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Stochastic Actuarial Modelling of a Defined-Benefit Social Security Pension Scheme: An Analytical Approach

Published online by Cambridge University Press:  10 May 2011

Subramaniam Iyer
Subramaniam Iyer
Affiliation:
Hon. FIA. 3, Rue Giovanni-Gambini, 1206 Geneva, Switzerland. Email: [email protected]
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Abstract

Among the systems in place in different countries for the protection of the population against the long-term contingencies of old-age (or retirement), disability and death (or survivorship), defined-benefit social security pension schemes, i.e. social insurance pension schemes, by far predominate, despite the recent trend towards defined-contribution arrangements in social security reforms. Actuarial valuations of these schemes, unlike other branches of insurance, continue to be carried out almost exclusively on traditional, deterministic lines. Stochastic applications in this area, which have been restricted mainly to occasional special studies, have relied on the simulation technique. This paper develops an analytical model for the stochastic actuarial valuation of a social insurance pension scheme. Formulae are developed for the expected values, variances and covariances of and among the benefit expenditure and salary bill projections and their discounted values, allowing for stochastic variation in three key input factors, i.e., mortality, new entrant intake, and interest (net of salary escalation). Each deterministic output of the valuation is thus supplemented with a confidence interval, that is, a range with an attached probability. The treatment covers the premiums under the different possible financial systems for these schemes, which differ from the funding methods of private pensions, as well as the testing of the level of the Fund ratio when the future contributions schedule is pre-determined. Although it is based on a relatively simplified approach and refers only to retirement pensions, with full adjustment in line with salary escalation, the paper brings out the stochastic features of pension scheme projections and illustrates a comprehensive stochastic valuation. It is hoped that the paper will stimulate interest in further research, both of a theoretical and a practical nature, and lead to progressively increasing recourse to stochastic methods in social insurance pension scheme valuations.

Keywords

Social SecuritySocial InsurancePensionsActuarial ValuationDeterministic MethodStochastic MethodDemographic ProjectionsFinancial ProjectionsFinancial Systems
Type
Papers
Information
Annals of Actuarial Science , Volume 3 , Issue 1-2 , September 2008 , pp. 127 - 185
Copyright
Copyright © Institute and Faculty of Actuaries 2008

