Joined‐Up Pensions Policy in the UK: An Asset‐Liability Model for Simultaneously Determining the Asset Allocation and Contribution Rate
Main Article Content
Abstract
The trustees of funded defined benefit pension schemes must make two vital and inter‐ related decisions ‐ setting the asset allocation and the contribution rate. While these decisions are usually taken separately, it is argued that they are intimately related and should be taken jointly. The objective of funded pension schemes is taken to be the minimization of both the mean and the variance of the contribution rate, where the asset allocation decision is designed to achieve this objective. This is done by splitting the problem into two main steps. First, the Markowitz mean‐variance model is generalised to include three types of pension scheme liabilities (actives, deferreds and pensioners), and this model is used to generate the effi‐ cient set of asset allocations. Second, for each point on the risk‐return efficient set of the asset‐liability portfo‐ lio model, the mathematical model of Haberman (1992) is used to compute the corresponding mean and vari‐ ance of the contribution rate and funding ratio. Since the Haberman model assumes that the discount rate for computing the present value of liabilities equals the investment return, it is generalised to avoid this restric‐ tion. This generalisation removes the trade‐off between contribution rate risk and funding ratio risk for a fixed spread period. Pension schemes need to choose a spread period, and it is shown how this can be set to minimise the variance of the contribution rate. Finally, using the result that the funding ratio follows an inverted gamma distribution, shortfall risk and expected tail loss are computed for funding below the mini‐ mum funding requirement, and funding above the taxation limit. This model is then applied to one of the largest UK pension schemes ‐ the Universities Superannuation Scheme.
Article Details
Section
Analysis
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References
1. Accounting Standards Board (1988) Statement of Standard Accounting Practice 24 ‐ Accounting for Pension Costs, May, ASB Publications, London.
2. Accounting Standards Board (2000) Financial Reporting Standard 17 ‐ Retirement Benefits, November, ASB Publications, London.
3. Actuarial Education Company (2002) ActEd Study Materials: 2002 Examinations, Subject 304, Course Notes, Actuarial Education Company, Oxford.
4. Artzner, P., Delbaen, F., Eber, J.M. and Heath, D. (1999) Coherent Measures of Risk, Mathematical Finance, vol. 9, no. 3, July, pp. 203‐228.
5. Association of Consulting Actuaries (2003) Occupational Pensions 2003 ‐ Pensions Reform: Too Little, Too Late?, ACA, March.
6. Bagehot, W. (1972) Risk and Reward in Corporate Pension Funds, Financial Analysts Journal, vol. 28, no. 1, January‐February, pp. 80‐84.
7. Bédard, D. (1999) Stochastic Pension Funding: Proportional Control and Bilinear Processes, ASTIN Bulletin, vol. 29, no. 2, November, pp. 271‐293.
8. Bédard, D. and Dufresne, D. (2001) Pension Funding with Moving Average Rates of Return, Scandinavian Actuarial Journal, vol. 2001, no. 1, March, pp. 1‐17.
9. Black, F. (1995) The Plan Sponsor’s Goal, Financial Analysts Journal, vol. 51, no. 4, July‐August, pp. 6‐7.
10. Blake, D., Lehmann, B.N. and Timmermann, A. (1999) Asset Allocation Dynamics and Pension Fund Performance, Journal of Business, vol. 72, no. 4, October, pp. 429‐461.
11. Board, J.L.G. and Sutcliffe, C.M.S. (1994) Estimation Methods in Portfolio Selection and the Effectiveness of Short Sales Restrictions: UK Evidence, Management Science, vol. 40, no. 4, April, pp. 516‐534.
12. Boender, C.G.E. (1997) A Hybrid Simulation‐Optimization Scenario Model for Asset‐Liability Management, European Journal of Operations Research, vol. 99, no. 1, May, pp. 126‐135.
13. Boender, C.G.E., Dert, C.L. and Hoek, H. (2006) ALM for Pension Funds. In Handbook of Asset and Liability Management, edited by S.A. Zenios and W.T. Ziemba, volume B, Elsevier Science.
14. Boender, C.G.E., Van Aalst, P.C. and Heemskerk, F. (1998) Modelling and Management of Assets and Liabilities of Pension Plans in the Netherlands. In Worldwide Asset and Liability Modelling, edited by W.T. Ziemba and J.M. Mulvey, Cambridge University Press, pp. 561‐580.
15. Boender, C.G.E. and Vos, M. (2000) Risk Return Budgeting at Pension Plans, The Institutional Investor, May, pp. 80‐88.
16. Bogentoft, E., Romeijn, H.E. and Uryasev, S. (2001) Asset‐Liability Management for Pension Funds Using CVaR Constraints, Journal of Risk Finance, vol. 3, no. 1, Fall, pp. 57‐71.
17. Booth, P., Chadburn, R., Cooper, D., Haberman, S. and James, D. (1999) Modern Actuarial Theory and Practice, Chapman and Hall/CRC, Boca Raton, Florida, chapter 25.
18. Bogentoft, E., Romeijn, H.E. and Uryasev, S. (2001) Asset‐Liability Management for Pension Funds Using CVaR Constraints, Journal of Risk Finance, vol. 3, no. 1, Fall, pp. 57‐71.
19. Boulier, J.F., Trussant, E, and Florens, D. (1995) A Dynamic Model for Pension Funds Management. In Proceedings of the 5th AFIR International Colloquium, Brussels 1995, edited by J. Janssen, pp. 361‐384.
20. Boulier, J.F., Michel, S. and Wisnia, V. (1996) Optimizing Investment and Contribution Policies of a Defined Benefit Pension Fund. In Proceedings of the 6th AFIR International Colloquium, Nuremberg, 1996, edited by P. Albrecht, pp. 593‐607.
21. Brinson, G.P., Hood, L.R. and Beebower, G.L. (1986) Determinants of Portfolio Performance, Financial Analysts Journal, vol. 42, no. 4, July‐August, pp. 39‐44.
22. Brinson, G.P., Singer, B.D. and Beebower, G.L. (1991) Determinants of Portfolio Performance II: An Update, Financial Analysts Journal, vol. 47, no. 3, May‐June, pp. 40‐48.
23. Cairns, A.J.G. (1995) Pension Funding in a Stochastic Environment: The Role of Objectives in Selecting an Asset Allocation Strategy. In Proceedings of the 5th AFIR International Colloquium, Brussels 1995, edited by J. Janssen, pp. 429‐453.
