Stochastic investment returns and contribution rate risk in a defined benefit pension scheme. (English) Zbl 0901.90012

Summary: We consider the “contribution rate risk” for defined benefit occupational pension schemes, and compare different approaches to funding from the viewpoint of minimizing the variability in the present value of future contributions as a means of controlling this type of risk to the scheme’s sponsor. This leads to a discussion of which periods for spreading valuation surpluses and deficiencies should be chosen to minimize this measure of risk. The underlying model of investment returns used is that real rates of investment return are independent and identically distributed.


91B28 Finance etc. (MSC2000)
91B30 Risk theory, insurance (MSC2010)
62P05 Applications of statistics to actuarial sciences and financial mathematics
Full Text: DOI


[1] Bühlmann, H., Stochastic discounting, Insurance: mathematics and economics, 11, 113-127, (1992) · Zbl 0763.62055
[2] Dufresne, D., The dynamic of pension funding, () · Zbl 0606.62123
[3] Dufresne, D., Moments of pension fund contributions and fund levels when rates of return are random, Journal of institute of actuaries, 115, 535-544, (1988)
[4] Haberman, S., Pension funding with time delays: A stochastic approach, Insurance: mathematics and economics, 11, 179-189, (1992) · Zbl 0764.62090
[5] Haberman, S., Autoregressive rates of return and the variability of pension contributions and fund levels for a defined benefit pension scheme, Insurance: mathematics and economics, 14, 219-240, (1994) · Zbl 0808.62097
[6] Haberman, S.; Dufresne, D., Variability of pension contributions and fund levels with random rates of return, (), 134-145
[7] Haberman, S.; Sung, J.H., Dynamic approaches to pension funding, Insurance: mathematics and economics, 15, 151-162, (1994) · Zbl 0818.62091
[8] Keyfitz, N., ()
[9] Lee, E.M., ()
[10] Marshall, D.R.; Reeve, J.G., Defined benefit pension schemes: funding for ongoing security, (), 2 February 1993, London, UK
[11] O’Brien, T., A stochastic-dynamic approach to pension funding, Insurance: mathematics and economics, 5, 141-146, (1986) · Zbl 0587.62191
[12] Owadally, M.I.; Haberman, S., Stochastic investment modelling and optimal pension funding strategies, ()
[13] Trowbridge, C.L., Fundamentals of pension funding, Transactions of the society of actuaries, 4, 17-43, (1952)
[14] Turner, J.A.; Beller, D.J., ()
[15] Uspensky, J.V., ()
[16] Zimbidis, A.; Haberman, S., Delay, feedback and the variability of pension contributions and fund levels, Insurance: mathematics and economics, 13, 271-285, (1993) · Zbl 0793.62063
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.