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Income Drawdown Schemes for a Defined‐Contribution Pension Plan

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  • 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.

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  • 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
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    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.
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    Cited by:

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    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Ayşegül İşcanog̃lu-Çekiç, 2016. "An Optimal Turkish Private Pension Plan with a Guarantee Feature," Risks, MDPI, vol. 4(3), pages 1-12, June.
    8. 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.

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