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On the Rate of Mortality amongst Europeans and their Descendents residing in the Island of Jamaica

Published online by Cambridge University Press:  18 August 2016

J. Marshall Esq.
J. Marshall Esq.*
Affiliation:
Jamaica Mutual Life Assurance Company
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Extract

As already stated by the writer, in a former paper on the subject, “In the absence of any large collection of facts and observations in Jamaica, from which such a table could have been deduced, he has necessarily been compelled to proceed upon probability and approximation, according to the experience and opinions of persons whose age and long residence in the community, or whose peculiar means of information, would give weight and authority to their statements; and, as a consequence, to any system which might be based upon them.

Type
Research Article
Information
Journal of the Institute of Actuaries , Volume 4 , Issue 1 , 1854 , pp. 39 - 51
Copyright
Copyright © Institute and Faculty of Actuaries 1854

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References

page 48 note * In determining the surplus, and the value of each policy, it will be proper to throwoff, whether after the age of 50 or in the case of lives taxed as below the average, any extra quantity beyond P (or mathematical premium, plus E).

With the preceding exception, under arrangements such as the above, it will be found most convenient and also most correct to take the entire value of the future premiums, without deduction, in the first instance; deducting at the conclusion of the process, from their aggregate value, that of three months' expenses plus the product of a life annuity of £1, payable quarterly, multiplied by the amount of the actual annual expenses; the value of the annuity being taken as of the mean age at investigation; no anticipation of future profits then occurring.

In throwing off E or any other quantity, and multiplying the difference in each case by the annuity plus 1, the effect is clearly to take one entire year's expenses, &c, in hand; which, is excessive.

The value of V will be most correctly arrived at by stating the ages, not as of the policy standard, but accordingly as the birthday may he nearer to the opening or termination of the Office year (which also would be the preferable mode of rating the premiums of entrants, and of stating the mortality results in a Society); and at whatever periods of the year the future premiums may be payable, all premiums should be taken at their yearly value, and all should be treated as due on the first day of the official year, their product being reckoned accordingly; the Society debiting itself with any past payments and the interest upon them, in respect to which risks may be still subsisting. Finally, in lieu of taking credit substantially for “assets” to the extent of the present value of the future premiums, by raising a second account for liabilities (in which the same are included), it were more correct, and more intelligible also, to raise one account only, showing the difference as constituting the “liability”—i. e., the value of the aggregate reversion minus that of the rent charge attaching to it; each being inseparable from the other—each, nevertheless, being exhibited at every investigation, with the features expressly given by which the value of such rent charge may be diminished; nor after the lapse of the first seven years of a Society's existence, does there appear any rational ground for longer intervals between the investigations than three years, if due regard is to be had to the true interests of the members of such an Association.

page 50 note * See the comparative rates of the London Equitable Society between the ages of 20 and 42, and between 30 and 50; as applied to an equated annual premium over the whole term of life, and to the equivalent premium rated yearly, for a single year's assurance, toties quoties. In the London Amicable and other Societies, the corresponding excess here referred to will be found to extend over a longer period even than the interval involved in the case of the Equitable.