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On Methods of Approximation*

Published online by Cambridge University Press:  28 May 2015

Peter Hardy
Peter Hardy*
Affiliation:
Institute of Actuaries of Great Britain and Ireland, and London Assurance Corporation
*
London Assurance Corporation, Royal Exchange
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Extract

To discover in the doctrine of life contingencies, convenient, and at the same time nearly true approximations, to be employed in determining the values of Survivorships, instead of the long and complex formulæ at present required for their solution, is an inquiry of no small importance to the practical actuary, more especially when it is remembered, that, even if the exact formulæ be employed, the results will in the greater number of cases be themselves mere approximations, in consequence of the defective nature of some of the elementary values employed in the solution

Type
Research Article
Information
Transactions of the Institute of Actuaries , Volume 1 , 1849 , pp. 1 - 16
Copyright
Copyright © Institute and Faculty of Actuaries 1849

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Footnotes

*

Since this paper was read before the Institute my friend, Mr. Scratchley, has drawn my attention to a passage in Professor De Morgan's Essay on Probability, p. 224, in which the germ of the idea, which I have here developed, is clearly enunciated; Mr. De Morgan is, therefore, manifestly entitled to claim priority in the discovery (if such it can be fairly termed) of this method of approximation, but as I had entirely overlooked the passage in question, I may still venture to believe mine to have been an independent investigation.

References

page 4 note * I have been recently informed, that although the greater number of Mr. Jones's tables, of the values of two joint lives, are the results of actual computation, some of them have been constructed by interpolation.