24. Cairns, A.J.G. (1996a) An Introduction to Stochastic Pension Fund Management, Working Paper 9607, Pensions Institute.
25. Cairns, A.J.G. (1996b) Continuous Time Pension Fund Modelling. In Proceedings of the 6th AFIR International Colloquium, Nuremberg, 1996, edited by P. Albrecht, pp. 609‐624.
26. Cairns, A.J.G. (1997) A Comparison of Optimal and Dynamic Control Strategies for Continuous Time Pension Plan Models. In Proceedings of the 7th AFIR International Colloquium, Cairns, 1997, pp. 309‐326.
27. Cairns, A.J.G. (2000) Some Notes on the Dynamics and Optimal Control of Stochastic Pension Fund Models in Continuous Time, ASTIN Bulletin, vol. 30, no. 1, May, pp. 19‐55.
28. Cairns, A.J.G., and Parker, G. (1997) Stochastic Pension Fund Modelling, Insurance: Mathematics and Economics, vol. 21, no. 1, October, pp. 43‐79.
29. Campbell, J.Y. and Viceira, L.M. (2002) Strategic Asset Allocation: Portfolio Choice for Long Term Investors, Oxford University Press.
30. Cariño, D.R., Kent, T,, Myers, D.H., Stacy, C,, Sylvanus, M,, Turner, A.L., Watanabe, K, and Ziemba, W.T. (1994) The Russell‐Yasuda Kasai Model: An Asset‐Liability Model for a Japanese Insurance Company Using Multistage Stochastic Programming, Interfaces, vol. 24, no.1, January‐February, pp. 29‐49.
31. Cariño, D.R., and Ziemba, W.T., (1998) Formulation of the Russell‐Yasuda Kasai Financial Planning Model, Operations Research, 46:4, July‐August, 433‐449.
32. Cariño, D.R., Myers, D.H., and Ziemba, W.T. (1998) Concepts, Technical Issues and Uses of the Russell‐ Yasuda Kasai Financial Planning Model, Operations Research, vol. 46, no. 4, July‐August, 450‐462.
33. Chang, S.C. and Chen, C.C. (2002) Allocating Unfunded Liability in Pension Valuation Under Uncertainty, Insurance: Mathematics and Economics, vol. 30, no. 3, June, pp. 371‐387.
34. Chopra, V.K. and Ziemba, W.T. (1993) The Effect of Errors in Means, Variances and Covariances on Optimal Portfolio Choice, Journal of Portfolio Management, vol. 19, no. 2, Winter, pp. 6‐11.
35. Constantinides, G.M. (2002) Rational Asset Prices, Journal of Finance, vol. 57, no. 4, August, pp. 1567‐1591.
36. Cornell, B. (1999) The Equity Risk Premium: The Long‐Run Future of the Stock Market, John Wiley And Sons.
37. Craft, T.M. (2001) The Role of Private and Public Real Estate in Pension Plan Portfolio Allocation Choices, Journal of Real Estate Portfolio Management, vol. 7, no. 1, January‐March, pp. 17‐23.
38. Craft, T.M. (2005) How Funding Ratios Affect Pension Plan Allocations, Journal of Real Estate Portfolio Management, vol. 11, no. 1, January‐April, pp. 29‐35.
39. Chun, G.H., Chiochetti, B.A. and Shilling, J.D. (2000) Pension Plan Real Estate Investment in an Asset‐Liability Framework, Real Estate Economics, vol. 28, no. 3, Fall, pp. 467‐491.
40. Dert, C.L. (1998) A Dynamic Model for Asset Liability Management for Defined Benefit Pension Funds. In Worldwide Asset and Liability Modelling, edited by W.T. Ziemba and J.M. Mulvey, Cambridge University Press, pp. 501‐536.
41. Dimson, E., Marsh, P. and Staunton, M. (2002) The Triumph of the Optimists: 101 Years of Global Investment Returns, Princeton University Press.
42. Dondi, G., Herzog, F., Schuman, L. & Geering, H.P. (2006) Dynamic Asset and Liability Management for Swiss Pension Funds. In Handbook of Asset and Liability Management, edited by S.A. Zenios and W.T. Ziemba, volume B, Elsevier Science.
43. Dowd, K. (2002) An Introduction to Market Risk Measurement, John Wiley.
44. Drijver, S.J., Klein Haneveld, W.K. and Van Der Vlerk, M.H. (2002) ALM Model for Pension Funds: Numerical Results for a Prototype Model, Research Report, University of Grongingen.
45. Drijver, S.J., Klein Haneveld, W.K. and Van Der Vlerk, M.H. (2003) Asset Liability Management Modelling Using Multi‐Stage Mixed Integer Stochastic Programming. In Asset and Liability Management Tools: A Handbook for Best Practice, edited by B. Scherer, Risk Books, pp. 309‐324.
46. Dufresne, D. (1986) Pension Funding and Random Rates of Return. In Insurance and Risk Theory edited by M. Goovaerts, F. De Vylder and J. Haezendonck, D. Reidel Publishing, pp. 277‐291.
47. Dufresne, D. (1988) Moments of Pension Contributions and Fund Levels When Rates of Return are Random, Journal of the Institute of Actuaries, vol. 115, no. 3, September, pp. 535‐544.
48. Dufresne, D. (1989) Stability of Pension Systems When Rates of Return are Random, Insurance: Mathematics and Economics, vol. 8, no. 1, March, pp. 71‐76.
49. Dufresne, D. (1990a) Fluctuations of Pension Contributions and Fund Level, Actuarial Research Clearing House, pp. 111‐120.
50. Dufresne, D. (1990b) The Distribution of a Perpetuity with Applications to Risk Theory and Pension Funding, Scandinavian Actuarial Journal, no. 1‐2, pp. 39‐79.
51. Ederington, L.H. (1979) The Hedging Performance of the New Futures Markets, Journal of Finance, vol. 34, no. 1, March, pp. 157‐170.
52. Evans, M., Hastings, N. and Peacock, B. (1993) Statistical Distributions, second edition, John Wiley and Sons, chapter 18 ‐ gamma distributions.
53. Exley, C.J., Mehta, S.J.B. and Smith, A.D. (1997) The Financial Theory of Defined Benefit Pension Schemes, British Actuarial Journal, vol. 3, part 4, pp. 835‐966.
