No mortality curve appears yet to have been devised which both fits the national statistics at all ages, and also has a simple philosophical explanation. The object of this paper may be stated as being the building up of a new mortality curve from its component parts, as many as possible of these parts having a philosophical background, and the whole being applicable to the national data.

The theme of this paper is that life office valuation can be based on an analysis of the characteristics of the individual cash flows which form the net cash flow of an office. These cash flows may be compared with the income and gains derived from traded securities such as equities and gilts in order to assess their values. Standard asset pricing models of modern portfolio theory enable one to allow for lapse, mortality and other risks.

The methodology outlined in the paper is illustrated by reference to the very different types of revenue generated by non-profit, unit-linked and with-profits products. It is also used, in the valuation of future new business, to allow for the risks that expected sales volumes and profitability levels will not be achieved.

The paper provides a rationale for the choice of discount rates used in the valuation of a life office and facilitates the comparison of life office and alternative investment opportunities.

Investment conditions have changed widely and rapidly in the post-war era; and since the publication of Mr Lewis G. Whyte's textbook, Principles of Finance and Investment, there has been a spate of papers on investment theory, each of them either covering a small part of the subject or setting forth a particular view.

The aims of this paper are:

I. To suggest a balanced and consistent approach to investment principles as they affect funds of actuarial interest.

II. To discuss the application of these principles to particular types of funds.

III. To discuss the characteristics of the securities that are available in present-day conditions to implement investment policy.

These aims may sound comprehensive, but within the limitations of a paper it is only possible to touch on them briefly.

Gentlemen,—I have to express my most sincere and cordial thanks to you for the honour which you have conferred upon me, by having for the third time elected me as President of the Actuarial Society.

I have been a member of the Society almost from its commencement; and before the date of my becoming a member, I was permitted, as a young student, to attend some of the meetings. Thus it happened that I was present at the first meeting, and had the privilege of hearing the first inaugural address, delivered by the first President, the late Mr. William Thomas Thomson, a gentleman who was practically the Founder of this Society and also of the Faculty of Actuaries, and to whom both Societies are under very great obligations.

When recalling what took place in the first session of the Society, I may be permitted to refer to three notable papers by Mr. James Meikle, which I also had the privilege of hearing read, on the Nature, Calculation, and Sufficiency of the Premium required for Assurance of a Sum at Death, afterwards published under the title of “The Rationale of Life Assurance Premiums.” The author of these early papers has frequently filled the Presidential Chair, and has been extremely helpful to this Society throughout its whole existence; but if (instead of being the most extensive contributor to the Transactions of the Society) he had done nothing beyond giving us these papers, he would nevertheless have placed the Society deeply in his debt.

Medical and social progress over the past 50 years has resulted in a large increase in the expectation of life, and this, together with a declining birthrate, has caused an increase in the proportion of old persons in the population. In 1901 less than 5% of the population of England and Wales was aged 65 and over; by 1949 the estimated percentage had increased to 11% and must inevitably increase still further in the future. A result of this is that more and more attention is being given to diseases of old age and in fact a new specialized branch of medicine, geriatrics, seems to have arisen. Heart diseases form by far the largest group of causes of death in old age and in 1949 were the certified cause of death in 37% of the deaths in England and Wales at ages 65 and over (Table 1). Even in the age-group 55-59 heart disease was responsible for 24% of all deaths in 1949.

1. In the three years since projections of occupational pension scheme membership and expenditure were made for the Wilson Committee more data about schemes has become available, such as that from the Government Actuary's survey of Occupational Pension Schemes 1979 (the G.A.'s Survey), so the occasion of the publication of the Government Actuary's National Insurance Fund Long Term Financial Estimate (the Quinquennial Review or Q.R.) has been taken to revise and extend the Wilson Committee projections, using the starting date and earnings and prices assumptions of the Q.R.

