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Further Remarks on the Valuation of Endowment Assurances in Groups
Published online by Cambridge University Press: 18 August 2016
Extract
In a Paper entitled “Some Remarks on the Valuation of Endowment Assurances in Groups”, read before the Institute in January 1898 (vide J.I.A., xxxiv, 61 et seq.), the writer described a new method of valuation by which it was claimed the labour of dealing with Endowment Assurances might be reduced to a minimum, and at the same time results might be obtained differing by only an insignificant amount from the exact results. In preparing that Paper it was felt that to encumber it with a mass of technical detail would have been to court the neglect which is the common fate of a lengthy essay, and that the method would be more likely to receive consideration and a fair trial if, in the first instance, no more than an outline of its main principles were given. Since then the author has applied the method, with very satisfactory results, to a volume of Endowment Assurance business much larger than that which was dealt with in the original Paper (vide J.I.A., xxxiv, 510-14), and very gratifying testimony has been received from a number of leading Actuaries who have adopted the plan, and have found it to work smoothly and efficiently in practice. It is thought, therefore, that the time has arrived when it will be useful to consider the subject in greater detail, and with special reference to some of the points that arise in the application of the method.
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- Research Article
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- Copyright © Institute and Faculty of Actuaries 1904
References
page 2 note * The ease of annual premiums alone is here dealt with; as to half-yearly and quarterly premiums, see pars. 26,27 and 29 of the earlier Paper, and notes to column (12) of Schedule I, p. 30.
page 3 note * Vide pars. 29 et seq.
page 7 note * This value, which is higher than those brought out in the preceding paragraphs, has been selected in order to allow for the effect of eases falling outside the assumed range of 20 years.
page 9 note * The assumptions have been based on the author's observations in respect of Endowment Assurances in his own office. It is thought that they will apply with sufficient accuracy to most Endowment Assurance business in Great Britain, but any Actuary wishing to calculate the extreme mean error on different assumptions can easily do so by means of Table A. ]Cf. Mr. Thomson's remarks in the discussion and the author's comments thereon, p. 47.]
page 9 note † If the usual range of Makeham's constants be considered, it will be found that the general results must be very similar in any ordinary Mortality Table following Makeham's Law.
page 19 note * In the case of a Company which has been transacting a fairly uniform Endowment Assurance for a long period this feature will be absent, and it will then be specially desirable to institute a test such as that referred to in par. 42.
page 25 note * It probably understates the valuation age very slightly, but this may be set against the fact that the Z method in itself tends to slightly overstate the age. An investigation of a complete year's endowment assurance business, transacted subject to all the modern conditions of dating back and crowding in business at the end of the year, showed the following results:
Average age by “nearest birthday” method was greater than true average age by ·019 year.
Average age by method of par. 57 was less than true average age by ·090 year.
page 27 note * An independent investigation by Mr. H. A, Thomson will be found J.I.A., xxxiv, 8–9; but it should be noted that this is based on a different assumption (namely, that the valuation age changes with k).
page 28 note * If it be assumed (as in par. 57) that the age next birthday at entry is attained (on the average) at the end of the calendar year of entry, we shall have, by Classification I, 
which is very convenient for numerical calculation.
page 46 note * See remarks on next page.