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Stochastic Models for Actuarial Use: The Equilibrium Modelling of Local Markets

  • Robert J. Thomson (a1) and Dmitri V. Gott (a1)


In this paper, a long-term equilibrium model of a local market is developed. Subject to minor qualifications, the model is arbitrage-free. The variables modelled are the prices of risk-free zero-coupon bonds – both index-linked and conventional – and of equities, as well as the inflation rate. The model is developed in discrete (nominally annual) time, but allowance is made for processes in continuous time subject to continuous rebalancing. It is based on a model of the market portfolio comprising all the above-mentioned asset categories. The risk-free asset is taken to be the one-year index-linked bond. It is assumed that, conditionally upon information at the beginning of a year, market participants have homogeneous expectations with regard to the forthcoming year and make their decisions in mean-variance space. For the purposes of illustration, a descriptive version of the model is developed with reference to UK data. The parameters produced by that process may be used to inform the determination of those required for the use of the model as a predictive model. Illustrative results of simulations of the model are given.



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Dai, Q. and Singleton, K.J. (2000) Specification analysis of affine term structure models. Journal of Finance 55(5), 1943–78.
Duffie, D. and Kahn, R. (1996) A yield factor model of interest rates. Mathematical Finance 51, 379406.
Elton, E.J. and Gruber, M.J. (1995) Modern Portfolio Theory and Investment Analysis. 5th edn. Wiley, New York.
Hibbert, J., Mowbray, P. and Turnbull, C. (unpublished) A stochastic model & calibration for long-term financial planning. Technical Report, Barrie & Hibbert Limited, 2001.
Hull, J. and White, A. (1990) Pricing interest rate derivative securities. The Review of Financial Studies 3(4), 573592.
Jackson, J.E. (2003). A User's Guide to Principal Components, Wiley, Hoboken, New Jersey.
Maitland, A.J. (2002). Interpolating the South African yield curve using principal components analysis: a descriptive approach. South African Actuarial Journal 2, 129–45.
Rebonato, R. (1998). Interest Rate Option Models. 2nd edn., Wiley, New York.
Thomson, R.J. (1996) Stochastic investment models: the case of South Africa. British Actuarial Journal 2, 765801.
Thomson, R.J. (2005) The pricing of liabilities in an incomplete market using dynamic meanvariance hedging. Insurance: Mathematics and Economics 36, 441–55.
Thomson, R.J. (2006) A typology of models used in actuarial science. South African Actuarial Journal 6, 1936.
Tong, H. (1990) Non-linear systems: a dynamical system approach. Oxford University Press, Oxford.
Van Deventer, D.R., Imai, K. and Mesler, M. (2004) Advanced Financial Risk Management, An Integrated Approach to Credit Risk and Interest Rate Risk Management. John Wiley & Sons.
Whitten, S.P. and Thomas, R.G. (1999) A non-linear stochastic asset model for actuarial use. British Actuarial Journal 5(5), 919–53
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.
Yakoubov, Y.H., Teeger, M.H. and Duval, D.B. (1999) A stochastic investment model for asset and liability management. Proceedings of the 9th International AFIR Colloquium, 237–66.


Stochastic Models for Actuarial Use: The Equilibrium Modelling of Local Markets

  • Robert J. Thomson (a1) and Dmitri V. Gott (a1)


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