ricardo & Rincon-Zapatero, Juan Pablo, 2006. "Optimal investment decisions with a liability: The case of defined benefit pension plans," Insurance: Mathematics and Economics, Elsevier, vol. 39(1), pages 81-98, August.
    17. 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.
    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. 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.
    20. Huang, Jianhui & Wang, Guangchen & Wu, Zhen, 2010. "Optimal premium policy of an insurance firm: Full and partial information," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 208-215, October.

    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:220:y:2012:i:2:p:404-413. 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.