Almost a quarter of a century ago—in 1958 to be precise—one of my predecessors devoted the main part of his Presidential Address to a discussion of state and occupational pensions. He spoke at a time when price inflation was 2¾%, growth in the national income had been averaging 2% p.a. in real terms and the number out of work was half a million. The redemption yield on long-dated Government stock was about 5¼% and the dividend yield on the Actuaries' Investment Index of Ordinary Shares was 5¾%—we did not yet have the reverse yield gap that recognizes the endemic nature of inflation.

In October 1900, on the morning of the first day of the autumnal meeting of the Actuarial Society of America, Mr. Emory McClintock, Actuary of the Mutual Life Insurance Company of New York, read a paper entitled “The Objects to be attained in Future Investigations of Mortality and Death Loss”, in which he stated that probably four-fifths of the publications of companies' general experience possessed only a “casual interest”, and that the same amount of effort might much better have been devoted to investigating special classes of business, adding that “it is “more important to the future interests of life insurance to learn “how fishermen compare with farmers, how physicians compare “with clergymen, and the like, than it is to gather all these “heterogeneous materials into one grand average in the form of “a new life table.”

The Address is a journey in three parts. The first part describes the world scene in the last century when the Institute was founded and traces the development of actuarial work to the present day. The current U.K. pension scene is then broadly reviewed and the journey ends with vistas of the future. The concentration of actuarial work towards life assurance and pensions is attributed to meeting the needs of the past and encouragement is given to the urgent extension of the work of the profession into wider fields.

The U.K. pension scene is described as being complex, confused and filled with uncertainty. The profession is urged to assist government actively and positively, to examine the expected future growth of pension funds, and to compare the financing of retirement benefits in the U.K. with other methods adopted in Europe.

Work in wider fields is envisaged as embracing general insurance, the health and care of the aged, banking and finance, and the appraisal of capital projects.

The problem of finding the rate of interest corresponding to a given annuity-value, has engaged considerable attention at various times; and many formulas have been proposed for obtaining approximate solutions by the aid of existing tables of annuities. Most of these will be found in Mr. Sutton's paper on the Rate of Interest yielded by Foreign Loans (J.I.A., xix, 77). Of the 5 formulas there given, (2) is probably the most generally useful, (3), (4), and especially (5) (Prof. De Morgan's formula), involving a good deal of calculation. The object of the present short paper is to suggest 2 new formulas, which give very accurate results, and at the same time require but little work in their practical application.

Let a be the value of an annuity for n years certain, at a rate of interest i, (which it is required to find), and let a1, a2, a3, be the tabulated annuity-values for the same term at the rates i1, i1 + h, i1 + 2h, where a lies between a1 and a2, and consequently i between i1 and i1 + h.

In this paper, everyday actuarial data have been examined by means of standard statistical techniques. The data in question have been drawn from the publications of the Continuous Mortality Investigation Committee, and the methods of statistical analysis have been applied to investigate the nature and extent of the heterogeneity which may exist in those data.

We explore some of the risks related to Artificial Intelligence (AI) from an actuarial perspective based on research from a transregional industry focus group. We aim to define the key gaps and challenges faced when implementing and utilising modern modelling techniques within traditional actuarial tasks from a risk perspective and in the context of professional standards and regulations. We explore best practice guidelines to attempt to define an ideal approach and propose potential next steps to help reach the ideal approach. We aim to focus on the considerations, initially from a traditional actuarial perspective and then, if relevant, consider some implications for non-traditional actuarial work, by way of examples. The examples are not intended to be exhaustive. The group considered potential issues and challenges of using AI, related to the following key themes:

• Ethical

  • ○ Bias, fairness, and discrimination

  • ○ Individualisation of risk assessment

  • ○ Public interest

• Professional

  • ○ Interpretability and explainability

  • ○ Transparency, reproducibility, and replicability

  • ○ Validation and governance

• Lack of relevant skills available

• Wider themes

This paper aims to provide observations that could help inform industry and professional guidelines or discussion or to support industry practitioners. It is not intended to replace current regulation, actuarial standards, or guidelines. The paper is aimed at an actuarial and insurance technical audience, specifically those who are utilising or developing AI, and actuarial industry bodies.

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.

From the fact that a very large amount of capital has been of recent years invested in loans to foreign governments, the question of sinking funds and other kindred matters has come prominently into notice; and matters which at one time were only looked upon as belonging to the theory of compound interest, are now become of great moment to thousands of persons who have invested, or purpose to invest, their money in the above-mentioned class of security. Various causes appear to have led to the large increase in the popularity of foreign loans among certain classes of investors. No doubt, the rapid growth of unemployed capital has considerably reduced the rate of interest realizable on first-class home securities, and has induced persons anxious to obtain a high rate of interest to invest their money elsewhere. From the nature of the case, however, even a fairly high rate of interest would not generally be sufficient inducement for an investor to lend money to a perfectly irresponsible foreign government, which might at any time, if it thought fit, renounce all its past financial obligations. Whether the general practice of providing for the repayment of loans has arisen from the scruples of foreign governments to accumulate a large national debt like our own, or whether, on the other hand, it has been found necessary to give an undertaking to repay the loan over a term of years, in order to make the loan at all palatable to investors, I cannot say; but the fact none the less remains, that very generally provision appears to be made, in the case of loans by foreign governments, for repayment in a shorter or longer period of time.