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Some Remarks on the Valuation of Endowment Assurances in groups

Published online by Cambridge University Press:  18 August 2016

George J. Lidstone
George J. Lidstone
Affiliation:
Institute of Actuaries Alliance Assurance Company
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Extract

One of the most striking features in the history of Life Assurance business during the past few years is the marked increase—both absolute and proportional—which has been shown in the number and amount of policies effected under the Endowment Assurance plan. There is every reason to expect that this increase will continue, and that ere long Endowment Assurances will divide honours with whole life policies as regards importance in the periodical valuations. It is consequently very desirable so to improve the methods of valuing such policies as to minimize the amount of labour involved, and it will become more and more necessary to abandon methods which answered very well so long as Endowment Assurances were looked upon as “Special Policies”, but which are extremely cumbersome when applied to a large mass of contracts. The shorter methods that have hitherto been suggested, though admirably adapted for use in test or check valuations, involve an error which many actuaries will consider too appreciable to be neglected, more especially as the approximate methods nearly always bring out a reserve which is smaller than the true reserve, and it accordingly becomes desirable to seek some process that will be free from this objection.

Type
Research Article
Information
Journal of the Institute of Actuaries , Volume 34 , Issue 1 , April 1898 , pp. 61 - 93
Copyright
Copyright © Institute and Faculty of Actuaries 1899

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References

page 62 note * Mr. King has pointed out that this method was not intended for valuation purposes, but was suggested by him simply for use in connection with the Valuation Returns to the Board of Trade, with the view of supplying sufficient information to enable an independent opinion to be formed as to the position of a company.

page 64 note * The value 1·085 for the ratio was actually fixed in the manner above mentioned, but it might have been determined approximately as follows. Let x be the mean valuation age and n the mean unexpired term, for the whole business, and t a term of years such that the bulk of the business in any group is included within a range of t years on either side of the mean valuation age for the group. Then r may be taken as approximately equal to Putting x=40, n=20. t=10, and making the calculations on the basis of the Text-Book graduation of the HM experience (in order to avoid the disturbing effect of irregularities), with 3 per-cent interest, it will be found that r=1·083, and practically the same result will be obtained if t be taken = 5 or 7. Again, putting x = 45, n = 15, t=5,7, or 10, the resulting value of r varies from 1·085 to 1·083, agreeing closely with the former result. In practice, it is recommended that the constant c be taken for the common ratio—see paragraphs 18·20, also Mr. G. F. Hardy's remarks in the discussion.

page 71 note * An extended table of Z has been prepared and is appended to the Paper. It should be stated that the particular form here given to the function Z has been adopted (in accordance with a suggestion made to the Author) as an improvement on the form originally proposed in the Paper. It is assumed that the assurances are payable, and that the groups are arranged, as explained in paragraph 23: if this be not the case, the definition of M may have to be slightly modified, according to circumstances.

page 72 note * Making t and n indefinitely great, we have the case of a whole life assurance, and n E x vanishes, so that εΔV0= εP.