XVII. A sketch of an analysis and notation applicable to the estimation of the value of life contingencies

Abstract

The estimation of the value of property, connected with life contingencies, has for many years occupied the attention of the philosophers, as well as the monied and landed interest of this country. The many institutions now existing in Eng­land, for the purpose of granting annuities and assurances on lives, are a sufficient evidence that they are conceived to yield advantages to the community:—advantages which seem to present themselves in two points of view; the one, the gain accruing to the parties granting the assurance or other ob­ject; the other, the benefit to be received by persons pur­chasing those grants. In a political point of view, it appears a question of great importance to decide, what ought to be the demands of those companies, so that the public may reap the greatest benefit from them? And the only means of answering this question, is the possession of the mathemati­cal and philosophical principles, by which those institutions ought to be guided. In the present improved state of the science of life assurances, it is not sufficient for a proper re­gulation to follow old customs, and calculations, drawn from a less perfect experience than we have now the means of obtaining ; but every company, to reap the advantage of the progressive state of the science, should not only possess every knowledge relative to this science, which it may be within its immediate power to acquire, but it should promul­gate its individual information; that the actuaries of the different societies may, by their mathematical skill, collect for the common good of all, from multiplied resources, that which they cannot obtain from a less general observation. I am induced to venture this hint, as it is my firm belief, that the tables generally adopted, might, by this means, receive many extremely necessary corrections; for those tables should be as accurate as they can possibly be made, and the interest should be calculated at that rate which shall appear to be the average interest to be made for money; but such additional demands should be made by the company or insti­tution, as to leave an adequate portion for its security, profit, and expenses; for it does not seem possible, in the various beneficial applications which can be made from a proper knowledge of this branch of the mathematics, to judge uni­versally how to adopt tables of mortality, which are not correct in themselves, connected with a rate of interest which is not the average rate made in reality, so that the advantage may tend to any one direction.