The paper gives an attempt at studying the effect of options under convertible Term Assurances by sub-dividing the assumed mortality into sections, some of which will have a light and others a heavy mortality, and seeing what would be the effect if the sections with the heavier mortality convert the assurances to a greater extent than those with a light mortality. (cf. Frank L. Griffin, jnr., in The Record (American Institute of Actuaries), vol. xxxi. pp. 374 et seq.)

A similar method is also used to examine the option to surrender a whole life assurance and the option to continue a child's deferred assurance.

The Paper reviews various types of mortality table used for actuarial calculations and suggestions are made whereby future tables might be rendered easier to work with in practice.

The matter is dealt with under two headings, viz. :–

• (a)The principles and methods by which future mortality tables might be constructed.

• (b)The form in which the factors based on mortality tables should be presented for practical use. The A1924-29 and earlier tables are criticised and a draft lay-out is submitted for future tables.

In this paper I should like to discuss a few legal questions which arise in connection with life assurance policies. For the sake of simplicity I shall assume that I am dealing with a mutual life assurance society constituted by Act of Parliament.

1. The theory of Integral Equations, which is an important branch of the wider theory of Functionals, has been developed by mathematicians during the past 60 years. Many valuable applications of these equations have been made in various branches of applied mathematics, including economics, biology, and especially physics. It is believed, too, that they may not be entirely void of interest to the actuary. In this paper, therefore, a brief discussion of integral equations is given, and various problems involving their use are considered. It may be that some of these problems will be thought artificial, or trivial, or both. The writer would request, however, that the examples be regarded as illustrative only. If any of them should suggest new and more important problems to actuaries, or if the methods developed herein should prove of value in the solution of present problems, the purpose of this paper will be achieved.

An examination is made of the more important events in past years, with the object of assessing their consequences on the structure of Life Office investments. Reference is made to certain monetary and trade developments during the period 1919-39. Some aspects of the world depression of 1929-32 are examined. Special attention is paid to the period following the suspension of the gold standard, when Treasury control of interest rates was initiated and developed.

Investment problems which arose during the 1939-45 war are then considered. This is followed by an analysis of the factors influencing (1) the yield on British Government securities, and (2) the outlook for British trade. Lastly, the probable effect on the investments of Life Offices of the nationalisation programme is discussed.

The paper discusses developments resulting from (1) the recent passage by most of the state legislatures of the “Standard Valuation Law” and the “Standard Non-forfeiture Law,” and (2) the general adoption by the companies of a lower interest assumption in the calculation of premiums, reserves and non-forfeiture values.

After a brief review of the system of regulation of life insurance in the United States and of the more important differences in practice as compared with practice in the United Kingdom, the paper proceeds to outline the background which led to the appointment of the “Guertin Committee” by the National Association of Insurance Commissioners to study and report on the need for a new mortality table and related matters and (subsequently) on non-forfeiture benefits. The main recommendations of the Committee and the subsequent modifications thereof as adopted by the Commissioners and later embodied in the Standard Laws are detailed.

The effects on life insurance operations of the new Standard Laws in conjunction with lower interest assumptions and the marked upward trend in expenses are discussed. The paper concludes with a brief reference to two important changes being made by some companies in their policy conditions.