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Optimal funding of defined benefit pension plans

  • DONATIEN HAINAUT (a1) and GRISELDA DEELSTRA (a2)

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.

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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, 361384.
Brennan, M. J. and Xia, Y. (2002) Dynamic asset allocation under inflation. The Journal of Finance, 57(3): 12011238.
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, 429453.
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): 1955.
Cairns, A. (2004) Interest Rate Models: An Introduction. Princeton, NJ: Princeton University Press.
Chan, T. (1997) Some applications of Lévy processes to stochastic investment models. ASTIN Bulletin, 28: 7793.
Cox, J. and Huang, C. F. (1989) Optimal consumption and portfolio policies when asset prices follow a diffusion process. Journal of Economic Theory, 49: 3383.
Duffie, D. (2001) Dynamic Asset Pricing Theory. Third edition. Princeton, NJ: Princeton University Press.
Fleming, W. and Rishel, R. (1975) Deterministic and Stochastic Optimal Control. New York: Springer-Verlag.
Haberman, S. and Sung, J. H. (1994) Dynamic approaches to pension funding. Insurance: Mathematics and Economics, 15: 151162.
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: 103116.
Hainaut, D. and Devolder, P. (2007a) A martingale approach applied to the management of life insurances. ICFAI Journal of Risk and Insurance, 4.
Hainaut, D. and Devolder, P. (2007b) Management of a pension funds under stochastic mortality and interest rates. Insurance: Mathematics and economics, 41.
Huang, H.-C. and Cairns, A. J. G. (2006) On the control of defined-benefit pension plans. Insurance: Mathematics and Economics, 38: 113131.
Josa-Fombellida, R. and Rincon-Zapatero, J. P. (2004) Optimal risk management in defined benefit stochastic pension funds. Insurance: Mathematics and Economics, 34: 489503.
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: 8198.
Karatzas, I. and Shreve, S. (1998) Methods of Mathematical Finance. New York: Springer-Verlag.
Møller, T. (1998) Risk minimizing hedging strategies for unit-linked life insurance contracts. ASTIN Bulletin, 28(1): 1747.
Nielsen, P. H. (2005) Utility maximization and risk minimization in life and pension insurance. Finance and Stochastics, 10(1): 7597.
Øksendal, B. and Sulem, A. (2004) Applied Stochastic Control of Jump Diffusions. New York: Springer-Verlag.
Sundaresan, S. and Zapatero, F. (1997) Valuation, optimal asset allocation and retirement incentives of pension plans. The Review of Financial Studies, 10(3): 631660.
Wilkie, A. D. (1986) A stochastic investment model for actuarial use. TFA, 39: 341403.
Wilkie, A. D. (1995) More on a stochastic asset model for actuarial use. Bristish Actuarial Journal, 1: 777964.
Yong, J. and Zhou, X. Y. (1999) Stochastic Controls: Hamiltonian Systems and HJB Equations. New York: Springer-Verlag.
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Journal of Pension Economics & Finance
  • ISSN: 1474-7472
  • EISSN: 1475-3022
  • URL: /core/journals/journal-of-pension-economics-and-finance
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