“The rate of interest has fallen.” “The rate of interest is falling.” “The rate of interest will probably continue to fall.” These sentences, and others of a similar nature, we have read so often, that I fear it is quite possible “familiarity” may, to some extent, have had its usual effect. The fact remains, however, that any further fall in the interest yield is of vital importance to insurance companies with large funds to invest, and bound by contracts, the fulfilment of which depends, to a large extent, on the rate of interest obtainable.

The Consumer Information Working Party has published this paper which explores how we can better engage consumers with long-term savings and investments. The working party considered the current state of consumer information, which is a long way from ideal, including: consumer insights and touch points, the current consumer information model, relevant considerations from behavioural economics, examples of information failures and some successes from other fields. They then propose a way to deliver more effective information, including a possible framework and some ideas for its application. They finish with proposals for immediate next steps and urge the Actuarial Profession to take a lead in this area.

On reading over my paper after it was published, I did not feel quite satisfied as to the accuracy of my approximate formula, given on page 235, for the adjustment of in respect of the excess of contributions included in the Table as constructed, so I have had the values of and , calculated. The constant summation of these columns, namely, and , will give the columnar values to be used for making accurate adjustments.

Let there be letters x, y, z,…each of which has values, choices, or drawings. Let their number be σ, and let, ξ, η, ζ,…be their several numbers of drawings : x1, x2,…xξ the drawings of x; and so on. Let Σx, Σy,…be the sums of the drawings of x, y, &c.; and Σ:x, Σ:y, the average drawings: so that , and so on.

An analysis is made of the effect on portfolio performance if assets are continually rebalanced to constant market value proportions, relative to the passive ‘buy and hold’ strategy. The probability that one strategy outperforms the other is evaluated on the basis of a geometric diffusion model of market prices and by reference to historical data.

In the investigation of a little curiosity in the matter of annuities, I had occasion to want four or five terms of log (a + bx + cx2 + …), and, by Arbogast's rules I accordingly wrote down the following, without a stroke of the pen more than is here given:—

This I might have continued to any number of terms for little beyond the trouble of writing. The method is easy to demonstrate and easy to practice; and it struck me that I might, in a few pages, give an account of it sufficient for use and detached from anything else. I therefore append it to the problem.

This paper is primarily concerned with investment by life offices and pension funds in British Government stocks with lives of more than 5 years, although there are important implications for all classes of investors. Investing in British Government stocks over the post-war period has become a highly technical process. The advent of the electronic computer has opened up an entirely new field of statistical data thus making some of the old methods obsolete. The paper illustrates some of the new techniques developed by the author and his colleagues. Other actuaries have also been developing new approaches and it is hoped that they will contribute to a lively and constructive discussion.

It is not usual in mortality investigations of insurance data to associate exactly one unit with each life. It is easier to use policies or sums assured or some variation of policies and sums assured. But a proper statistical test of graduated rates of mortality derived from such an investigation cannot be made unless the effect of the variable number of units associated with each life is known. Beard and Perks (1949, J.I.A. lxxv, 75) gave, for four different sampling processes, formulae for the variance of the distribution of deaths for a mortality study based on policies, and Daw (1951, J.I.A. lxxvii, 261) illustrated the formulae by numerical examples on various hypotheses. In particular, he showed that the sampling process employed had little effect on the numerical results, but that the frequency distribution of the number of policies held was very important. The formulae derived by Beard and Perks assumed that the frequency distribution of the universe of number of policies held was known.

Traditional life insurance accounting standards rely on various types of book and cost values, the result being that the income and balance sheet statements do not necessarily give a true and transparent picture of the result of the life business. As examples, assets are typically stated at a mix of cost, current and amortised cost values, whereas life insurance provisions are calculated according to the approved technical basis.

In this paper, it is suggested that this deficiency can be corrected by preparing life insurance accounts at current value. The proposed method implies that the life insurance provisions shall amount to the present value of the company's net liabilities to the policyholders including a provision for future bonus distribution. Moreover, any unrealized investment reserves are thrown into light, and it is shown how a bonus equalization provision at current value may serve as a key indicator of the financial strength of the company.

The method has been designed primarily for the Danish market, but aspects of the method should be of relevance more widely.

Finally, the results are illustrated by a number of numerical examples.

The mortality data (registered deaths and population size) over the years 1961–2007 for the population of England and Wales and for Scotland were obtained from the Office for National Statistics (ONS) and from the Scottish Registrar General. This paper addresses the following questions:

(i) Is there statistical evidence for a cohort effect (i.e. a generation effect separate from the period effect) being present in the data?

(ii) Do both males and females exhibit similar cohort (generation) effects?

(iii) Are period effects (i.e. the improvement in mortality with time) more significant than cohort effects?

(iv) How should one allow, in forecasts of population mortality, for age, period and cohort effects?

(v) Is it sensible to combine male and female mortality experience to determine the period effect and the cohort effect?

(vi) How do the forecasts for the expectation of life at birth, using the Extended-Lee–Carter-Combined (ELCC) model (described in the paper) differ from the (2008 based) Office of National Statistics (ONS) forecasts of the expectation of life at birth?

This is a study into the future of the actuarial profession. Its main purpose is to assist the United Kingdom profession to respond effectively to the changes and opportunities of the next ten plus years. Scenarios are developed to show where the profession could progress to in that period; the major changes and developments implied by these forward views are identified and actions to take the profession in the desired directions are proposed.

The study covers the key issues relating to most of the various business areas in which actuaries practise, and considers, in particular: the future supply of, and demand for, actuaries; actuarial education and training and relations with other professions.

There are in existence numerous charitable funds which provide financial assistance to members or their dependants in the form of either grants or annuities and of which the principal characteristics are usually:

(1) that the benefits are neither legally claimable nor clearly defined,

(2) that membership is voluntary,

(3) that the members' contributions are usually inadequate to support the benefits, and

(4) that donations, voluntary subscriptions and legacies frequently form a large part of the income.

This Working Paper should not be reported as representing the views of the IMF.

The views expressed in this Working Paper are those of the author(s) and do not necessarily represent those of the IMF or IMF policy. Working Papers describe research in progress by the author(s) and are published to elicit comments and to further debate.

In today's financial system, complex financial institutions are connected through an opaque network of financial exposures. These connections contribute to financial deepening and greater savings allocation efficiency, but are also unstable channels of contagion. Basel III and Solvency II should improve the stability of these connections, but could have unintended consequences for cost of capital, funding patterns, interconnectedness, and risk migration.

If a pebble on a steep hill is disturbed from a state of rest, it will probably roll down the hill gathering speed as it goes, and, if the hill ends in a precipice, the pebble will, unless it is checked in its course, eventually fall over the edge. So long as the pebble is rolling down the hill it is within sight of an observer on the hill, but when it falls over the precipice it passes out of his sight; its disappearance occurs suddenly. There is no violent change in the pebble's speed or direction as it passes over the edge, so the suddenness of its disappearance is not due to any alteration in its motion but to the fact that it has rolled down beyond the level of the edge of the hill.