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IMPLEMENTING INDIVIDUAL SAVINGS DECISIONS FOR RETIREMENT WITH BOUNDS ON WEALTH

Published online by Cambridge University Press:  30 October 2017

Catherine Donnelly ,
Montserrat Guillen ,
Jens Perch Nielsen  and
Ana Maria Pérez-Marín
Catherine Donnelly
Affiliation:
Department of Actuarial Mathematics and Statistics, and the Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK E-mail: [email protected]
Montserrat Guillen*
Affiliation:
Department of Econometrics, Riskcenter-IREA, University of Barcelona, Avinguda Diagonal 690, 08034 Barcelona, Spain
Jens Perch Nielsen
Affiliation:
Cass Business School, City University London, 106 Bunhill Row, London EC1Y 8TZ, UK E-Mail: [email protected]
Ana Maria Pérez-Marín
Affiliation:
Department of Econometrics, Riskcenter-IREA, University of Barcelona, Avinguda Diagonal 690, 08034 Barcelona, Spain E-Mail: [email protected]
*
E-Mail: [email protected]
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Abstract

We present a savings plan for retirement that removes risk by fixing a constraint on a life-long pension so that it has an upper and a lower bound. This corresponds to the ideas of Nobel laureate R.C. Merton whose implementation has never been published. We show with an illustration that our proposed practical algorithm reproduces the theoretical results after a savings period of around 30 years by using daily, monthly, weekly or yearly updates of the investment positions. We calculate the percentiles of the final accumulated wealth distribution for the adjusted implementation. In the simulated illustration, we observe that the adjusted values converge to the theoretical values of the percentiles when the frequency of update increases. We conclude that monthly adjustments result in a practical way to implement theoretical results that were obtained under the hypothesis of a continuous process by Donnelly et al. (2015). This method is easy to use in practice by pension savers and fund managers.

Keywords

Pensionslongevityinvestmentsavings strategyguaranteed annuities
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 48 , Issue 1 , January 2018 , pp. 111 - 137
Copyright
Copyright © Astin Bulletin 2017 

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References

Basak, S. (1995) A general equilibrium model of portfolio insurance. The Review of Financial Studies, 8 (4), 1059–1090.Google Scholar
Basu, A.K., Byrne, A. and Drew, M.E. (2011) Dynamic lifecycle strategies for target date retirement funds. Journal of Portfolio Management, 37, 83–96.Google Scholar
Behrman, J.R., Mitchell, O.S., Soo, C.K. and Bravo, D. (2012) How financial literacy affects household wealth accumulation. The American Economic Review, 102 (3), 300.Google Scholar
Bernard, C., Chen, J.S. and Vanduffel, S. (2014) Optimal portfolios under worst-case scenarios. Quantitative Finance, 14 (4), 657–671.Google Scholar
Bouchard, B., Elie, R. and Imbert, C. (2010) Optimal control under stochastic target constraints. SIAM Journal on Control and Optimization, 48, 3501–3531.Google Scholar
Boyle, P. and Tian, W. (2007) Portfolio management with constraints. Mathematical Finance, 17, 319–343.Google Scholar
Browne, S. (1999) Reaching goals by a deadline: digital options and continuous time active portfolio management. Advances in Applied Probability, 31, 551–577.Google Scholar
Cuoco, D. (1997) Optimal consumption and equilibrium prices with portfolio constraints and stochastic income. Journal of Economic Theory, 72, 33–73.Google Scholar
Dhaene, J., Vanduffel, S., Goovaerts, Kaas R. and Vyncke, D. (2005) Comonotonic approximations for optimal portfolio selection problems. Journal of Risk and Insurance, 72, 253–300.Google Scholar
Dimson, E., Marsh, P. and Staunton, M. (2002) Triumph of the Optimist: 101 Years of Global Investment Returns. Princeton, NJ: Princeton University Press.Google Scholar
Donnelly, C., Gerrard, R., Guillen, M. and Nielsen, J.P. (2015) Less is more: increasing retirement gains by using an upside terminal wealth constraint. Insurance: Mathematics and Economics, 64, 259–267.Google Scholar
Gaibh, A., Sass, J. and Wunderlich, R. (2009) Utility maximization under bounded expected loss. Stochastic Models, 25, 375–407.Google Scholar
Gerrard, R., Guillen, M., Nielsen, J.P. and Pérez-Marín, A.M. (2014) Long-run savings and investment strategy optimization. The Scientific World Journal, 2014, Article ID 510531.CrossRefGoogle Scholar
Greninger, S., Hampton, V., Kitt, K. and Jacquet, S. (2000) Retirement planning guidelines: A delphi study of financial planners and educators. Financial Services Review, 6, 231–245.Google Scholar
Grossman, S.J. and Zhou, Z. (1996) Equilibrium analysis of portfolio insurance. Journal of Finance, 51, 1379–1403.Google Scholar
Guillen, M., Jørgensen, P.L. and Nielsen, J.P. (2006) Return smoothing mechanisms in life and pension insurance: Path-dependent contingent claims. Insurance: Mathematics and Economics, 38 (4), 229–252.Google Scholar
Guillen, M., Nielsen, J.P., Pérez-Marín, A.M. and Petersen, K.S. (2013) Performance measurement of pension strategies: A case study of Danish life-cycle products. Scandinavian Actuarial Journal, 2013, 49–68.CrossRefGoogle Scholar
Hainaut, D. and Devolder, P. (2007) Management of a pension fund under mortality and financial risks. Insurance: Mathematics and Economics, 41 (4), 134–155.Google Scholar
Korn, R. and Trautmann, S. (1995) Continuous-time portfolio optimization under terminal wealth constraints. Mathematical Methods of Operations Research, 42, 69–92.Google Scholar
Lusardi, A. and Mitchell, O.S. (2007) Financial literacy and retirement preparedness: Evidence and implications for financial education. Business Economics, 42 (1), 35–44.Google Scholar
Maurer, R., Mitchell, O.S., Rogalla, R. and Siegelin, I. (2016) Accounting and actuarial smoothing of retirement payouts in participating life annuities. Insurance: Mathematics and Economics, 71, 268–283.Google Scholar
Merton, R.C. (2014) The crisis in retirement planning. Harvard Business Review, 92 (4), 42–50.Google Scholar
R Core Team (2014) R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. URL: http://www.R-project.org/.Google Scholar
Van Weert, K., Dhaene, J. and Goovaerts, M. (2010) Optimal portfolio selection for general provisioning and terminal wealth problems. Insurance: Mathematics and Economics, 47, 90–97.Google Scholar
Zariphopoulou, T. (1994) Consumption-investment models with constraints. SIAM Journal on Control and Optimization, 32, 59–85.Google Scholar