This paper considers the variety of social security and complementary pension scheme arrangements which have developed in different countries, and examines some recent trends in pension reforms, designed to address the problem of the ageing population and other structural shortcomings in existing structures.

It is now June 1959—only eight years after the first magnetic tape computer was put to work in the U.S. Bureau of the Census. But it was not until mid-1954 that the appropriate auxiliary machines needed to complement this computer became available. In a very real sense, magnetic tape data processing facilities suitable for business operations are only five years old at this time.

Yet, in so short a time, possibly 300 or more tape-operated data processing systems have already been installed in the United States. A great deal has been written and said regarding the use of this equipment and its impact on current practices. There is much yet to be said. As we come to grips with the immediate and difficult job of putting it to work we can be encouraged by the very substantial progress already achieved by both manufacturers and users. In just a few years, the initial approach to computers has changed so much that the key question ‘Can electronic computers be relied upon?’ has become for many ‘Which one should I get?’

The principal circumstances affecting the value of individual live, have reference to sex, age, personal peculiarities, habits, occupation, residence, family history, previous ailments, and present health. These are brought before the medical referee, in the printed forms of examination and inquiry adopted by Life Assurance Societies, in a series of questions calculated to elicit the information required. In the present treatise they will be considered under several heads.

By the definition of generalized assurances and annuities, the relation 1 = Ās + δās is shown to be the simplest member of a family of relations in which the present value of the capital and interest repayments is equated to the original amount of a loan. When the force of interest is constant over time, the relation takes the simple form above, but when the force is a polynomial in time, the interest payments become a series of annuities, the payments on which increase over time at different rates.

Mr. President and gentlemen, I should like to express my pleasure at being back in the Faculty Hall, where I was privileged to listen to your interesting discussion last year on “The Growth of Pension Rights”. I am glad to find that the number of occasions on which economists and actuaries are not only on speaking terms but able to take counsel of one another is increasing, for I am sure that there are many problems, of which the future of pensions is only one, that can only be satisfactorily resolved through our joint efforts and deliberations. This conviction rests partly on my experience as a member of the Phillips Committee, which was heavily dependent both on the actuaries who served on it and on the members of the profession who, in one way or another, helped it along; but it is a conviction that is just as forcibly brought home to me when I look across the Atlantic to the inquiry that has been in progress since 1950 into the long-term trends in savings and investment in the United States—an inquiry carried out by economists but sponsored and largely financed by the Life Assurance Association of America.

In the course of some recent work (cf. reference 2) it proved necessary to construct a life table from a set of graduated values of mx, the central death rate at exact age x. This meant that values of qx had to be derived in order to produce the life table from a given radix. Since the values of mx were known only for integer values of x, it was necessary to use an approximate method to derive the corresponding values of qx at each age. In this note we discuss briefly the approximations which we adopted. Our results are necessarily of an elementary nature and the principal reason for setting them down is to provide a reference for possible future use. It is perhaps worth pointing out that in a situation where the values of mx are given by an explicit mathematical formula values of qx may be obtained exactly using the results of reference 1.

This paper describes how statistical methods can be tested on computer-generated data from known models. We explore bias and percentile tests in detail, illustrating these with examples based on insurance claims and financial time series.