54. Ezra, D.D. (1991) Asset Allocation by Surplus Optimization, Financial Analysts Journal, vol. 47, no. 1, January‐February, pp. 51‐57.
55. Fabozzi, F.J., Focardi, S.M. and Jonas, C.L. (2005) Market Experience with Modelling for Defined Benefit Pension Funds: Evidence from Four Countries, Journal of Pension Economics and Finance, vol. 4, no. 3, November, pp. 313‐327.
56. Faculty and Institute of Actuaries (2003) Pensions and Other Benefits, Subject 304 Core Reading, GN26: Pension Fund Terminology, Faculty and Institute of Actuaries, Oxford.
57. Frankfurter, G.M. and Hill, J.M. (1981) A Normative Approach to Pension Fund Management, Journal of Financial and Quantitative Analysis, vol. 16, no. 4, November, pp. 533‐558.
58. Gerrard, R. and Haberman, S. (1996) Stability of Pension Systems When Gains‐Losses are Amortized and Rates of Return are Autoregressive, Insurance: Mathematics and Economics, vol. 18, no. 1, May, pp. 59‐71.
59. Geyer, A., Herold, W., Kontriner, K. and Ziemba, W.T. (2005) The Innovest Austrian Pension Fund Financial Planning Model InnoALM, Working paper, University of British Columbia, February.
60. Gondzio, J. and Kouwenberg, R. (2001) High Performance Computing for Asset‐Liability Management, Operations Research, vol. 49, no. 6, November‐December, pp. 879‐891.
61. Haberman, S. (1990a) Stochastic Approach to Pension Funding Methods. In Proceedings of the 1st AFIR International Colloquium, Paris, 1990, pp. 93‐112.
62. Haberman, S. (1990b) Variability of Pension Contributions and Fund Levels With Random and Autoregressive Rates of Return, Actuarial Research Clearing House, pp. 141‐171.
63. Haberman, S. (1992) Pension Funding with Time Delays: A Stochastic Approach, Insurance: Mathematics and Economics, vol. 11, no. 3, October, pp. 179‐189.
64. Haberman, S. (1993a) Pension Funding with Time Delays and Autoregressive Rates of Investment Return, Insurance: Mathematics and Economics, vol. 13, no. 1, September, pp. 45‐56.
65. Haberman, S. (1993b) Pension Funding: The Effect of Changing the Frequency of Valuations, Insurance: Mathematics and Economics, vol. 13, no. 3, December, pp. 263‐270.
66. Haberman, S. (1994a) Autoregressive Rates of Return and the Variability of Pension Contributions and Fund Levels for a Defined Benefit Pension Scheme, Insurance: Mathematics and Economics, vol. 14, no. 3, July, pp. 219‐240.
67. Haberman, S, (1994b) Defined Benefit Pension Funding Models and Stochastic Investment Returns. Paper presented to a joint meeting of the Staple Inn Actuarial Society and the Royal Statistical Society, March, 50 pages.
68. Haberman, S. (1995) Pension Funding with Time Delays and the Optimal Spread Period, ASTIN Bulletin, vol. 25, no. 2, November, pp. 177‐187.
69. Haberman, S. (1997a) Stochastic Investment Returns and Contribution Rate Risk in a Defined Benefit Pension Scheme, Insurance: Mathematics and Economics, vol. 19, no. 2, April, pp. 127‐139.
70. Haberman, S. (1997b) Risk in a Defined Benefit Pension Scheme, Singapore International Insurance and Actuar‐ial Journal, vol. 1, pp. 93‐103.
71. Haberman, S. (1998) Stochastic Modelling of Pension Scheme Dynamics, Actuarial Research Report, No. 106, February, 35 pages.
72. Haberman, S., Butt, Z. and Megaloudi, C. (2000) Contribution and Solvency Risk in a Defined Benefit Pension Scheme, Insurance: Mathematics and Economics, vol. 27, no. 2, October, pp. 237‐259.
73. Haberman, S., Day, C., Fogarty, D., Khorasanee, Z., McWhirter, M., Nash. N., Ngwira, B., Wright, I.D. and Yakoubov, Y. (2003) A Stochastic Approach to Risk Management and Decision Making in Defined Benefit Pension Schemes, Paper presented to the Institute of Actuaries, 27th January, 95 pages.
74. Haberman, S. and Dufresne, D. (1991) Variability of Pension Contributions and Fund Levels with Random Rates of Return. In Managing the Insolvency Risk of Insurance Companies, edited by J.D. Cummins and R.A. Derrig, Kluwer Academic Press, pp. 133‐145.
75. Haberman, S. and Owadally, I. (2001) Modelling Defined Benefit Pension Schemes: Funding and Asset Valuation. Paper presented to the International Actuarial Association International Pensions Seminar, Brighton, 36 pages.
76. 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, vol. 20, no. 2, September, pp. 115‐135.
77. Hakansson, N. (1970) Optimal Investment and Consumption Strategies Under Risk for a Class of Utility Functions, Econometrica, vol. 38, no. 5, September, pp. 587‐607.
78. Hakansson, N. (1971) On Optimal Myopic Portfolio Policies with and Without Serial Correlation of Yields, Journal of Business, vol. 44, no. 3, July, pp. 324‐334.
79. Hilli, P, Koivu, M., Pennanen, T. and Ranne, A. (Forthcoming) A Stochastic Programming Model for Asset Liability Management of a Finnish Pension Company. Annals of Operations Research.
80. Ibbotson, R.G. and Kaplan, P.D. (2000) Does Asset Allocation Policy Explain 40, 90 or 100 Percent of Performance?, Financial Analysts Journal, vol. 56, no. 1, January‐February, pp. 26‐33.
81. Johnson, N.L., Kotz, S. and Balakrishnan, N. (1994) Continuous Univariate Distributions, volume 1, second edition, John Wiley and Sons, New York, chapter 17 ‐ gamma distributions.
82. Josa‐Fombellida, R. and Rincón‐Zapatero, J.P. (2001) Minimization of Risks in Pension Funding by Means of Contributions and Portfolio Selection, Insurance: Mathematics and Economics, vol. 29, no. 1, August, pp. 35‐45.
