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On the Calculation of Life Contingencies. (Part II)*

Published online by Cambridge University Press:  18 August 2016

A. De Morgan
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Extract

The present paper is a continuation of that in the Companion for 1840, on the application of Barrett's method of calculating Me contingencies. No tables were then published for contingencies involving two lives; but since that time Mr. Jones's tables have appeared, in his work on the subject in the Library of Useful Knowledge. It may therefore be worth while to collect and describe the formulæ relative to two lives which are most likely to be useful in practice; with some other matters, which may partly interest the actuary and partly the commencing; student.

Type
Research Article
Information
Journal of the Institute of Actuaries , Volume 13 , Issue 3 , October 1866 , pp. 129 - 149
Copyright
Copyright © Institute and Faculty of Actuaries 1867

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References

page 130 note * It was not contemplated in the last paper that any one would have had the courage to compute tables for two lives. Had it been thought likely, what was there denoted by N x, y would have been denoted by N x|y .

page 136 note * The superior exactness of the above method, as it stands, is not owing to anything in the method, but solely arises from the greater extent of the tables published.

page 138 note * As we give no demonstration, we should say that, besides obtaining this expression from demonstration, we have tried several verifications: the simplest is that in which ak is a constant, and Ak= 1: r, which gives the perpetual annuity.

page 139 note * Cab. Cyclop. Probabilities and Life Contingencies, p, 163.

page 147 note * In particular, the temptation of spending the interest of his savings in making a greater appearance, a folly which has prevented many a competency from being acquired.

page 148 note * As far as I know, this exact method is due to Mr. Griffith Davies, and the first proof of it is in Mr. Jones's work (p. 189).