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On the Objectionable Character of certain Methods very generally adopted for the Determination and Division of Surplus in Life Assurance Companies
Published online by Cambridge University Press: 18 August 2016
Extract
In a short paper read before the Institute at the early part of this year, after alluding to the erroneous methods commonly adopted for the determination and division of surplus in Life Assurance Companies, I intimated my intention to investigate the nature and character of those methods, and to endeavour to demonstrate the mischievous and injurious consequences resulting from them. In the present paper I propose to commence this undertaking, trusting that the undeniable importance of the subject will be considered a sufficient apology for my somewhat frequent introduction of it at these meetings.
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- Copyright © Institute and Faculty of Actuaries 1852
References
page 186 note *
In the paper above alluded to it is shown that 
where A is the factitious value of an annuity, such as that of the Northampton Table, and 'A the true value; and it is from this property that the discrepancies now adverted to take their origin. By “true value” and “true premium” I would beg to be understood, once for all, as meaning such value and such premium as result from a combination of rates of mortality and interest as nearly as practicable assimilating to the actually prevailing rates.
page 188 note * I have adopted the term “guaranty fund” for want of a better. It is, of course, the value of the difference between the premiums charged and those required to provide the sums assured, and its proportion to the value of the gross premiums represents the “bonus giving power” of a Society. This power is, probably, as high as it ever need be when the ratio is as one to three—that is, when the fund in question is one-third of the value of the gross premiums. The less this proportion, the less, of course, the “bonus giving power.” The severity of this test may not be understood very well by the public just at present, but there can be no doubt that it soon will be.
page 189 note * The advocates for maintaining the old system, who are so tenacious of introducing into the account the item above referred to, lest such introduction should lead to the appropriation of any part of it, appear to forget that there may be a very little margin as well as a very large one; and that, in their anxious desire to conceal the latter state of affairs, they quite keep out of sight the danger arising from the former.
page 189 note †
That is, the share of each contributor is made equal to 
adopting the same notation as that given on former occasions.
page 189 note ‡
That is, the share of each contributor is made equal to 
page 191 note *
That is, the share of each contributor is made equal to 
.
page 192 note † That is, the share of each contributor is made equal to
and I may here add, that when the premiums charged are made up of the “true ones,”increased by a per centage, this method would be correct, otherwise not.
page 192 note †
That is, the share of each contributor is made equal to 
page 194 note * See Euclid, book v., proposition 19.