83. Jorion, P. (2000) Value at Risk : The New Benchmark for Managing Financial Risk, Second edition, McGrawHill.
84. Kallberg, J.G. and Ziemba, W.T. (1984) Mis‐specification in Portfolio Selection Problems. In Risk and Capital edited by G. Bämberg and K. Spremann, Springer‐Verlag, pp. 74‐87.
85. Kingsland, L. (1982) Projecting the Financial Condition of a Pension Plan Using Simulation Analysis, Journal of Finance, vol. 37, no. 2, May, pp. 577‐584.
86. Kouwenberg, R. (1997) Asset Liability Management for Pension Funds: Elements of Dert’s Model. In New Operational Approaches for Financial Modelling, edited by C. Zopounidis, Physica‐Verlag, pp. 37‐48.
87. Kouwenberg, R. (2001) Scenario Generation and Stochastic Programming Models for Asset Liability Management, European Journal of Operations Research, vol. 134, no. 2, October, pp. 279‐292.
88. Kusy, M.L. and Ziemba, W.T. (1986) A Bank Asset and Liability Management Model, Operations Research, vol 34, no. 3, May‐June, 356‐376.
89. Leibowitz, M.L., Bader, L.N. and Kogelman, S. (1996) Return Targets and Shortfall Risks: Studies in Strategic Asset Allocation, Irwin Professional Publishing.
90. Logan, D. (1985) The Birth of a Pension Scheme: A History of the Universities Superannuation Scheme, Liverpool University Press.
91. MacBeth, J.D., Emanuel, D.C. and Heatter, C.E. (1994) An Investment Strategy for Defined Benefit Plans, Financial Analysts Journal, vol. 50, no. 3, May‐June, pp. 34‐41.
92. Mandl, P. and Mazurová, L. (1996) Harmonic Analysis of Pension Funding Methods, Insurance: Mathematics and Economics, vol. 17, no. 3, pp. 203‐214.
93. Merton, R.C. (1992) Continuous‐Time Finance, Revised edition, Blackwell Publishing.
94. Michaud, R.O. (1989) The Markowitz Optimization Enigma: Is ‘Optimized’ Optimal?, Financial Analysts Journal, vol. 45, no. 1, January‐February, pp. 31‐42.
95. Mossin, J. (1968) Optimal Multiperiod Portfolio Policies, Journal of Business, vol. 41, no. 2, April, pp. 215‐229.
96. Mulvey, J.M., Fabozzi, F.J., Pauling, W.R., Simsek, K.D. and Zhang, Z. (2005) Modernizing the Defined Benefit Pension System, Journal of Portfolio Management, vol. 31, no. 2, Winter, pp. 73‐82.
97. Mulvey, J.M., Gould, G. and Morgan, C. (2000) An Asset and Liability Management System for Towers Perrin - Tillinghast, Interfaces, vol. 30, no. 1, January‐February, pp. 96‐114.
98. Mulvey, J.M., Simsek, K.D. and Pauling, B. (2003) A Stochastic Network Approach for Integrating Pension and Corporate Financial Planning. In Innovations in Financial and Economic Networks, edited by A. Nagurney, Edward Elgar, pp. 67‐83.
99. Mulvey, J.M. and Thorlacius, A.E. (1998) The Towers Perrin Global Capital Market Scenario Generation System. In Worldwide Asset and Liability Modelling, edited by W.T. Ziemba and J.M. Mulvey, Cambridge University Press, pp. 286‐312.
100. Nijman, T. and Swinkels, L. (2003) Strategies and Tactical Allocation to Commodities for Retirement Savings
Schemes, Discussion paper no. 20, February, Tilburg University.
101. Owadally, M.I. and Haberman, S. (1999) Pension Fund Dynamics and Gains/Losses Due to Random Rates of
Investment Return, North American Actuarial Journal, vol. 3, no. 3, pp. 105‐117.
102. Owadally, M.I. and Haberman, S. (2000) Efficient Amortization of Actuarial Gains and Losses in Pension Plans, Actuarial Research Clearing House, pp. 275‐317.
103. Ralfe, J. (2001) Why Bonds Are Right for Pension Funds, Risk, vol. 14, no. 11, November, pp. 54‐55.
104. Ralfe, J., Speed, C. and Palin, J. (2003) Pensions and Capital Structure: Why Hold Equities in the Pension Fund? Society of Actuaries Symposium on the Great Controversy: Current Pension Actuarial Practice in Light of Financial Economics, Vancouver, June.
105. Rudolf, M. & Ziemba, W.T. (2004) Intertemporal Surplus Management, Journal of Economic Dynamics and Control, vol. 28, no, 5, February, pp. 975‐990.
106. Secretary of State for Work and Pensions (2002) Simplicity, Security and Choice: Working and Saving for Retirement, Green Paper, Cm 5677, December.
107. Sharpe, W.F. (1990) Asset Allocation. In Managing Investment Portfolios: A Dynamic Process, Second edition, edited by J.L. Maginn and D.L. Tuttle, Warren, Gorham and Lamont, chapter 7, pp. 7.1‐7.71.
108. Sharpe, W.F. and Tint, L.G. (1990) Liabilities ‐ A New Approach, Journal of Portfolio Management, vol. 16, no. 2, Winter, pp. 5‐10.
109. Siegel, J.J. (2002) Stocks for the Long Run, Third edition, McGraw Hill.
110. Sutcliffe, C.M.S. (2005) The Cult of the Equity for Pension Funds: Should it Get the Boot?, Journal of Pension Economics and Finance, vol. 4, no. 1. March, pp. 57‐85.
111. Tepper, I. (1974) Optimal Financial Strategies for Trusteed Pension Plans, Journal of Financial and Quantitative Analysis, vol. 9, no. 3, June, pp. 357‐376.
112. Thornton, P.N. and Wilson, A.F. (1992) A Realistic Approach to Pension Funding, Journal of the Institute of Actuaries, vol. 119, pp. 229‐277.
113. Universities Superannuation Scheme (2002) Report and Accounts for the Year Ended 31 March 2002.
114. Universities Superannuation Scheme (2003) Actuarial Valuation Report as at 31 March 2002, March 2003.
115. Waring, M.B. (2004) Liability‐Relative Investing II, Journal of Portfolio Management, vol. 31, no. 1, Fall, pp. 40‐53.
116. Wright, I.D. (1998) Traditional Pension Fund Valuation in a Stochastic Asset and Liability Environment, British Actuarial Journal, vol. 4, part 4, pp. 865‐901.
