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On the Conditions which give rise to Surplus in Life Assurance Companies, and on the Amount of the Return, or “Bonus” which such Conditions justify
Published online by Cambridge University Press: 28 May 2015
Extract
To trace the succession of events which have given rise to the duplex system of assurance in this country, known as the Participating, and Non-participating, would not be altogether uninteresting or unprofitable. There is little doubt, that the immoderate premiums required at the outset by the few who were disposed to embark in the then novel speculation of life assurance, suggested the idea of mutual association, as a means of achieving the same objects on more advantageous terms; and thus the participating system owed, to a certain extent, its origin to the non-participating. But a few years' experience soon sufficed to demonstrate to the keen eye of competition, that the payments required under the new arrangements were unnecessarily high; and that, after a large reduction in them, they might be acted upon, not only with safety, but with a considerable profit to boot.
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- Copyright © Institute and Faculty of Actuaries 1849
References
page 3 note * See Report on application of the “Equitable” for a charter, page 89*, Vol. I., of the Assurance Magazine.
page 4 note * p′ x here denoting the premium for the risk; φ x , the difference between it and the premium charged; c and e, the claims and expenses respectively; and ƒ being used as a symbol of summation merely.
page 5 note * There are, no doubt, others of an accidental description—such, for instance, as the abandonment of assurances by their owners; but although this was a matter of frequent occurrence formerly, it is no longer so at the present day; and it is very important to bear in mind, that it is only the value of the policy which in such cases falls into the general fund, not the amount of the premiums paid in respect of it, as the statements frequently put forth would seem to imply.
page 11 note *
Take, for instance, the generally prevailing method of dividing the surplus in the proportion indicated by the difference between the amount of premiums paid at compound interest and the value of the assurance. That is to say, in the proportion shewn by 
Since 
the former expression is equal to 
so that the surplus is thus actually allotted amongst the assurances by this method, not simply in the proportion in which each has contributed there to, but in the extraordinary ratio of its contribution to surplus, and to the payment of claims.