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References

Alho, J.M. (2007). Methods used in drawing up mortality projections. Fifteenth International Conference of Social Security Actuaries and Statisticians. International Social Security Association, Helsinki.Google Scholar
Alho, J.M. & Spencer, B.D. (2005). Statistical demography and forecasting, Springer.Google Scholar
American Academy of Actuaries (2005). Issue brief: a guide to the use of stochastic models in analyzing social security.Google Scholar
Board of Trustees, Federal OASDI Trust Funds (2007). The 2007 annual report of the board of trustees of the federal old-age and survivors insurance and disability insurance trust funds, US Government Printing Office, Washington, D.C.Google Scholar
Bongaarts, J. & Bulatao, R.A. (eds) (2000). Beyond six billion: forecasting the world's population. National Research Council, National Academy Press, Washington, D.C.Google Scholar
Booth, H. (2006). Demographic forecasting: 1980 to 2005 in review. International Journal of Forecasting, 22(3), 547–581.CrossRefGoogle Scholar
Booth, P., Chadburn, R., Cooper, D., Haberman, S. & James, D. (1999). Modern actuarial theory and practice. Chapman & Hall/CRC, London.Google Scholar
Buffin, K.G. (2007). Stochastic projection methods for social security systems. PBSS Colloquium, International Actuarial Association, Helsinki.Google Scholar
Burdick, C. & Manchester, J. (2003). Stochastic models of the social security trust fund. Office of Policy Research, Social Security Administration, Washington, D.C.Google Scholar
Congressional Budget Office (2001). Uncertainty in social security's long-term finances: a stochastic analysis. Washington, D.C.Google Scholar
Daykin, C.D., Pentikainen, T. & Pesonen, M. (1994). Practical risk theory for actuaries. Chapman & Hall, London.Google Scholar
Daykin, C.D. & Lewis, D. (1999). A crisis of longer life: reforming pension systems. British Actuarial Journal, 5(1), 55–97.Google Scholar
Daykin, C.D. (2000). Social security and the consulting actuary. International Actuarial Association, Social Security Committee.Google Scholar
Daykin, C.D. (2001). The role of the Government Actuary's Department in social security in the United Kingdom. British Actuarial Journal, 7(V), 765–790.Google Scholar
Engen, S., Bakke, O. & Islam, A. (1998). Demographic and environmental stochasticity — concepts and definitions. Biometrics, 54, 840–846.Google Scholar
Engen, S. & Saether, B.-E. (2003). Stochastic population dynamics in ecology and conservation: an introduction. Oxford University Press.Google Scholar
Fenton, L.F. (1960). The sum of lognormal probability distributions in scatter transmission systems. IRE Trans. Commun. Syst., CS(8), 57–67.CrossRefGoogle Scholar
Fieller, E.C. (1932). The distribution of the index in a normal bivariate population. Biometrika, 24, 428–440.Google Scholar
Gillion, C., Turner, J., Bailey, C. & Latulippe, D. (eds) (2000). Social security pensions: development and reform. International Labour Office, Geneva.Google Scholar
Government Actuary's Department (2003). Government Actuary's Quinquennial Review of the National Insurance Fund as at April 2000. London.Google Scholar
Government Actuary's Department (2005). Variant projections of the update of the Government Actuary's Quinquennial Review of the National Insurance Fund as at April 2000. London.Google Scholar
Hinkley, D.V. (1969, 1970). On the ratio of two correlated random variables. Biometrika, 56(3), 635–639 and 57(3), 683.Google Scholar
Holzmann, R. & Hinz, R. (2005). Old-age income support in the 21st century. The World Bank, Washington, D.C.CrossRefGoogle Scholar
Holzmann, R. & Palmer, E. (2003). Pension reform: issues and prospects for non-financial defined contribution (NDC) schemes. The World Bank, Washington, D.C.CrossRefGoogle Scholar
International Actuarial Association (2003). Final IAA Guidelines of Actuarial Practice for Social Security Programs.Google Scholar
Iyer, S. (1999). Actuarial mathematics of social security pensions. International Labour Office, Geneva.Google Scholar
Iyer, S. (2003). Application of stochastic methods in the valuation of social security pension schemes. CASS Business School, City University, London.Google Scholar
Iyer, S. (2006). A stochastic approach to the actuarial valuation of social security pension schemes. Institute of Insurance and Pension Research, University of Waterloo, Waterloo.Google Scholar
Keilman, N., Pham, D.Q. & Hetland, A. (2002). Why population forecasts should be probabilistic. Demographic Research, 6(15), 409–454.CrossRefGoogle Scholar
Lee, R.D., Anderson, M.W. & Tuljapurkar, S. (2003). Stochastic forecasts of the social security trust fund. Institute of Business and Economic Research, University of California, Berkeley.Google Scholar
Lee, R. (2004). Quantifying our ignorance: stochastic forecasts of population and public budgets. In Waite, Linda I. (ed.). Population and Development Review, V(30), 153–176.Google Scholar
Li, S.-H., Hardy, M.R. & Tan, K.S. (2006). Uncertainty in mortality forecasting: an extension to the classical Lee-Carter approach. Institute of Insurance and Pension Research, University of Waterloo, Waterloo.Google Scholar
Limpert, E., Stahel, W.A. & Abbt, M. (2001). Lognormal distributions across the sciences: keys and clues. Bioscience, 51(5), 341–352.CrossRefGoogle Scholar
McGillivray, W.R. (1996). Actuarial valuations of social security schemes: Necessity, utility and misconceptions. Social security financing: issues and perspectives. International Social Security Association, Geneva.Google Scholar
Office of the Superintendent of Financial Institutions, Canada: Office of the Chief Actuary (2007). Actuarial Report (23rd) on the Canada Pension Plan as at 31 December 2006. Ottawa.Google Scholar
Parker, G. (1994). Two stochastic approaches for discounting actuarial functions. ASTIN Bulletin, 24(2), 167–181.Google Scholar
Picard, J.-P. (1996). Valuation of the financial equilibrium of long-term benefit schemes. Social security financing: issues and perspectives. International Social Security Association, Geneva.Google Scholar
Pitacco, E. (2004). Survival models in a dynamic context: a survey. Insurance: Mathematics and Economics, 35, 279–298.Google Scholar
Plamondon, P., Drouin, A., Binet, G., Cichon, M., McGillivray, W.R., Bedard, M. & Perez-Montas, H. (2002). Actuarial Practice in Social Security. International Labour Office, Geneva.Google Scholar
Redington, F.M. (1952). Review of the principles of life-office valuations. Journal of the Institute of Actuaries, LXXVIII, 286–315.Google Scholar
Regie des Rentes du Quebec (2007). Actuarial Report of the Quebec Pension Plan as at 31 December 2006. Quebec.Google Scholar
Renshaw, A.E. & Haberman, S. (2006). A cohort-based extension to the Lee-Carter model for mortality reduction factors. Insurance: Mathematics and Economics, 38(3), 556–570.Google Scholar
Renshaw, E. (1991). Modelling biological populations in space and time. Cambridge University Press, Cambridge.CrossRefGoogle Scholar
Sloan, I.H. & Joe, S. (1994). Lattice models for multiple integration. Clarendon Press, Oxford.Google Scholar
Social Security Administration (2004). A stochastic model of the long-range financial status of the OASDI program (Actuarial Study No. 117). Office of the Chief Actuary, Washington, D.C.Google Scholar
Social Security Administration (2005). Social Security Programs throughout the World: Africa 2005. Washington, D.C.Google Scholar
Social Security Administration (2006a). Social Security Programs throughout the World: The Americas 2005. Washington, D.C.Google Scholar
Social Security Administration (2006b). Social Security Programs throughout the World: Europe 2006. Washington, D.C.Google Scholar
Social Security Administration (2007). Social Security Programs throughout the World: Asia and the Pacific 2006. Washington, D.C.Google Scholar
Tuljapurkar, S. & Boe, C. (1998). Mortality change and forecasting: How much and how little do we know? North American Actuarial Journal, 2(4), 13–47.Google Scholar
United Nations (1982). Unabridged model life tables corresponding to the new United Nations Model Life Tables for Developing Countries. New York.Google Scholar
Van Duffel, S., Hoedemakers, T. & Dhaene, J. (2005). Comparing approximations for risk measures of sums of non-independent lognormal random variables. North American Actuarial Journal, 9(4), 71–82.Google Scholar
Von Luxburg, U. & Franz, V.H. (2004). Confidence sets for ratios: a purely geometric approach to Fieller's theorem. Max-Planck Institute for Biological Cybernetics, Tubingen.Google Scholar
Wilkie, A.D. (1986). A stochastic investment model for actuarial use. Transactions of the Faculty of Actuaries, 39, 341–403.Google Scholar