117. Yang, T. (2003) Defined Benefit Pension Plan Liabilities and International Asset Allocation, Pension Research Council Working Paper no. 2003‐5, University of Pennsylvania.
118. Ziemba, W.T. (2003) The Stochastic Programming Approach to Asset, Liability, and Wealth Management, The Research Foundation of AIMR, Charlottesville, Virginia.
119. Ziemba, W.T. (2006) The Russell Yasuda, InnoALM and Related Models for Pensions, Insurance Companies and High Net Worth Individuals. In Handbook of Asset and Liability Management, edited by S.A. Zenios and W.T. Ziemba, volume B, Elsevier Science.
120. Zimbidis, A. and Haberman, S. (1993) Delay, Feedback and Variability of Pension Contributions and Fund Levels, Insurance: Mathematics and Economics, vol. 13, no. 3, December, pp. 271‐285.
2. Accounting Standards Board (2000) Financial Reporting Standard 17 ‐ Retirement Benefits, November, ASB Publications, London.
3. Actuarial Education Company (2002) ActEd Study Materials: 2002 Examinations, Subject 304, Course Notes, Actuarial Education Company, Oxford.
4. Artzner, P., Delbaen, F., Eber, J.M. and Heath, D. (1999) Coherent Measures of Risk, Mathematical Finance, vol. 9, no. 3, July, pp. 203‐228.
5. Association of Consulting Actuaries (2003) Occupational Pensions 2003 ‐ Pensions Reform: Too Little, Too Late?, ACA, March.
6. Bagehot, W. (1972) Risk and Reward in Corporate Pension Funds, Financial Analysts Journal, vol. 28, no. 1, January‐February, pp. 80‐84.
7. Bédard, D. (1999) Stochastic Pension Funding: Proportional Control and Bilinear Processes, ASTIN Bulletin, vol. 29, no. 2, November, pp. 271‐293.
8. Bédard, D. and Dufresne, D. (2001) Pension Funding with Moving Average Rates of Return, Scandinavian Actuarial Journal, vol. 2001, no. 1, March, pp. 1‐17.
9. Black, F. (1995) The Plan Sponsor’s Goal, Financial Analysts Journal, vol. 51, no. 4, July‐August, pp. 6‐7.
10. Blake, D., Lehmann, B.N. and Timmermann, A. (1999) Asset Allocation Dynamics and Pension Fund Performance, Journal of Business, vol. 72, no. 4, October, pp. 429‐461.
11. Board, J.L.G. and Sutcliffe, C.M.S. (1994) Estimation Methods in Portfolio Selection and the Effectiveness of Short Sales Restrictions: UK Evidence, Management Science, vol. 40, no. 4, April, pp. 516‐534.
12. Boender, C.G.E. (1997) A Hybrid Simulation‐Optimization Scenario Model for Asset‐Liability Management, European Journal of Operations Research, vol. 99, no. 1, May, pp. 126‐135.
13. Boender, C.G.E., Dert, C.L. and Hoek, H. (2006) ALM for Pension Funds. In Handbook of Asset and Liability Management, edited by S.A. Zenios and W.T. Ziemba, volume B, Elsevier Science.
14. Boender, C.G.E., Van Aalst, P.C. and Heemskerk, F. (1998) Modelling and Management of Assets and Liabilities of Pension Plans in the Netherlands. In Worldwide Asset and Liability Modelling, edited by W.T. Ziemba and J.M. Mulvey, Cambridge University Press, pp. 561‐580.
15. Boender, C.G.E. and Vos, M. (2000) Risk Return Budgeting at Pension Plans, The Institutional Investor, May, pp. 80‐88.
16. Bogentoft, E., Romeijn, H.E. and Uryasev, S. (2001) Asset‐Liability Management for Pension Funds Using CVaR Constraints, Journal of Risk Finance, vol. 3, no. 1, Fall, pp. 57‐71.
17. Booth, P., Chadburn, R., Cooper, D., Haberman, S. and James, D. (1999) Modern Actuarial Theory and Practice, Chapman and Hall/CRC, Boca Raton, Florida, chapter 25.
18. Bogentoft, E., Romeijn, H.E. and Uryasev, S. (2001) Asset‐Liability Management for Pension Funds Using CVaR Constraints, Journal of Risk Finance, vol. 3, no. 1, Fall, pp. 57‐71.
19. Boulier, J.F., Trussant, E, and Florens, D. (1995) A Dynamic Model for Pension Funds Management. In Proceedings of the 5th AFIR International Colloquium, Brussels 1995, edited by J. Janssen, pp. 361‐384.
20. Boulier, J.F., Michel, S. and Wisnia, V. (1996) Optimizing Investment and Contribution Policies of a Defined Benefit Pension Fund. In Proceedings of the 6th AFIR International Colloquium, Nuremberg, 1996, edited by P. Albrecht, pp. 593‐607.
21. Brinson, G.P., Hood, L.R. and Beebower, G.L. (1986) Determinants of Portfolio Performance, Financial Analysts Journal, vol. 42, no. 4, July‐August, pp. 39‐44.
22. Brinson, G.P., Singer, B.D. and Beebower, G.L. (1991) Determinants of Portfolio Performance II: An Update, Financial Analysts Journal, vol. 47, no. 3, May‐June, pp. 40‐48.
23. Cairns, A.J.G. (1995) Pension Funding in a Stochastic Environment: The Role of Objectives in Selecting an Asset Allocation Strategy. In Proceedings of the 5th AFIR International Colloquium, Brussels 1995, edited by J. Janssen, pp. 429‐453.
24. Cairns, A.J.G. (1996a) An Introduction to Stochastic Pension Fund Management, Working Paper 9607, Pensions Institute.
25. Cairns, A.J.G. (1996b) Continuous Time Pension Fund Modelling. In Proceedings of the 6th AFIR International Colloquium, Nuremberg, 1996, edited by P. Albrecht, pp. 609‐624.
26. Cairns, A.J.G. (1997) A Comparison of Optimal and Dynamic Control Strategies for Continuous Time Pension Plan Models. In Proceedings of the 7th AFIR International Colloquium, Cairns, 1997, pp. 309‐326.
27. Cairns, A.J.G. (2000) Some Notes on the Dynamics and Optimal Control of Stochastic Pension Fund Models in Continuous Time, ASTIN Bulletin, vol. 30, no. 1, May, pp. 19‐55.
