Optimal management under stochastic interest rates: the case of a protected defined contribution pension fund. (English) Zbl 0976.91034

Summary: This paper deals with the pension fund management issue. We focus on defined-contribution plans where a guarantee is given on the benefits, and the guarantee depends on the level of the stochastic interest rate when the employee retires. It is particularly shown that the optimal composition of this kind of pension fund can be divided into three different parts: a loan which amounts to the present value of the contributions, a contingent claim delivering the guarantee and a hedging fund. A Vasicek interest rate model is considered as an illustration of our analysis.


91B30 Risk theory, insurance (MSC2010)
91G30 Interest rates, asset pricing, etc. (stochastic models)
Full Text: DOI


[3] Bielecki, T. R.; Pliska, S. R., Risk-sensitive dynamic asset allocation, Asset and Liability Management, 8, 129-138 (1998) · Zbl 0984.91047
[4] Black, F.; Perold, A., Theory of constant proportion portfolio insurance, Journal of Economic Dynamics and Control, 16, 403-426 (1992) · Zbl 0825.90056
[5] Bodie, Z.; Crane, D. B., The design and production of new retirement savings products, The Journal of Portfolio Management, 25, 77-82 (1999)
[6] Bodie, Z.; Merton, R. C.; Samuelson, W. F., Labor supply flexibility and portfolio choice in a life cycle model, Journal of Economic Dynamics and Control, 3-4, 16, 427-449 (1992)
[11] Brennan, M. J.; Schwartz, E. S.; Lagnado, R., Strategic asset allocation, Journal of Economic Dynamics and Control, 21, 8-9, 1377-1403 (1997) · Zbl 0901.90008
[20] Khorasanee, M. Z., A pension plan incorporation both defined benefit and defined contribution principles, Journal of Actuarial Practice, 3, 2, 269-300 (1996) · Zbl 1060.91063
[21] Khorasanee, M. Z., Deterministic modeling of defined-contribution pension fund, North American Actuarial Journal, 1, 4, 83-103 (1997) · Zbl 1080.91521
[23] Merton, R., Optimum consumption and portfolio rules in a continuous-time model, Journal of Economic Theory, 3, 373-413 (1971) · Zbl 1011.91502
[24] Pardoux, E.; Peng, S., Adapted solution of a backward stochastic differential equation, Systems and Control Letters, 14, 55-61 (1990) · Zbl 0692.93064
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.