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Joint Life Annuities – Some Experiments with the A1924–29 Table

Published online by Cambridge University Press:  07 November 2014

A. E. King  and
A. R. Reid
A. E. King
Affiliation:
Standard Life Assurance Company
A. R. Reid
Affiliation:
Standard Life Assurance Company
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Synopsis

The two main objects of the paper are :—

(1) To ascertain what modifications in Makeham's Law are necessary in order that the principle of Uniform Seniority may be applied to the A1924–29 ult. table.

(2) To ascertain whether some approximate method is readily available for the calculation of joint life annuity values according to the A1924–29 ult. table.

As regards (1) developments of the suggestions put forward in the discussion following Mr. C. L. Stoodley's paper to the Faculty in February 1934 are examined, and the conclusion is reached that, while the results are somewhat disappointing so far as the A1924-29 table is concerned, some of the formulae brought out may yet prove of practical use when applied to a mortality table more free from heterogeneous matter.

In the second part of the paper the results of applying to the A1924–29 ult. table several standard approximate methods are first examined, and it is shown that such methods are liable to produce systematic errors when applied to this table. Two new methods of approximation are then developed, which are shown to yield much more satisfactory results, and tables are reproduced to facilitate the practical application of these methods.

Type
Research Article
Information
Transactions of the Faculty of Actuaries , Volume 15 , Issue 1 , 1936 , pp. 93 - 140
Copyright
Copyright © Institute and Faculty of Actuaries 1936

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References

page 93 note * Although we are concerned in this paper with approximations to the values of joint life annuities with reference to joint life annuities in respect of equal ages, no treatment of the subject of approximating to the value of joint life annuities would be complete without referring to the valuable paper by Mr. Lidstone in J.I.A., xlvi. p. 1. The method described in that paper is of course applicable also to Last Survivor Annuities.

page 95 note * vide (i) T.F.A., xi. pp. 194–206.

(ii) “Death Rates in Great Britain and Sweden” ; W. O. Kermack, A. G. McKendrick and P. L. McKinlay, The Lancet, 31st March 1934, p. 698.

(iii) “The Development of the Mortality of the Adult Swedish Population since 1800,” H. Cramer and H. Wold, Nordic Statistical Journal, vol. 5.

page 95 note † T.F.A., xv. pp. 26–28.

page 96 note * J.I.A., lxiv. p. 497.

page 97 note * The rates of interest involved would also, as in the case of (1), includ certain large negative rates.

page 99 note * J.I.A., lxiii. p. 12.

page 105 note * This method may be described as the method.

page 108 note * The method may be termed the nPx method.

page 111 note * vide The Theory of the Construction of Tables of Mortality, G. F. Hardy, p. 68.