Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-19T23:27:24.890Z Has data issue: false hasContentIssue false

The moments and distributions of actuarial functions

Published online by Cambridge University Press:  20 April 2012

Extract

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.

Type
Research Article
Copyright
Copyright © Institute and Faculty of Actuaries 1978

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1) Aitchison, J & Brown, J. A. C. (1963). The Lognormal Distribution. Cambridge University Press.Google Scholar
(2) Boyle, P. P. Rates of return as random variables. The Journal of Risk and Insurance, XLIII, 693.Google Scholar
(3) Elderton, W. P. & Johnson, N. L. (1969). Systems of Frequency Curves. Cambridge University Press.CrossRefGoogle Scholar
(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.Google Scholar
(5) Kahn, P. M. Projections of variable life insurance operations. Transactions of the Society of Actuaries, 23, 335.Google Scholar
(6) Ord, J. K. (1972). Families of Frequency Distributions. Griffin, London.Google Scholar
(7) Pollard, A. H. & Pollard, J. H. A stochastic approach to actuarial functions. J.I.A. 95, 79.Google Scholar
(8) Pollard, J. H. On fluctuating interest rates. Bulletin de L'Association Royale des Actuaires Belges, 66, 68.Google Scholar
(9) Pollard, J. H. Premium loadings for non-participating business. J.I.A., 103, 205.Google Scholar
(10) Scott, W. F. A reserve basis for maturity guarantees in unit-linked life assurance. T.F.A. 35, 365.Google Scholar
(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.Google Scholar