28. Cairns, A.J.G., and Parker, G. (1997) Stochastic Pension Fund Modelling, Insurance: Mathematics and Economics, vol. 21, no. 1, October, pp. 43‐79.
29. Campbell, J.Y. and Viceira, L.M. (2002) Strategic Asset Allocation: Portfolio Choice for Long Term Investors, Oxford University Press.
30. Cariño, D.R., Kent, T,, Myers, D.H., Stacy, C,, Sylvanus, M,, Turner, A.L., Watanabe, K, and Ziemba, W.T. (1994) The Russell‐Yasuda Kasai Model: An Asset‐Liability Model for a Japanese Insurance Company Using Multistage Stochastic Programming, Interfaces, vol. 24, no.1, January‐February, pp. 29‐49.
31. Cariño, D.R., and Ziemba, W.T., (1998) Formulation of the Russell‐Yasuda Kasai Financial Planning Model, Operations Research, 46:4, July‐August, 433‐449.
32. Cariño, D.R., Myers, D.H., and Ziemba, W.T. (1998) Concepts, Technical Issues and Uses of the Russell‐ Yasuda Kasai Financial Planning Model, Operations Research, vol. 46, no. 4, July‐August, 450‐462.
33. Chang, S.C. and Chen, C.C. (2002) Allocating Unfunded Liability in Pension Valuation Under Uncertainty, Insurance: Mathematics and Economics, vol. 30, no. 3, June, pp. 371‐387.
34. Chopra, V.K. and Ziemba, W.T. (1993) The Effect of Errors in Means, Variances and Covariances on Optimal Portfolio Choice, Journal of Portfolio Management, vol. 19, no. 2, Winter, pp. 6‐11.
35. Constantinides, G.M. (2002) Rational Asset Prices, Journal of Finance, vol. 57, no. 4, August, pp. 1567‐1591.
36. Cornell, B. (1999) The Equity Risk Premium: The Long‐Run Future of the Stock Market, John Wiley And Sons.
37. Craft, T.M. (2001) The Role of Private and Public Real Estate in Pension Plan Portfolio Allocation Choices, Journal of Real Estate Portfolio Management, vol. 7, no. 1, January‐March, pp. 17‐23.
38. Craft, T.M. (2005) How Funding Ratios Affect Pension Plan Allocations, Journal of Real Estate Portfolio Management, vol. 11, no. 1, January‐April, pp. 29‐35.
39. Chun, G.H., Chiochetti, B.A. and Shilling, J.D. (2000) Pension Plan Real Estate Investment in an Asset‐Liability Framework, Real Estate Economics, vol. 28, no. 3, Fall, pp. 467‐491.
40. Dert, C.L. (1998) A Dynamic Model for Asset Liability Management for Defined Benefit Pension Funds. In Worldwide Asset and Liability Modelling, edited by W.T. Ziemba and J.M. Mulvey, Cambridge University Press, pp. 501‐536.
41. Dimson, E., Marsh, P. and Staunton, M. (2002) The Triumph of the Optimists: 101 Years of Global Investment Returns, Princeton University Press.
42. Dondi, G., Herzog, F., Schuman, L. & Geering, H.P. (2006) Dynamic Asset and Liability Management for Swiss Pension Funds. In Handbook of Asset and Liability Management, edited by S.A. Zenios and W.T. Ziemba, volume B, Elsevier Science.
43. Dowd, K. (2002) An Introduction to Market Risk Measurement, John Wiley.
44. Drijver, S.J., Klein Haneveld, W.K. and Van Der Vlerk, M.H. (2002) ALM Model for Pension Funds: Numerical Results for a Prototype Model, Research Report, University of Grongingen.
45. Drijver, S.J., Klein Haneveld, W.K. and Van Der Vlerk, M.H. (2003) Asset Liability Management Modelling Using Multi‐Stage Mixed Integer Stochastic Programming. In Asset and Liability Management Tools: A Handbook for Best Practice, edited by B. Scherer, Risk Books, pp. 309‐324.
46. Dufresne, D. (1986) Pension Funding and Random Rates of Return. In Insurance and Risk Theory edited by M. Goovaerts, F. De Vylder and J. Haezendonck, D. Reidel Publishing, pp. 277‐291.
47. Dufresne, D. (1988) Moments of Pension Contributions and Fund Levels When Rates of Return are Random, Journal of the Institute of Actuaries, vol. 115, no. 3, September, pp. 535‐544.
48. Dufresne, D. (1989) Stability of Pension Systems When Rates of Return are Random, Insurance: Mathematics and Economics, vol. 8, no. 1, March, pp. 71‐76.
49. Dufresne, D. (1990a) Fluctuations of Pension Contributions and Fund Level, Actuarial Research Clearing House, pp. 111‐120.
50. Dufresne, D. (1990b) The Distribution of a Perpetuity with Applications to Risk Theory and Pension Funding, Scandinavian Actuarial Journal, no. 1‐2, pp. 39‐79.
51. Ederington, L.H. (1979) The Hedging Performance of the New Futures Markets, Journal of Finance, vol. 34, no. 1, March, pp. 157‐170.
52. Evans, M., Hastings, N. and Peacock, B. (1993) Statistical Distributions, second edition, John Wiley and Sons, chapter 18 ‐ gamma distributions.
53. Exley, C.J., Mehta, S.J.B. and Smith, A.D. (1997) The Financial Theory of Defined Benefit Pension Schemes, British Actuarial Journal, vol. 3, part 4, pp. 835‐966.
54. Ezra, D.D. (1991) Asset Allocation by Surplus Optimization, Financial Analysts Journal, vol. 47, no. 1, January‐February, pp. 51‐57.
55. Fabozzi, F.J., Focardi, S.M. and Jonas, C.L. (2005) Market Experience with Modelling for Defined Benefit Pension Funds: Evidence from Four Countries, Journal of Pension Economics and Finance, vol. 4, no. 3, November, pp. 313‐327.
56. Faculty and Institute of Actuaries (2003) Pensions and Other Benefits, Subject 304 Core Reading, GN26: Pension Fund Terminology, Faculty and Institute of Actuaries, Oxford.
57. Frankfurter, G.M. and Hill, J.M. (1981) A Normative Approach to Pension Fund Management, Journal of Financial and Quantitative Analysis, vol. 16, no. 4, November, pp. 533‐558.
