Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-29T07:48:52.287Z Has data issue: false hasContentIssue false
  • English
  • Français

Stochastic Pension Funding: Proportional Control and Bilinear Processes

Published online by Cambridge University Press:  29 August 2014

Diane Bédard
Diane Bédard*
Affiliation:
Université Laval, August 1999
*
École d'actuariat, Local 1620, Pavilion Vachon Universite Laval Quebec, PQ GIK 7P4, Canada
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper, we find explicit expressions for the moments of the fund level and the value of the total contribution when arithmetic or geometric rates of return are modeled by a moving average process of order q and when a proportional control is applied to the contributions. Our approach is based on the bilinear Markovian representation.

Keywords

Bilinear Markovian representationgeometric bilinear processesmoving average rate of returnpension funding
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 29 , Issue 2 , November 1999 , pp. 271 - 293
Copyright
Copyright © International Actuarial Association 1999

References

[1]Bédard, D. (1997). Modélisation stochastique des caisses de retraite. Ph.D. Thesis, Université de Montréal, Montréal.Google Scholar
[2]Bedard, D. and Dufresne, D. (1999). Pension funding with moving average rates of return. To be published.Google Scholar
[3]Cairns, A.J.G. and Parker, G. (1997). Stochastic pension fund modelling. Insurance: Mathematics and Economics 21: 43–79.Google Scholar
[4]Dufresnk, D. (1986). Pension funding and random rates of return. In: Insurance and Risk Theory, Goovaerts, M.et al. (eds.): 277–291.CrossRefGoogle Scholar
[5]Dufresne, D. (1988). Moments of pension contributions and fund levels when rates of return are random. Journal of the Institute of Actuaries 115: 535–544.CrossRefGoogle Scholar
[6]Dufresne, D. (1989). Stability of pension systems when rates of return are random. Insurance: Mathematics and Economics 8: 71–76.Google Scholar
[7]Dufresne, D. (1990). Fluctuations of pension contributions and fund levels. Actuarial Research Clearing House 1990.1: 111–120.Google Scholar
[8]Dufresne, D. (1993). Some aspects of statement of financial accounting standards no. 87. Actuarial Research Clearing House 1993.2: 1–130.Google Scholar
[9]Dufresne, D. (1994). Mathématiques des caisses de retraite. Editions Suprémum, Montreal.Google Scholar
[10]Gerrard, R.J. and Haberman, S. (1996). Stability of pension systems when gains/losses are amortized and rates of return are autoregressive. Insurance: Mathematics and Economics 18: 59–71.Google Scholar
[11]Granger, C.W. and Andersen, A.P. (1978). An Introduction to Bilinear Time Series Model. Vanderhoeck and Ruprecht, Gottingern.Google Scholar
[12]Guegan, D. (1987). Different representations for bilinear models. J. Time Ser. Anal. 8: 389–408.CrossRefGoogle Scholar
[13]Haberman, S. (1993a). Pension funding with time delays and autoregressive rates of investment return. Insurance: Mathematics and Economics 13: 45–56.Google Scholar
[14]Haberman, S. (1993b). Pension funding: The effect of changing the frequency of valuations. Insurance: Mathematics and Economics 13: 263–270.Google Scholar
[15]Haberman, S. (1994). 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.Google Scholar
[16]Haberman, S. and Wong, L.Y.P. (1997). Moving average rates of return and the variability of pension contributions and fund levels for a defined benefit pension scheme. Insurance: Mathematics and Economics 20: 115–135.Google Scholar
[17]Nicholls, D.F. and Quinn, B.G. (1982). Random coefficient autoregressive models: an introduction. Lectures Notes in Statistics. Vol. No. 11. Springer, New York.CrossRefGoogle Scholar
[18]Pham, D.T. (1986). The mixing property of bilinear and generalised random coefficient autoregressive models. Stochastic Processes Appl. 23: 291–300.Google Scholar
[19]Zimbidis, A. and Haberman, S. (1993). Delay, feedback and the variability of pension contributions and fund levels. Insurance: Mathematics and Economics 13: 271–285.Google Scholar