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Report on the Wilkie stochastic investment model

Published online by Cambridge University Press:  20 April 2012

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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Abstract

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.

Keywords

Stochastic Investment ModelsWilkie Model
Type
Other
Information
Journal of the Institute of Actuaries , Volume 119 , Issue 2 , 1992 , pp. 173 - 228
Copyright
Copyright © Institute and Faculty of Actuaries 1992

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References

REFERENCES AND SELECT BIBLIOGRAPHY

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