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Lidstone has shown that the solution to the theoretical problem of valuing a life interest is essentially indeterminate. For a uniform life interest this is generally avoided by requiring of the formula that at the end of any policy-year the purchaser will have received sufficient income to discharge all premiums to date on the supporting policy, and to provide the predetermined interest on his total outlay.
Consider a life interest to be valued of 1 per annum, and let P be the office rate of premium on the whole-life non-profit policy required to return to the purchaser his initial outlay. In the evolution of a formula three unknown quantities are involved:
G, the gross purchase price (including expenses);
T, the total initial outlay;
S, the sum assured.
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- Research Article
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- Copyright © Institute of Actuaries Students' Society 1955
References
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