Skip to main content Accessibility help

A Stochastic Approach to Risk Management and Decision Making in Defined Benefit Pension Schemes

  • S. Haberman (a1), C. Day (a2), D. Fogarty (a3), M. Z. Khorasanee (a4), M. McWhirter (a5), N. Nash (a6), B. Ngwira (a7), I. D. Wright (a8) and Y. Yakoubov (a9)...


The trustees and sponsors of defined benefit schemes rely on the advice of the Scheme Actuary to make important decisions concerning the funding of the scheme, the investment of its assets, and the use of surplus assets to improve benefits. These decisions have to be made in the face of considerable uncertainty about financial and demographic factors that will affect the future experience of the scheme and its success in meeting various objectives.

The traditional actuarial valuation combined with actuarial judgement has played an important role in guiding decision making; but we argue that stochastic methods can add value in certain crucial areas, in particular the financial risk management of defined benefit schemes. Rather than dealing with risk by incorporating margins in the valuation basis, a stochastic approach allows the actuary to evaluate specific and quantifiable risk and performance measures for alternative funding and investment strategies.

This paper recommends a framework that, when combined with a suitable stochastic model, measures the risks inherent in contribution rate and asset allocation decisions, allowing better decisions to be made. In doing this, we suggest and apply various risk and performance measures that may be thought appropriate, although our intention is to illustrate their use rather than prescribe them as objective standards. The framework provides the means to explore the trade-offs involved in possible contribution and asset allocation decisions, and points to decision strategies expected to give improved outcomes for the same level of risk. A feature of the approach that marks it out from current asset/liability techniques is that it examines the funding and investment decisions together. It does not derive a contribution rate in the traditional way, but leaves this as free variable, in the same way that the investment decision is taken to be a free variable. Another distinctive feature of our framework is that it is based on projection rather than on valuation, involving stochastic simulation of the experience of the scheme over a time horizon reflecting the concerns of the trustees and the sponsoring employer.

The paper provides a case study (based on a model final salary pension scheme) showing the advantages of the framework, and goes on to explain how the results may practically be communicated to trustees and scheme sponsors.