58. Gerrard, R. and Haberman, S. (1996) Stability of Pension Systems When Gains‐Losses are Amortized and Rates of Return are Autoregressive, Insurance: Mathematics and Economics, vol. 18, no. 1, May, pp. 59‐71.
59. Geyer, A., Herold, W., Kontriner, K. and Ziemba, W.T. (2005) The Innovest Austrian Pension Fund Financial Planning Model InnoALM, Working paper, University of British Columbia, February.
60. Gondzio, J. and Kouwenberg, R. (2001) High Performance Computing for Asset‐Liability Management, Operations Research, vol. 49, no. 6, November‐December, pp. 879‐891.
61. Haberman, S. (1990a) Stochastic Approach to Pension Funding Methods. In Proceedings of the 1st AFIR International Colloquium, Paris, 1990, pp. 93‐112.
62. Haberman, S. (1990b) Variability of Pension Contributions and Fund Levels With Random and Autoregressive Rates of Return, Actuarial Research Clearing House, pp. 141‐171.
63. Haberman, S. (1992) Pension Funding with Time Delays: A Stochastic Approach, Insurance: Mathematics and Economics, vol. 11, no. 3, October, pp. 179‐189.
64. Haberman, S. (1993a) Pension Funding with Time Delays and Autoregressive Rates of Investment Return, Insurance: Mathematics and Economics, vol. 13, no. 1, September, pp. 45‐56.
65. Haberman, S. (1993b) Pension Funding: The Effect of Changing the Frequency of Valuations, Insurance: Mathematics and Economics, vol. 13, no. 3, December, pp. 263‐270.
66. Haberman, S. (1994a) Autoregressive Rates of Return and the Variability of Pension Contributions and Fund Levels for a Defined Benefit Pension Scheme, Insurance: Mathematics and Economics, vol. 14, no. 3, July, pp. 219‐240.
67. Haberman, S, (1994b) Defined Benefit Pension Funding Models and Stochastic Investment Returns. Paper presented to a joint meeting of the Staple Inn Actuarial Society and the Royal Statistical Society, March, 50 pages.
68. Haberman, S. (1995) Pension Funding with Time Delays and the Optimal Spread Period, ASTIN Bulletin, vol. 25, no. 2, November, pp. 177‐187.
69. Haberman, S. (1997a) Stochastic Investment Returns and Contribution Rate Risk in a Defined Benefit Pension Scheme, Insurance: Mathematics and Economics, vol. 19, no. 2, April, pp. 127‐139.
70. Haberman, S. (1997b) Risk in a Defined Benefit Pension Scheme, Singapore International Insurance and Actuar‐ial Journal, vol. 1, pp. 93‐103.
71. Haberman, S. (1998) Stochastic Modelling of Pension Scheme Dynamics, Actuarial Research Report, No. 106, February, 35 pages.
72. Haberman, S., Butt, Z. and Megaloudi, C. (2000) Contribution and Solvency Risk in a Defined Benefit Pension Scheme, Insurance: Mathematics and Economics, vol. 27, no. 2, October, pp. 237‐259.
73. Haberman, S., Day, C., Fogarty, D., Khorasanee, Z., McWhirter, M., Nash. N., Ngwira, B., Wright, I.D. and Yakoubov, Y. (2003) A Stochastic Approach to Risk Management and Decision Making in Defined Benefit Pension Schemes, Paper presented to the Institute of Actuaries, 27th January, 95 pages.
74. Haberman, S. and Dufresne, D. (1991) Variability of Pension Contributions and Fund Levels with Random Rates of Return. In Managing the Insolvency Risk of Insurance Companies, edited by J.D. Cummins and R.A. Derrig, Kluwer Academic Press, pp. 133‐145.
75. Haberman, S. and Owadally, I. (2001) Modelling Defined Benefit Pension Schemes: Funding and Asset Valuation. Paper presented to the International Actuarial Association International Pensions Seminar, Brighton, 36 pages.
76. 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, vol. 20, no. 2, September, pp. 115‐135.
77. Hakansson, N. (1970) Optimal Investment and Consumption Strategies Under Risk for a Class of Utility Functions, Econometrica, vol. 38, no. 5, September, pp. 587‐607.
78. Hakansson, N. (1971) On Optimal Myopic Portfolio Policies with and Without Serial Correlation of Yields, Journal of Business, vol. 44, no. 3, July, pp. 324‐334.
79. Hilli, P, Koivu, M., Pennanen, T. and Ranne, A. (Forthcoming) A Stochastic Programming Model for Asset Liability Management of a Finnish Pension Company. Annals of Operations Research.
80. Ibbotson, R.G. and Kaplan, P.D. (2000) Does Asset Allocation Policy Explain 40, 90 or 100 Percent of Performance?, Financial Analysts Journal, vol. 56, no. 1, January‐February, pp. 26‐33.
81. Johnson, N.L., Kotz, S. and Balakrishnan, N. (1994) Continuous Univariate Distributions, volume 1, second edition, John Wiley and Sons, New York, chapter 17 ‐ gamma distributions.
82. Josa‐Fombellida, R. and Rincón‐Zapatero, J.P. (2001) Minimization of Risks in Pension Funding by Means of Contributions and Portfolio Selection, Insurance: Mathematics and Economics, vol. 29, no. 1, August, pp. 35‐45.
83. Jorion, P. (2000) Value at Risk : The New Benchmark for Managing Financial Risk, Second edition, McGrawHill.
84. Kallberg, J.G. and Ziemba, W.T. (1984) Mis‐specification in Portfolio Selection Problems. In Risk and Capital edited by G. Bämberg and K. Spremann, Springer‐Verlag, pp. 74‐87.
85. Kingsland, L. (1982) Projecting the Financial Condition of a Pension Plan Using Simulation Analysis, Journal of Finance, vol. 37, no. 2, May, pp. 577‐584.
86. Kouwenberg, R. (1997) Asset Liability Management for Pension Funds: Elements of Dert’s Model. In New Operational Approaches for Financial Modelling, edited by C. Zopounidis, Physica‐Verlag, pp. 37‐48.
87. Kouwenberg, R. (2001) Scenario Generation and Stochastic Programming Models for Asset Liability Management, European Journal of Operations Research, vol. 134, no. 2, October, pp. 279‐292.
