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Damaged Lives and Options

Published online by Cambridge University Press:  18 August 2016

P. H. McCormack
P. H. McCormack
Affiliation:
Provident Mutual Life Assurance Association
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Extract

The question whether the number of mixed lives at any age in the ultimate column of a select table can be subdivided into the number of lives still select and the number of damaged lives is a point of considerable interest in the practical use of mortality tables. And it was in connexion with a difference of opinion on this problem that the late Dr. Sprague made his last contribution to actuarial literature. Moreover, this was one of the few discussions in which he was apparently unable to carry conviction that his views were sound.

Type
Research Article
Information
Journal of the Institute of Actuaries , Volume 54 , Issue 2 , July 1923 , pp. 123 - 149
Copyright
Copyright © Institute and Faculty of Actuaries 1923

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References

page 125 note * If lx contains σx select lives and δx damaged lives and lx+n contains σx+n select lives and δx+n damaged lives,

then

But σ x+n does not equal 0 (as proved by duplicate policies in experience).

Abandoning the assumption that a life select at age x + n was necessarily select at age x.

Number of survivors of σx select lives after n years select lives damaged lives.

But σx + δx (i.e., lx) lives give after n years σx+n select lives damaged + δx+n damaged lives.

Out of δx damaged lives survive select lives and damaged lives, which are in the proportion of σx+n to δx+n .