IDEAS home Printed from https://ideas.repec.org/a/bla/jrinsu/v75y2008i3p739-761.html
   My bibliography  Save this article

Income Drawdown Schemes for a Defined‐Contribution Pension Plan

Author

Listed:
  • Paul Emms
  • Steven Haberman

Abstract

In retirement a pensioner must often decide how much money to withdraw from a pension fund, how to invest the remaining funds, and whether to purchase an annuity. These decisions are addressed here by introducing a number of income drawdown schemes, which are relevant to a defined‐contribution personal pension plan. The optimal asset allocation is defined so that it minimizes the expected loss of the pensioner as measured by the performance of the pension fund against a benchmark. Two benchmarks are considered: a risk‐free investment and the price of an annuity. The fair‐value income drawdown rate is defined so that the fund performance is a martingale under the objective measure. Annuitization is recommended if the expected fair‐value drawdown rate falls below the annuity rate available at retirement. As an illustration, the annuitization age is calculated for a Gompertz mortality distribution function and a power law loss function.

Suggested Citation

  • Paul Emms & Steven Haberman, 2008. "Income Drawdown Schemes for a Defined‐Contribution Pension Plan," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 75(3), pages 739-761, September.
    • Handle: RePEc:bla:jrinsu:v:75:y:2008:i:3:p:739-761
    DOI: 10.1111/j.1539-6975.2008.00282.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1539-6975.2008.00282.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1539-6975.2008.00282.x?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
    ---><---

    References listed on IDEAS

    as
    1. Amartya Sen, 1997. "Maximization and the Act of Choice," Econometrica, Econometric Society, vol. 65(4), pages 745-780, July.
    2. Ralf Korn, 2000. "Value Preserving Strategies and a General Framework for Local Approaches to Optimal Portfolios," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 227-241, April.
    3. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    4. Harry Markowitz, 1952. "The Utility of Wealth," Journal of Political Economy, University of Chicago Press, vol. 60(2), pages 151-151.
    5. Biffis, Enrico, 2005. "Affine processes for dynamic mortality and actuarial valuations," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 443-468, December.
    6. 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.
    7. Emms, P. & Haberman, S., 2007. "Asymptotic and numerical analysis of the optimal investment strategy for an insurer," Insurance: Mathematics and Economics, Elsevier, vol. 40(1), pages 113-134, January.
    8. Blake, David & Cairns, Andrew J. G. & Dowd, Kevin, 2003. "Pensionmetrics 2: stochastic pension plan design during the distribution phase," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 29-47, August.
    9. Blake, David & Cairns, Andrew J. G. & Dowd, Kevin, 2001. "Pensionmetrics: stochastic pension plan design and value-at-risk during the accumulation phase," Insurance: Mathematics and Economics, Elsevier, vol. 29(2), pages 187-215, October.
    10. 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.
    11. Milevsky, Moshe A. & David Promislow, S., 2001. "Mortality derivatives and the option to annuitise," Insurance: Mathematics and Economics, Elsevier, vol. 29(3), pages 299-318, December.
    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 & Deelstra, Griselda, 2014. "Optimal timing for annuitization, based on jump diffusion fund and stochastic mortality," Journal of Economic Dynamics and Control, Elsevier, vol. 44(C), pages 124-146.
    2. Ayşegül İşcanog̃lu-Çekiç, 2016. "An Optimal Turkish Private Pension Plan with a Guarantee Feature," Risks, MDPI, vol. 4(3), pages 1-12, June.
    3. Hong‐Chih Huang, 2010. "Optimal Multiperiod Asset Allocation: Matching Assets to Liabilities in a Discrete Model," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 77(2), pages 451-472, June.
    4. Nancy Quinceno Cárdenas, 2014. "Modelación basada en agentes en el sistema pensional colombiano. Una aproximación desde el mercado laboral y la dinámica poblacional," Revista CIFE, Universidad Santo Tomás, September.
    5. Maria Alexandrova & Nadine Gatzert, 2019. "What Do We Know About Annuitization Decisions?," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 22(1), pages 57-100, March.
    6. Han, Nan-Wei & Hung, Mao-Wei, 2015. "The investment management for a downside-protected equity-linked annuity under interest rate risk," Finance Research Letters, Elsevier, vol. 13(C), pages 113-124.
    7. Mauricio Arias & Juan Carlos Mendoza, 2009. "Un modelo de simulación del Régimen Pensional de Ahorro Individual con Solidaridad en Colombia," Temas de Estabilidad Financiera 044, Banco de la Republica de Colombia.
    8. Iqbal Owadally & Steven Haberman & Denise Gómez Hernández, 2013. "A Savings Plan With Targeted Contributions," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(4), pages 975-1000, December.