Hide All
Albrecht, P., Maurer, R. & Ruckpaul, U. (2001). The risk of stocks in the long run: unconditional vs conditional shortfall. Proceedings of 11th Annual International AFIR Colloquium, 1, 3962.
Allais, M. (1953). Le comportement de l'homme rationnel devant le risque: critiques des postulats et axiomes de l'école Américaine. Econometrica, 21, 4, 503546.
Artzner, P., Delbaen, F., Eber, J.-M. & Heath, D. (1997). Thinking coherently. Risk, 10 (November), 6871.
Artzner, P., Delbaen, F., Eber, J.-M. & Heath, D. (1999). Coherent measures of risk. Mathematical Finance, 9, 203228.
Bacinello, A.R. (1988). A stochastic simulation procedure for pension schemes. Insurance: Mathematics and Economics, 7, 153161.
Begg, D., Fischer, S. & Dornbusch, R. (2000). Economics. (Sixth edition), McGraw-Hill, London.
Bertsekas, D.P. (1976). Dynamic programming and stochastic control. New York: Academic Press.
Black, F. & Jones, R. (1987). Simplifying portfolio insurance. Journal of Portfolio Management, fall, 4851.
Boulier, J.-F., Trussant, E. & Florens, D. (1995). A dynamic model for pensions funds management. Proceedings of the 5th AFIR International Colloquium, Leuven, Belgium, 1, 361384.
Bowers, N.L., Hickman, J.C. & Nesbitt, C.J. (1979). The dynamics of pension funding: contribution theory. Transactions of the Society of Actuaries 31, 93122.
Bowers, N.L., Gerber, H.U., Hickman, J.C., Jones, D.A. & Nesbitt, C.J. (1997). Actuarial Mathematics. Society of Actuaries.
Cairns, A.J.G. (1997). A comparison of optimal and dynamic control strategies for continuous-time pension fund models. Proceedings of the 7th AFIR International Colloquium, Cairns, Australia 1, 309326.
Cairns, A.J.G. (2000). Some notes on the dynamics and optimal control of stochastic pension fund models in continuous time. ASTIN Bulletin, 30, 1955.
Cairns, A.J.G. (2000)a. A discussion of parameter and model uncertainty in insurance. Insurance: Mathematics and Economics, 27, 313330.
Chapman, R.J., Gordon, T.J. & Speed, C.A. (2001). Pensions, funding and risk. British Actuarial Journal, 7, 605662.
Chopra, V.K. & Ziemba, W.T. (1993). The effect of errors in means, variances and covariances on optimal portfolio choice. Journal of Portfolio Management, 19, 614.
Clarkson, R.S. & Plymen, J. (1988). Improving the performance of equity portfolios. Journal of the Institute of Actuaries, 115, 631674, and Transactions of the Faculty of Actuaries, 41, 631–675, 730–750.
Daykin, C.D., Pentikainen, T. & Pesonen, M. (1994). Practical risk theory for actuaries. Chapman and Hall, London.
Dowd, K. (1998). Beyond value at risk. John Wiley and Sons, Chichester.
Dufresne, D. (1988). Moments of pension contributions and fund levels when rates of return are random. Journal of the Institute of Actuaries, 115, 535544.
Exley, C.J., Mehta, S.J.B. & Smith, A.D. (1997). The financial theory of defined benefit pension schemes. British Actuarial Journal, 3, 835996.
Geoghegan, T.J., Clarkson, R.S., Feldman, K.S., Green, S.J., Kitts, A., Lavecky, P., Ross, J.M., Smith, W.J. & Toutounchi, A. (1992). Report on the Wilkie stochastic investment model. Journal of the Institute of Actuaries, 119, 173212.
Haberman, S., Butt, Z. & Rickayzen, B.D. (2000). Multiple state models, simulation and insurer insolvency. Giornale dell' Istituto Italiano degli Attuari, 43, 83109.
Haberman, S. & Vigna, E. (2002). Optimal investment strategies and risk measures in defined contribution pension schemes. Insurance: Mathematics and Economics, 31, 3569.
Hairs, C.J., Belsham, D.J., Bryson, N.M., George, C.M., Hare, D.J.P., Smith, D.A. & Thompson, S. (2001). Fair valuation of liabilities. British Actuarial Journal, 8, 203340.
Head, S.J., Adkins, D.R., Cairns, A.J.G., Corvesor, A.J., Cule, D.O., Exley, C.J., Johnson, I.S., Spain, J.G. & Wise, A.G. (2000). Pension fund valuations and market values. British Actuarial Journal, 6, 55118.
Huber, P.P. (1998). A note on the jump-equilibrium model. British Actuarial Journal, 4, 615636.
Kemp, M.H.D. (1996). Asset-liability modelling for pension funds. Presented to the Staple Inn Actuarial Society.
Khorasanee, M.Z. (1999). Actuarial modelling of defined contribution pension schemes. PhD thesis, City University, London.
Lee, E.M. (1986). An introduction to pension schemes. Faculty and Institute of Actuaries.
Lee, P.J. & Wilkie, A.D. (2000). A comparison of stochastic asset models. Presented to the Institute and Faculty of Actuaries Investment Conference.
Lintner, J. (1971). The aggregation of investors' diverse judgement and preferences in purely competitive security markets. Journal of Finance and Quantitative Analysis, 4, 347450.
McGill, D.M., Brown, K.N., Haley, J.J. and Schieber, S.J. (1996). Fundamentals of private pensions. 7th Ed.Philadelphia, Pennsylvania: University of Pennsylvania Press.
Maurer, R. & Schlag, C. (2002). Money-back guarantees in individual pension accounts: evidence from the German pension reform. Centre for Financial Studies working paper No 2002/03. Johan Wolfgang Goethe-Universitat, Frankfurt am Main.
Modigliani, F. & Miller, M.H. (1958). The cost of capital, corporation finance and the theory of investment. American Economic Review, 48, 261297.
Myners, P. (2001). Institutional investment in the United Kingdom: a review. HM Treasury website,
O'Regan, W.S & Weeder, J. (1988). A dissection of pension funding. Presented to the Staple Inn Actuarial Society.
Owadally, M.I. & Haberman, S. (1999) Pension fund dynamics and gains/losses due to random rates of investment return. North American Actuarial Journal, 3 (3), 105117.
Owadally, M.I. & Haberman, S. (2004). Efficient amortization of actuarial gains/losses and optimal funding in pension plans. North American Actuarial Journal, 8. (to appear)
Ramsay, C.M. (1993). Percentile pension cost methods: a new approach to pension valuations. Transactions of the Society of Actuaries, 45, 351415.
Shoemaker, P.J.H. (1980). Experiments on decisions under risk: the expected utility hypothesis. Nijhoff, Boston.
Siegmann, A.H. & Lucas, A. (1999). Continuous-time dynamic programming for ALM with risk averse loss functions. Proceedings of the 9th AFIR International Colloquium.
Sloman, J. (1999). Economics. Third edition. Prentice Hall.
Smith, A.D. (1996). How actuaries can use financial economics. British Actuarial Journal, 2, 10571193.
Subject 304 Core Reading — Pensions and Other Benefits (2001). Faculty and Institute of Actuaries.
Treynor, J.L., Regan, P.J. & Priest, W.W. (1978). Pension claims and corporate assets. Financial Analysts Journal, May-June 1978, 8488.
Trowbridge, C.L. & Farr, C.E. (1976). The theory and practice of pension funding. Homewood, Illinois: Richard D., Irwin.
Tversky, A. (1969). Intransitivity of preferences. Psychological Review, 76, 3148.
Von Neumann, J. & Morgenstern, O. (1944). Theory of games and economic behaviour. Princeton University Press.
Wason, S. (2001). IAA solvency project: report of working party. Presented to the 11th Annual International AFIR Colloquium, Toronto.
Whitten, S.P. & Thomas, R.G. (1999). A non-linear stochastic model for actuarial use. British Actuarial Journal, 5, 919953.
Wilkie, A.D. (1986). A stochastic investment model for actuarial use. Transactions of the Faculty of Actuaries, 39, 341403.
Wilkie, A.D. (1995). More on a stochastic asset model for actuarial use. British Actuarial Journal, 1, 777964.
Wirch, J.L. & Hardy, M.R. (1999). A synthesis of risk measures for capital adequacy. Insurance: Mathematics and Economics, 25, 337347.
Wise, A.J. (1984). The matching of assets to liabilities. Journal of the Institute of Actuaries, 111, 375402.
Yakoubov, Y., Teeger, M. & Duval, D.B. (1999). A stochastic investment model for asset and liability management. Presented to the Staple Inn Actuarial Society.


A Stochastic Approach to Risk Management and Decision Making in Defined Benefit Pension Schemes

  • S. Haberman (a1), C. Day (a2), D. Fogarty (a3), M. Z. Khorasanee (a4), M. McWhirter (a5), N. Nash (a6), B. Ngwira (a7), I. D. Wright (a8) and Y. Yakoubov (a9)...


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed