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Consistent Extra Premiums and Equivalent Decreasing Debts for Endowment Assurances

Published online by Cambridge University Press:  11 August 2014

K. Sandom
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Extract

This article attempts to develop a practical system for dealing with extra-risks whilst retaining consistency in the terms offered to proposers. The extra premiums derived vary according to the view taken of the incidence of the extra-risk, and tables are produced to enable the underwriter to deduce quickly the required special terms.

W. Perks' paper, ‘The Treatment of Sub-Standard Lives in Practice’ (J.I.A.78, 205), describes a system whereby the special terms are fixed according to uniform percentage increases in mortality throughout the term. This approach does not make a broad assessment of the incidence of the extra-risk. The present writer feels that some allowance for incidence should be made, and the process that follows attempts to adhere to the narrow theoretical path. The scope of this article does not include the interesting fields of underwriting practice and experience which were admirably discussed in W. Perks' paper.

Type
Research Article
Information
Journal of the Staple Inn Actuarial Society , Volume 15 , Issue 2 , August 1958 , pp. 141 - 152
Copyright
Copyright © Institute of Actuaries Students' Society 1958

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References

* Four significant figures were found necessary.

† Unloaded premium functions were used throughout. ‘Loaded’ extra premiums could have been used, but the refinement is not justified. The use of the ratio of extra premiums would normally eliminate the effect of loadings.

‡ A constant addition to the force of mortality is equivalent to an equal addition to the force of interest for annuity functions. It can be shown that the d in the formula (1/ä) — d remains at the rate of interest i for an increase of α in the rate of mortality. Strictly speaking, continuous functions for mortality and interest should be used, but the loss in accuracy by assuming that an increase of α in the rate of interest is equivalent to an increase of α in the rate of mortality is negligible for practical purposes.