88. Kusy, M.L. and Ziemba, W.T. (1986) A Bank Asset and Liability Management Model, Operations Research, vol 34, no. 3, May‐June, 356‐376.
89. Leibowitz, M.L., Bader, L.N. and Kogelman, S. (1996) Return Targets and Shortfall Risks: Studies in Strategic Asset Allocation, Irwin Professional Publishing.
90. Logan, D. (1985) The Birth of a Pension Scheme: A History of the Universities Superannuation Scheme, Liverpool University Press.
91. MacBeth, J.D., Emanuel, D.C. and Heatter, C.E. (1994) An Investment Strategy for Defined Benefit Plans, Financial Analysts Journal, vol. 50, no. 3, May‐June, pp. 34‐41.
92. Mandl, P. and Mazurová, L. (1996) Harmonic Analysis of Pension Funding Methods, Insurance: Mathematics and Economics, vol. 17, no. 3, pp. 203‐214.
93. Merton, R.C. (1992) Continuous‐Time Finance, Revised edition, Blackwell Publishing.
94. Michaud, R.O. (1989) The Markowitz Optimization Enigma: Is ‘Optimized’ Optimal?, Financial Analysts Journal, vol. 45, no. 1, January‐February, pp. 31‐42.
95. Mossin, J. (1968) Optimal Multiperiod Portfolio Policies, Journal of Business, vol. 41, no. 2, April, pp. 215‐229.
96. Mulvey, J.M., Fabozzi, F.J., Pauling, W.R., Simsek, K.D. and Zhang, Z. (2005) Modernizing the Defined Benefit Pension System, Journal of Portfolio Management, vol. 31, no. 2, Winter, pp. 73‐82.
97. Mulvey, J.M., Gould, G. and Morgan, C. (2000) An Asset and Liability Management System for Towers Perrin - Tillinghast, Interfaces, vol. 30, no. 1, January‐February, pp. 96‐114.
98. Mulvey, J.M., Simsek, K.D. and Pauling, B. (2003) A Stochastic Network Approach for Integrating Pension and Corporate Financial Planning. In Innovations in Financial and Economic Networks, edited by A. Nagurney, Edward Elgar, pp. 67‐83.
99. Mulvey, J.M. and Thorlacius, A.E. (1998) The Towers Perrin Global Capital Market Scenario Generation System. In Worldwide Asset and Liability Modelling, edited by W.T. Ziemba and J.M. Mulvey, Cambridge University Press, pp. 286‐312.
100. Nijman, T. and Swinkels, L. (2003) Strategies and Tactical Allocation to Commodities for Retirement Savings
Schemes, Discussion paper no. 20, February, Tilburg University.
101. Owadally, M.I. and Haberman, S. (1999) Pension Fund Dynamics and Gains/Losses Due to Random Rates of
Investment Return, North American Actuarial Journal, vol. 3, no. 3, pp. 105‐117.
102. Owadally, M.I. and Haberman, S. (2000) Efficient Amortization of Actuarial Gains and Losses in Pension Plans, Actuarial Research Clearing House, pp. 275‐317.
103. Ralfe, J. (2001) Why Bonds Are Right for Pension Funds, Risk, vol. 14, no. 11, November, pp. 54‐55.
104. Ralfe, J., Speed, C. and Palin, J. (2003) Pensions and Capital Structure: Why Hold Equities in the Pension Fund? Society of Actuaries Symposium on the Great Controversy: Current Pension Actuarial Practice in Light of Financial Economics, Vancouver, June.
105. Rudolf, M. & Ziemba, W.T. (2004) Intertemporal Surplus Management, Journal of Economic Dynamics and Control, vol. 28, no, 5, February, pp. 975‐990.
106. Secretary of State for Work and Pensions (2002) Simplicity, Security and Choice: Working and Saving for Retirement, Green Paper, Cm 5677, December.
107. Sharpe, W.F. (1990) Asset Allocation. In Managing Investment Portfolios: A Dynamic Process, Second edition, edited by J.L. Maginn and D.L. Tuttle, Warren, Gorham and Lamont, chapter 7, pp. 7.1‐7.71.
108. Sharpe, W.F. and Tint, L.G. (1990) Liabilities ‐ A New Approach, Journal of Portfolio Management, vol. 16, no. 2, Winter, pp. 5‐10.
109. Siegel, J.J. (2002) Stocks for the Long Run, Third edition, McGraw Hill.
110. Sutcliffe, C.M.S. (2005) The Cult of the Equity for Pension Funds: Should it Get the Boot?, Journal of Pension Economics and Finance, vol. 4, no. 1. March, pp. 57‐85.
111. Tepper, I. (1974) Optimal Financial Strategies for Trusteed Pension Plans, Journal of Financial and Quantitative Analysis, vol. 9, no. 3, June, pp. 357‐376.
112. Thornton, P.N. and Wilson, A.F. (1992) A Realistic Approach to Pension Funding, Journal of the Institute of Actuaries, vol. 119, pp. 229‐277.
113. Universities Superannuation Scheme (2002) Report and Accounts for the Year Ended 31 March 2002.
114. Universities Superannuation Scheme (2003) Actuarial Valuation Report as at 31 March 2002, March 2003.
115. Waring, M.B. (2004) Liability‐Relative Investing II, Journal of Portfolio Management, vol. 31, no. 1, Fall, pp. 40‐53.
116. Wright, I.D. (1998) Traditional Pension Fund Valuation in a Stochastic Asset and Liability Environment, British Actuarial Journal, vol. 4, part 4, pp. 865‐901.
117. Yang, T. (2003) Defined Benefit Pension Plan Liabilities and International Asset Allocation, Pension Research Council Working Paper no. 2003‐5, University of Pennsylvania.
118. Ziemba, W.T. (2003) The Stochastic Programming Approach to Asset, Liability, and Wealth Management, The Research Foundation of AIMR, Charlottesville, Virginia.
119. Ziemba, W.T. (2006) The Russell Yasuda, InnoALM and Related Models for Pensions, Insurance Companies and High Net Worth Individuals. In Handbook of Asset and Liability Management, edited by S.A. Zenios and W.T. Ziemba, volume B, Elsevier Science.
120. Zimbidis, A. and Haberman, S. (1993) Delay, Feedback and Variability of Pension Contributions and Fund Levels, Insurance: Mathematics and Economics, vol. 13, no. 3, December, pp. 271‐285.