Under the European Union’s Solvency II regulations, insurance firms are required to use a one-year VaR (Value at Risk) approach. This involves a one-year projection of the balance sheet and requires sufficient capital to be solvent in 99.5% of outcomes. The Solvency II Internal Model risk calibrations require annual changes in market indices/term structure for the estimation of risk distribution for each of the Internal Model risk drivers. This presents a significant challenge for calibrators in terms of:

• Robustness of the calibration that is relevant to the current market regimes and at the same time able to represent the historically observed worst crisis;

• Stability of the calibration model year on year with arrival of new information.

The above points need careful consideration to avoid credibility issues with the Solvency Capital Requirement (SCR) calculation, in that the results are subject to high levels of uncertainty.

For market risks, common industry practice to compensate for the limited number of historic annual data points is to use overlapping annual changes. Overlapping changes are dependent on each other, and this dependence can cause issues in estimation, statistical testing, and communication of uncertainty levels around risk calibrations.

This paper discusses the issues with the use of overlapping data when producing risk calibrations for an Internal Model. A comparison of the overlapping data approach with the alternative non-overlapping data approach is presented. A comparison is made of the bias and mean squared error of the first four cumulants under four different statistical models. For some statistical models it is found that overlapping data can be used with bias corrections to obtain similarly unbiased results as non-overlapping data, but with significantly lower mean squared errors. For more complex statistical models (e.g. GARCH) it is found that published bias corrections for non-overlapping and overlapping datasets do not result in unbiased cumulant estimates and/or lead to increased variance of the process.

In order to test the goodness of fit of probability distributions to the datasets, it is common to use statistical tests. Most of these tests do not function when using overlapping data, as overlapping data breach the independence assumption underlying most statistical tests. We present and test an adjustment to one of the statistical tests (the Kolmogorov Smirnov goodness-of-fit test) to allow for overlapping data.

Finally, we explore the methods of converting “high”-frequency (e.g. monthly data) to “low”-frequency data (e.g. annual data). This is an alternative methodology to using overlapping data, and the approach of fitting a statistical model to monthly data and then using the monthly model aggregated over 12 time steps to model annual returns is explored. There are a number of methods available for this approach. We explore two of the widely used approaches for aggregating the time series.

The Presidential Address relates events which occurred during significant years in the life of the President with matters relevant to the Institute, past, present and still to come, and with what was written by previous Presidents. It considers actuarial education, and specially its links with universities, and then comments on the President's career as a life actuary.

The role of the Appointed Actuary is discussed, and also what an actuary is and does. The international actuarial perspective is covered through a description of the Groupe Consultatif and of the President's other international involvement, especially with Africa. Other subjects covered include with-profits contracts, the dispersion of actuaries throughout England and Wales, the role of the actuary in today's changing world, the relationship between the Institute and the Faculty, and the role of the President. Finally, the President looks forward to what actuaries might be and do in the future.

The text of this paper, together with the abstract of the discussion held by the Institute of Actuaries on 25 October 2004, are printed in British Actuarial Journal, 11, I, 63-131.

Using an empirical approach to capital market returns analogous to that used for mortality rates by Halley more than three centuries ago to establish life assurance on a sound and scientific footing, a theory of option pricing is built up in terms of the same three key components as for life assurance premiums, namely the expected cost of claims, an allowance for expenses, and a contingency margin as a reserve against the risk of insolvency. The dimensionality of the process describing security returns to any future point in time is increased from two to three by the addition of systematic variability around ‘central values’ to the standard descriptors of expected return and variance of return. It is shown that this approach, which involves only common sense principles and elementary mathematics, has important theoretical, practical and regulatory advantages over the Black-Scholes and related methodologies of modern finance theory.

The paper examines the suitability of the stable family of distributions with the Maturity Guarantees Working Party's stochastic investment model (Ford et al, 1980). It then examines the effect of replacing the Gaussian assumption made by the working party with a more general stable distribution. It also explains how the appropriate stable distribution can be fitted.

It is regretted that in these two places Jhr. G. M. M. Alting von Geusau was wrongly described as Chairman of the Association of Dutch Life Offices (Nederlandse Vereniging ter Bevordering van het Levensverzekeringwezen).

