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Optimal funding of defined benefit pension plans

Published online by Cambridge University Press:  25 June 2010

DONATIEN HAINAUT  and
GRISELDA DEELSTRA
DONATIEN HAINAUT
Affiliation:
ESC Rennes Business School, Rennes, France (e-mail: [email protected])
GRISELDA DEELSTRA
Affiliation:
Dpt des Mathématiques, Université Libre de Bruxelles, Belgium (e-mail: [email protected])
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Abstract

In this paper, we address the issue of determining the optimal contribution rate of a defined benefit pension fund. The affiliate's mortality is modelled by a jump process and the benefits paid at retirement are function of the evolution of future salaries. Assets of the fund are invested in cash, stocks, and a rolling bond. Interest rates are driven by a Vasicek model. The objective is to minimize both the quadratic spread between the contribution rate and the normal cost, and the quadratic spread between the terminal wealth and the mathematical reserve required to cover benefits. The optimization is done under a budget constraint that guarantees the actuarial equilibrium between the current asset and future contributions and benefits. The method of resolution is based on the Cox–Huang approach and on dynamic programming.

Type
Articles
Information
Journal of Pension Economics & Finance , Volume 10 , Issue 1 , January 2011 , pp. 31 - 52
Copyright
Copyright © Cambridge University Press 2010

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References

Boulier, J. F., Trussant, E., and Florens, D. (1995) A dynamic model for pension fund management. Proceedings of the 5th AFIR International Symposium, Brussels, Vol 1, 361–384.Google Scholar
Brennan, M. J. and Xia, Y. (2002) Dynamic asset allocation under inflation. The Journal of Finance, 57(3): 1201–1238.CrossRefGoogle Scholar
Cairns, A. J. G. (1995) Pension funding in a stochastic environment: the role of objectives in selecting an asset allocation strategy. Proceedings of the 5th AFIR International Symposium, Brussels, Vol 1, 429–453.Google Scholar
Cairns, A. J. G. (2000) Some notes on the dynamics and optimal control of stochastic pension fund models in continuous time. ASTIN Bulletin, 30(1): 19–55.Google Scholar
Cairns, A. (2004) Interest Rate Models: An Introduction. Princeton, NJ: Princeton University Press.Google Scholar
Chan, T. (1997) Some applications of Lévy processes to stochastic investment models. ASTIN Bulletin, 28: 77–93.CrossRefGoogle Scholar
Cox, J. and Huang, C. F. (1989) Optimal consumption and portfolio policies when asset prices follow a diffusion process. Journal of Economic Theory, 49: 33–83.Google Scholar
Duffie, D. (2001) Dynamic Asset Pricing Theory. Third edition. Princeton, NJ: Princeton University Press.Google Scholar
Fleming, W. and Rishel, R. (1975) Deterministic and Stochastic Optimal Control. New York: Springer-Verlag.Google Scholar
Haberman, S. and Sung, J. H. (1994) Dynamic approaches to pension funding. Insurance: Mathematics and Economics, 15: 151–162.Google Scholar
Haberman, S. and Sung, J. H. (2005) Optimal pension funding dynamics over infinite control horizon when stochastic rates of return are stationary. Insurance: Mathematics and Economics, 36: 103–116.Google Scholar
Hainaut, D. and Devolder, P. (2007a) A martingale approach applied to the management of life insurances. ICFAI Journal of Risk and Insurance, 4.Google Scholar
Hainaut, D. and Devolder, P. (2007b) Management of a pension funds under stochastic mortality and interest rates. Insurance: Mathematics and economics, 41.Google Scholar
Huang, H.-C. and Cairns, A. J. G. (2006) On the control of defined-benefit pension plans. Insurance: Mathematics and Economics, 38: 113–131.Google Scholar
Josa-Fombellida, R. and Rincon-Zapatero, J. P. (2004) Optimal risk management in defined benefit stochastic pension funds. Insurance: Mathematics and Economics, 34: 489–503.Google Scholar
Josa-Fombellida, R. and Rincon-Zapatero, J. P. (2006) Optimal investment decisions with a liability: the case of defined benefits pension plans. Insurance: Mathematics and Economics, 36: 81–98.Google Scholar
Karatzas, I. and Shreve, S. (1998) Methods of Mathematical Finance. New York: Springer-Verlag.Google Scholar
Møller, T. (1998) Risk minimizing hedging strategies for unit-linked life insurance contracts. ASTIN Bulletin, 28(1): 17–47.Google Scholar
Nielsen, P. H. (2005) Utility maximization and risk minimization in life and pension insurance. Finance and Stochastics, 10(1): 75–97.Google Scholar
Øksendal, B. and Sulem, A. (2004) Applied Stochastic Control of Jump Diffusions. New York: Springer-Verlag.Google Scholar
Sundaresan, S. and Zapatero, F. (1997) Valuation, optimal asset allocation and retirement incentives of pension plans. The Review of Financial Studies, 10(3): 631–660.Google Scholar
Wilkie, A. D. (1986) A stochastic investment model for actuarial use. TFA, 39: 341–403.Google Scholar
Wilkie, A. D. (1995) More on a stochastic asset model for actuarial use. Bristish Actuarial Journal, 1: 777–964.Google Scholar
Yong, J. and Zhou, X. Y. (1999) Stochastic Controls: Hamiltonian Systems and HJB Equations. New York: Springer-Verlag.Google Scholar