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Report on the Wilkie stochastic investment model

  • T. J. Geoghegan, R. S. Clarkson, K. S. Feldman, S. J. Green, A. Kitts, J. P. Lavecky, F. J. M. Ross, W. J. Smith and A. Toutounchi...


A FIMAG Working Party was set up in 1989 to consider the stochastic investment model proposed by A. D. Wilkie, which had been used by a number of actuaries for various purposes, but had not itself been discussed at the Institute. This is the Report of that Working Party. First, the Wilkie model is described. Then the model is reviewed, and alternative types of model are discussed. Possible applications of the model are considered, and the important question of ‘actuarial judgement’ is introduced. Finally the Report looks at possible future developments. In appendices, Clarkson describes a specific alternative model for inflation, and Wilkie describes some experiments with ARCH models. In further appendices possible applications of stochastic investment models to pension funds, to life assurance and to investment management are discussed.



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This list of references on the subject of stochastic modelling is far from exhaustive. Many more references can be found in the proceedings of the 1 st and 2nd AFIR International Colloquiums (Paris 1990 and Brighton 1991) and in the financial economics literature.

Box, G. E. P. & Jenkins, G. M. (1976). Time series analysis, forecasting and control. Holden-Day, San Francisco.
Boyle, P. P. (1978). Immunization under stochastic models of the term structure. J.I.A. 105, 177.
Boyle, P. P. (1980). Recent models of the term structure of interest rales with actuarial applications. Trans. 21st I.C.A. 4, 95.
Clarkson, R. S. (1983). A market equilibrium model for the management of ordinary share portfolios. J.I.A. 110, 17.
Clarkson, R. S. (1991). A non-linear stochastic model for inflation. Proceedings of the 2nd AFIR International Colloquium, 3, 233.
Clarkson, R. S. & Plymkn, J. (1988). Improving the performance of equity portfolios. J.I.A. 115, 631.
Coutts, S. M. & Deviti, E. R. (1988). Simulation models and the management of a reinsurance company. Trans. 23rd I.C.A. 1, 109.
Cox, J. C., Ingersoli, J. E. & Ross, S. A. (1985). A theory of the term structure of interest rates. Econometrica, 53, 385.
Cox, J. C., Ross, S. A. & Rubinstein, M. (1979). Option pricing: a simplified approach. Journal of Financial Economics, 7, 229.
Daykin, C. D. (1988). Handling uncertainty in examining the financial strength of a general insurance company. Trans. 23rd I.C.A. 1, 119.
Daykin, C. D. el al. (1987). Assessing the solvency and financial strength of a general insurance company. J.I.A. 114, 227.
Daykin, C. D. & Hey, G. B. (1990). Managing uncertainty in a general insurance company. J.I.A. 117, 173.
Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50, 987.
Forfar, D. O. & Paul, D. R. L. (1988). A stochastic demonstration of immunisation theory. Trans. 23rd I.C.A. 1, 157.
Forfar, D. O. et ai. (1989). Bonus rates, valuation and solvency during the transition between higher and lower investment returns. T.F.A. 40, 490.
Harvey, A. C. (1989). Forecasting structural time-series models, and the Kaiman filter. Cambridge University Press.
Harvey, A. C. (1990). The econometric analysis of time series. Second Edition. Oxford: Philip Allan.
Hey, G. B. & Bernstein, G. D. (1988). Simulating the cash flow of a general insurer. Trans. 23rd I.C.A. 1, 243.
Kitts, A. (1990). Comments on a model of retail price inflation. J.I. A. 117, 407.
Loades, D. H. (1988). Assessing the security of pension fund valuation bases using a stochastic investment model. Trans. 23rd I.C.A. 5, 105.
Maturity Guarantees Working Party (1980). Report ofthe maturity guarantees working party. J.I.A. 107, 103.
Pkntikainen, T. & Pisones, M. (1988). Stochastic dynamic analysis of life insurance. Trans. 23rd I.C.A. 1, 421.
Pitacco, E. (1988). A stochastic model for deposit administration plan analysis. Trans. 23rd I.C.A. 5, 195.
Pollard, J. H. (1988). Fluctuating interest rates revisited: pensions and insurances in a fluctuating environment. Trans. 23rd I.C.A. 1, 439.
Purchase, D. E. et al. (1989). Reflections on resilience: some considerations of mismatching tests, with particular reference to non-linked long-term insurance business. J.I.A. 116, 347.
Reynolds, D. I. W. & Smith, P.D. (1988). Changes in the probability of insolvency- results from a general insurance simulation model. Trans. 23rd I.C.A. 1, 485.
Richard, S. F. (1978). An arbitrage model ofthe term structure of interest rates. Journal of Financial Economics, 6, 33.
Ross, M. D. (1989). Modelling a with-profits life office. J.I.A. 116, 691.
Sharp, K. P. (1988). Stochastic models of interest rates. Trans. 23rd I.C.A. 5, 247.
Sims, C. (1980). Macroeconomics and reality. Econometrica, 48, 1.
Solvency Working Party (1986). The solvency of life assurance companies. T.F.A. 39, 251.
Taylor, S. (1986). Modelling financial time series. John Wiley, Chichester.
Toutounchi, A. (1984). ‘A comprehensive time-series analysis ofthe dividends and dividend yields of sectors ofthe Financial Times-Actuaries and the Standard & Poor's share indices.’ Ph.D. Thesis, Heriot-Watt University.
Vasicek, O. (1977). An equilibrium characterisation of the term structure. Journal of Financial Economics, 5, 177.
Vaupel, J. & Yashin, A. I. (1985). Heterogeneity's ruses: some surprising effects of selection on population dynamics. The American Statistician, 39, 176.
Wilkie, A. D. (1984a). The cost of minimum money guarantees on index-linked annuities. Trans. 22nd I.C.A. 2, 137.
Wilkie, A. D. (1984b). Using a stochastic model to estimate the distribution of real rates of return on ordinary shares. Trans. 22nd I.C.A. 5, 1.
Wilkie, A. D. (1984c). Steps towards a comprehensive stochastic investment model. O.A.R.D.P. 36.
Wilkie, A. D. (1986a). A stochastic investment model for actuarial use. T.F.A. 39, 341.
Wilkie, A. D. (1986b). Some applications of stochastic investment models. J.I.A.S.S. 29, 25.
Wilkie, A. D. (1987a). Stochastic investment models—theory and application. Insurance: Mathematics and Economics, 6, 65.
Wilkie, A. D. (1987b). An option pricing approach to bonus policy. J.I.A. 114, 21.
Wilkie, A. D. (1988). The use of option pricing theory for valuing benefits with ‘cap and collar’ guarantees. Trans. 23rd I.C.A. 5, 277.
Wise, A. J. (1984a). The matching of assets to liabilities. J.I.A. 111, 445.
Wise, A. J. (1984b). A theoretical analysis of the matching of assets to liabilities. J.I.A. 111, 375.
Wish, A. J. (1987). Matching and portfolio selection, Parts 1 and 2. J.I.A. 114, 113 and 551.


Report on the Wilkie stochastic investment model

  • T. J. Geoghegan, R. S. Clarkson, K. S. Feldman, S. J. Green, A. Kitts, J. P. Lavecky, F. J. M. Ross, W. J. Smith and A. Toutounchi...


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