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Actuarial Applications of Autoregressive Models of Economic Variables

written by members or affiliates of the Actuarial and Demographic Studies Department, Macquarie University. Although unrefereed, the papers are under the review and supervision of an editorial board. Additional copies of the papers are available from the World Wide Web site of the Views expressed in this paper are those of the author and not necessarily those of the Actuarial Studies and Demography Department. Summary The first autogregressive model of fluctuating interest rates in the actuarial context appeared in 1971. Since then, several alternative but similar models have been proposed. In this paper, we summarize some of the earlier results and provide improved approximations for some of the moment formulae of annuities and assurances certain, and of life annuities and life assurances. It is shown that matrix analysis can be a very useful tool for deriving many of the asymptotic results, which are convenient for " rule-of-thumb " calculations. The behaviour of the interest process in the steady state is discussed, and methods are developed for analysing accumulations, which are important for maturity guarantee products. Although exact formulae and accurate approximations are available for the moments of the various interest rate functions, the actual distribution in many cases is unknown. It is suggested that the lognormal distribution can be used as an accurate approximation, and simulation studies confirm this. The matrix methods developed for the fluctuating interest rate models are generalised to allow the study of simultaneous autoregressive models of inflation, market interest rates and fund investment returns.