Following a brief outline of the origins of the actuarial profession in the United Kingdom, the paper traces the involvement of actuaries in the supervision of insurance in the U.K., and recalls the origins and early development of actuaries in government. In 1919, the Government Actuary's Department (GAD) was formed, and the paper explores the developing role of GAD in the supervision of insurance and how insurance supervision has evolved into a close partnership between the actuarial profession and the supervisors.

In the course of work undertaken as members of the Executive Committee of the Continuous Mortality Investigation Bureau in the preparation of graduated tables of mortality for the experiences of 1979–82, we have had occasion to make use of and develop a number of statistical techniques with which actuaries may not be familiar, and which are not fully discussed in the current textbook by Benjamin & Pollard (1980), though some of them have been referred to in previous papers by the CMI Committee (1974, 1976). We therefore felt that it would be useful to the profession if we were to present these methods comprehensively in one paper. We do this with the permission of the other members of the CMI Committee, who do not, however, take responsibility for what follows, whether good or bad.

1.1. Section 78 of the Insurance Companies Act 1974 makes provision for Regulations to be made for the valuation of assets and liabilities. Regulations relating to the valuation of assets, although not published at the time of writing, are expected to be laid before Parliament in the near future.

It is expected that the corresponding Regulations for the valuation of liabilities will be issued later in 1975.

1.2. The Department of Trade has consulted interested bodies, including the Faculty and the Institute, with regard to proposals for the content of the Valuation of Liabilities Regulations and with its permission part of the relevant Consultative Note is reproduced in Appendix I.

Some years ago I read before the Institute a paper bearing on this subject (see Journal, vol. xi., p. 90) in which I examined at considerable length the method of valuation which has been on various occasions so strongly advocated by Mr. Tucker, and which is denominated by him the “reinsurance method.” This term, however, appeared to me unsuitable, and I termed the method the “hypothetical method” of valuation; because the sums assured and the premiums are valued by means of a hypothetical table of the values of reversions and annuities, deduced by an inverse process from the premiums actually charged by the office. In that paper I compared Mr. Tucker's method with the net-premium method of valuation, and gave my reasons for believing the latter to be not only greatly superior to the former, but the method that should be generally employed. Subsequent consideration has however satisfied me that the net-premium method of valuation is also open to very serious objections, and that it is not applicable in all cases; and I propose on the present occasion, first to point out some of these objections, and then to consider briefly what method of valuation should be followed when the net-premium method is inapplicable. The subject however is a very wide one; and the present paper must be considered rather as a contribution to the discussion of a question that is all-important to those who have the responsibility of advising as to the liabilities of Life Insurance Companies, than as claiming to be itself a complete essay on the subject.

All tabular numbers drawn directly from observations, especially those appertaining to statistics, are more or less affected by unavoidable imperfections arising from defective information, insufficiency in the number of observations recorded by the experience, and other known or unknown incidental causes. When a consecutive series of tabular numbers is taken and differenced up to a certain order, the existence of the imperfections or errors alluded to, is at once revealed by the differences, which exhibit a conspicuous disturbance of their law of progression. To eradicate the errors and effect a proper adjustment of the original numbers is, however, an operation of peculiar and somewhat novel difficulty, and a critical examination of the empirical expedients, usually resorted to for such purpose, will show that instead of meeting the indispensable requirements of the problem, they only evade its most essential conditions, and thereby impregnate the results with a new series of theoretical errors, which too readily evade detection in consequence of the systematic uniformity of their law.

This paper considers the application of loglinear models to claims run-off triangles which contain negative incremental claims. Maximum likelihood estimation is applied using the three parameter lognormal distribution. The method can be used in conjunction with any model which can be expressed in lognormal form. In particular the chain ladder technique is considered. An example is given and the results compared with the basic actuarial method.

Actuaries tend to use deterministic rather than stochastic methods and confine their calculations to the computation of expectations. The adverse effects of statistical fluctuations are usually avoided by including contingency margins in the calculations and professional judgment plays a large part in the determination of the margins. In this paper, we show how the results of two recent theoretical papers can be used to supplement professional judgment in the area of premium loadings for non-participating business. The methods are also of interest in connection with participating business.