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

Abstract

SynopsisThe 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.