It is with considerable diffidence that I submit this paper to the Institute seeing that there are many members who are far better qualified to deal with the subject.

However, it was suggested that a paper of this character would be acceptable, and I have endeavoured to make it as complete as possible without transgressing reasonable limits of space.

In the first place I have given a general account of the law of bankruptcy, following, in the main, the general arrangement of the subject adopted by Ringwood in “The Principles of Bankruptcy”, and I hope sufficiently full to make the paper useful to Students for Part IV of the examination syllabus. This has inevitably made it somewhat long and formal.

The complete calculation and tabulation of annuity values depending on two or more lives present considerable practical difficulties, owing to the multiplicity of age combinations to be dealt with. When the mortality table follows Makeham’s Law the difficulty is completely avoided so far as joint life annuities are concerned by the method of equal ages and uniform seniority, but this in no way meets the case of last survivor annuities, which necessitate a special calculation increasing in complexity with the number of lives involved. When the mortality table does not follow Makeham’s Law, the difficulty extends to joint life annuities as well as last survivor annuities. In the case of a great standard table, like the OM, the labour of calculation and expense of printing a complete set of two-life annuities may be justified, but this will rarely be so with a table of less general importance, while in any case the complete tabulation of three-life and four-life annuities will be quite impracticable; so that at the present time even for OM Mortality there are no tables that enable such annuity values to be readily calculated.

British Offices Life Tables, 1893—Aggregate Tables.

The following notes are an attempt to show

(1) How select and aggregate rates of mortality can be found from insurance office data by the methods at present used to find rates of mortality from censuses and the records of deaths among the general population, and

(2)How the census method can be modified in the case of a prolonged investigation to give a continuous mortality investigation.

We have also tried to deal with a few of the objections to the method, and some of the practical points that arise in its application.

The Metropolitan Boroughs in their existing form were established by the London Government Act, 1899 (62 and 63 Vict., Ch. 14), by the provisions of which the Vestries and District Boards and Metropolitan Board of Works, constituted under the Metropolis Management Act, 1855 (18 and 19 Vict., Ch. 120), were replaced by 28 Boroughs, of which 19 consisted of former parishes, or combined parishes, 2 of District Boards, and 7 of Parliamentary Boroughs, or combined boroughs or districts, included within the area dealt with by the Act of 1899. The following particulars as to the population and rateable value of each Borough are taken from Whitaker’s Almanac for 1912. The yield from a rate of one penny in the £ of rateable value has also been added.

Probably everyone who has been responsible in any way for the underwriting of life assurance has paused on some occasions to consider whether an extra premium which it is proposed to charge for personal or family history is really justifiable. It is comparatively easy to express this hesitancy as a problem that requires solution by asking whether the mortality among those persons having a certain family history or personal defect is heavier than that among other assured lives, and if so, to what extent. At present there is, however, little to help towards a direct solution and the amount of extra premium is based on an “educated guess.” It is, of course, only statistical evidence that can finally prove the necessity for an extra or justify its amount, but although insurance offices have been doing business and charging extra premiums for many years no complete attempt has been made to solve the problem.

At first sight one might perhaps be loth to admit that a very close analogy can be drawn between the insurance of under-average lives and the investment of life assurance funds. It seems to me, however, that in some important respects the two operations are comparable.

I think it must be admitted that practically any life, however bad, would be insurable provided the risk to be run could be accurately assessed and the requisite premium charged. Similarly, almost any investment would be worth buying provided that the risk of the loss of capital could be accurately gauged and the rate of interest was sufficiently large to pay what may be called an investment rate and to provide a sufficient margin to cover the risk of loss of capital.