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On the Value of Selection as exercised by the Policy-holder against the Company
Published online by Cambridge University Press: 18 August 2016
Extract
During the last session of the Institute of Actuaries, I had the honour to read a paper on the Value of the Principle of Selection as exercised by the Offices in granting Assurances upon Lives, and to submit some calculations which I had made with reference to that subject, in which calculations the lives admitted at particular ages were kept apart from others during their subsequent existence. I have now to offer to the Institute an extended set of Tables of a similar character; and, after stating the course which I have followed in constructing them, I shall make a few observations on the value of selection as exercised by the policy-holder against the Company.
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- Copyright © Institute and Faculty of Actuaries 1851
References
page 186 note * The number exposed to risk at age m is (in the greater part of the table), to the number exposed to risk at age m + 4, about as 10 to 6. Supposing the intermediate numbers to be 9, 8 and 7, and the probabilities to diminish by second differences, the probability deduced from the quinary combination, which I refer to age m + 1 ¾ as respects the mixed lives, will be
The real probability is
The difference is 
, a quantity so small during the early and middle ages as to be immaterial. As d2 is negative, the error lies on the side of underrating the chance of life. For this, abundant compensation will be suggested hereafter.
page 186 note † It is assumed (agreeably to the precedent of the Committee who collected the data) that the assured entered on an average at the middle of the calendar year; being on an average half a year younger than their office age. The Equitable and Amicable data are given for actual calendar years, but they do not afford the means of determining the probability of living from the time of admission to the 1st of January following.
page 195 note * Perhaps there is no department of insurance practice which calls more strongly for reconsideration than that of valuing policies for surrender. There can he no doubt that we constantly pay consideration for the discontinuance of insurances, which it would be better for the Company should remain in force. Those Companies, too, which furnish forms of assignment, arm the assured with an additional power against themselves, by facilitating the transfer of policies to third parties whose knowledge of the state of health of the assured may induce them as a speculation to offer higher terms than the official values.