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The moments and distributions of actuarial functions

  • H. R. Waters


In 1969, A. H. Pollard and J. H. Pollard published a paper in which they treated actuarial functions as random variables, the randomness being caused only by variations in the age at death. In 1971, J. H. Pollard took this one step further by allowing the rate of interest as well as the age at death to vary and used these results to determine premium loadings for non-profit assurances.



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(1) Aitchison, J & Brown, J. A. C. (1963). The Lognormal Distribution. Cambridge University Press.
(2) Boyle, P. P. Rates of return as random variables. The Journal of Risk and Insurance, XLIII, 693.
(3) Elderton, W. P. & Johnson, N. L. (1969). Systems of Frequency Curves. Cambridge University Press.
(4) Johnson, N. L., Nixon, E., Amos, D. E. & Pearson, E. S. Table of percentage points of Pearson curves, for given √β1 and β2, expressed in standard measure. Biometrika. 50, 459.
(5) Kahn, P. M. Projections of variable life insurance operations. Transactions of the Society of Actuaries, 23, 335.
(6) Ord, J. K. (1972). Families of Frequency Distributions. Griffin, London.
(7) Pollard, A. H. & Pollard, J. H. A stochastic approach to actuarial functions. J.I.A. 95, 79.
(8) Pollard, J. H. On fluctuating interest rates. Bulletin de L'Association Royale des Actuaires Belges, 66, 68.
(9) Pollard, J. H. Premium loadings for non-participating business. J.I.A., 103, 205.
(10) Scott, W. F. A reserve basis for maturity guarantees in unit-linked life assurance. T.F.A. 35, 365.
(11) Wiikie, A. D. (1976) The rate of interest as a stochastic process-theory and applications. Proc. 20th International Congress of Actuaries, Tokyo, 1, 325.

The moments and distributions of actuarial functions

  • H. R. Waters


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