    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. Hong‐Chih Huang, 2010. "Optimal Multiperiod Asset Allocation: Matching Assets to Liabilities in a Discrete Model," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 77(2), pages 451-472, June.
    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. Alessandra Milazzo & Elena Vigna, 2018. "The Italian Pension Gap: a Stochastic Optimal Control Approach," Carlo Alberto Notebooks 553, Collegio Carlo Alberto.
    4. Blake, David & Wright, Douglas & Zhang, Yumeng, 2013. "Target-driven investing: Optimal investment strategies in defined contribution pension plans under loss aversion," Journal of Economic Dynamics and Control, Elsevier, vol. 37(1), pages 195-209.
    5. Jacobs Martin, 2016. "Accounting for Changing Tastes: Approaches to Explaining Unstable Individual Preferences," Review of Economics, De Gruyter, vol. 67(2), pages 121-183, August.
    6. Alessandro Milazzo & Elena Vigna, 2018. "The Italian Pension Gap: A Stochastic Optimal Control Approach," Risks, MDPI, vol. 6(2), pages 1-20, April.
    7. Blake, David & Cairns, Andrew & Dowd, Kevin, 2008. "Turning pension plans into pension planes: What investment strategy designers of defined contribution pension plans can learn from commercial aircraft designers," MPRA Paper 33749, University Library of Munich, Germany.
    8. 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.
    9. Cairns, Andrew J.G. & Blake, David & Dowd, Kevin, 2006. "Pricing Death: Frameworks for the Valuation and Securitization of Mortality Risk," ASTIN Bulletin, Cambridge University Press, vol. 36(1), pages 79-120, May.
    10. Elena Vigna, 2009. "Mean-variance inefficiency of CRRA and CARA utility functions for portfolio selection in defined contribution pension schemes," CeRP Working Papers 89, Center for Research on Pensions and Welfare Policies, Turin (Italy).
    11. Alessandro Fiori Maccioni, 2011. "A Stochastic Model for the Analysis of Demographic Risk in Pay-As-You-Go Pension Funds," Papers 1106.5081, arXiv.org.
    12. Elena Vigna, 2009. "Mean-variance inefficiency of CRRA and CARA utility functions for portfolio selection in defined contribution pension schemes," Carlo Alberto Notebooks 108, Collegio Carlo Alberto, revised 2009.
    13. Gao, Jianwei, 2009. "Optimal investment strategy for annuity contracts under the constant elasticity of variance (CEV) model," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 9-18, August.
    14. Marina Di Giacinto & Elena Vigna, 2012. "On the sub-optimality cost of immediate annuitization in DC pension funds," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 20(3), pages 497-527, September.
    15. Alessandro Milazzo & Elena Vigna, 2018. "“The Italian Pension Gap: a Stochastic Optimal Control Approach"," CeRP Working Papers 179, Center for Research on Pensions and Welfare Policies, Turin (Italy).
    16. Alessandro Milazzo & Elena Vigna, 2018. "The Italian Pension Gap: a Stochastic Optimal Control Approach," Papers 1804.05354, arXiv.org.
    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. Christian Grund & Dirk Sliwka, 2007. "Reference-Dependent Preferences and the Impact of Wage Increases on Job Satisfaction: Theory and Evidence," Journal of Institutional and Theoretical Economics (JITE), Mohr Siebeck, Tübingen, vol. 163(2), pages 313-335, June.
    19. Wiafe, Osei K. & Basu, Anup K. & Chen, En Te, 2020. "Portfolio choice after retirement: Should self-annuitisation strategies hold more equities?," Economic Analysis and Policy, Elsevier, vol. 65(C), pages 241-255.
    20. Lovric, M. & Kaymak, U. & Spronk, J., 2008. "A Conceptual Model of Investor Behavior," ERIM Report Series Research in Management ERS-2008-030-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.

    More about this item

    Statistics

    Access and download statistics

    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:bla:jrinsu:v:75:y:2008:i:3:p:739-761. 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: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/ariaaea.html .

    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.