The literature on ‘Term-Structure Models’ is extensive with many contributions from financial economists over the last twenty years. This paper reviews examples of term-structure models from different categories (‘equilibrium’, ‘evolutionary’ and ‘descriptive’) with particular emphasis on their intended application. The Vasicek (one-factor equilibrium), Richard (two-factor), and Hull & White (evolutionary) models are discussed in some detail.

The paper reviews a particular class of descriptive polynomial models which is flexible and in widespread use both in the academic and the practitioner community. The model is cast in terms of forward rates, applied to the gilt market, and techniques are used to determine how many terms in the polynomial expansion are statistically required in order to describe the market accurately. The model is a linear model of forward and spot rates and is stable; this allows the calculation of risk measures for each bond which give a superior approach, in principle, to portfolio hedging.

Selection of model should be driven by its application. If the objective is a reasonably accurate description of the curve and, by implication, an accurate indication of yields which can be obtained in the market, then a model which fits the market accurately is preferable. The ‘descriptive’ approach is therefore most appropriate in this context.

This problem concerns n couples around a circular table, husbands and wives seated alternately. The number of ways in which the n couples can be seated such that no husband and wife sit next to each other is required. This problem is not covered in the standard texts such as Feller (1950) or Whitworth (1901) who concentrate on the simpler linear problem, i.e. seating arrangements in a row. In this paper we obtain a solution for the circular problem, deriving thereby the probability that no such matching occurs when the seating is made at random, and showing finally that this probability has a limiting value when n is large.

All UK insurers exposed to longevity risk need to perform stress tests for their Individual Capital Assessment (ICA). Some have put in place deterministic models which are arguably too simple; others have developed stochastic models that can be demanding and complex.

This paper presents a simple model to turn any deterministic mortality scenario into a stochastic model. We propose a simple model of stochastic variation that is easy to explain and to implement, which could be an alternative to and/or complete some of the well known models. The model can be applied to any best estimates of future mortality rates, as it aims to describe how longevity behaves around the projected expected values.

The paper proposes a possible calibration on the England and Wales population mortality that produces a minimum indication of possible future variation and uses the results to validate the model's assumptions. Using sample portfolios and the stochastic model, we can simulate cash flows to determine the distribution of the net present values (NPV) of annuity outgo.

The Presidential Address argues that, by acting in the public interest, the power of actuaries to benefit individuals financially can become a competitive advantage for the profession. This theme is explored by reference to professionalism being under threat, the negative impact of professional negligence claims, the need for unity in the profession, nationally and internationally, and the consequences for our education. The future of the profession will be brighter, and can be expansionist, if actuaries are recognised and valued for serving the public interest in the wider fields, but this will require effective public relations.

As already stated by the writer, in a former paper on the subject, “In the absence of any large collection of facts and observations in Jamaica, from which such a table could have been deduced, he has necessarily been compelled to proceed upon probability and approximation, according to the experience and opinions of persons whose age and long residence in the community, or whose peculiar means of information, would give weight and authority to their statements; and, as a consequence, to any system which might be based upon them.

In a note in the introduction to Milne's Treatise on Annuities, the author remarks—“There can, I think, be no doubt but that the mortality is greater among the higher than the middle classes of society. They form too small a proportion of the population to have any sensible effect here; but it would be of importance to the Life Offices to determine the law of mortality among them.” Since the publication of this work, forty-six years ago, some attempts have been made to test the accuracy of this assertion, and to supply the desideratum; but none with which we are acquainted are by any means conclusive.

Various numerical procedures have been developed in recent years for estimating the provisions for outstanding claims of a general insurer. (See, for example, Benjamin, 1977, 234–66.) These procedures do not in general have a theoretical statistical basis, and consequently they do not provide information about the reliability of the resulting outstanding claims estimates. An exception is the complex procedure of Reid (1978).

It is not surprising that actuaries have been daunted in their quest for an appropriate statistical model: the claim process is very complicated, particularly for ‘long tail’ business. One has to consider the incident leading to a claim, the size of the resulting claim, the time to settlement, and the distribution of payments up to the time of settlement both by amount and epoch. There are also the additional complications of inflation and investment earnings on the provisions.

In this paper, a theory is developed in which the complications of the claim process are overcome by considering the joint distribution of payments for a single claim in successive development periods. The model is distribution-free in that it does not assume specific distributions for claim size, time to settlement, or payments prior to settlement by amount and epoch. The method requires that payments which have been made be expressed in ‘constant-dollar’ terms (i.e. adjusted for past inflation).

We examine the roles of actuaries in UK life offices, along with trends, challenges to and opportunities for actuaries. We carry out an analysis of senior roles in life offices, a questionnaire survey and interviews with relevant senior personnel. We find that actuaries occupy many important roles in life offices and are regarded as having good industry knowledge and technical skills, especially in financial modelling. There are fewer executive directors and more non-executive directors of life offices who are actuaries compared with the position in 1990. A higher proportion of reserved roles is outsourced to consultants than was the case in 1990. Only a small number of Actuarial Function Holders are directors. Actuaries are more siloed than was the case in the past, although actuaries are well represented in the finance and risk functions of many offices. Although actuarial work in connection with the preparation for Solvency II will decline, there will be important ongoing requirements for actuaries following Solvency II implementation. We also see opportunities for actuaries in four areas: in risk management, in financial analysis and management based on Solvency II and international financial reporting standards, in connection with “big data”, and in product development and the customer proposition. There are implications for the examination syllabus, continuing professional development and research.

This Presidential Address is a call for a debate about change, to meet the demands of the 21st century. Change in how actuaries are educated to encourage wider thinking and more flexible careers. Change in how the profession is governed, to introduce more external input, to encourage more challenge of accepted practices and standards and to encourage a greater readiness to embrace change itself. To boost our public image and our influence on public policy. Change in the United Kingdom's social security and pensions systems, the better to achieve a secure retirement for tomorrow's pensioners. Change in how insurers are regulated, ensuring that consumer protection is not diminished in the process. The importance of research is emphasised, as are our relationships with other professions. These are areas where the Faculty is particularly well placed to play its part in taking the U.K. profession forward.

Climate change is at the forefront of discussions for many companies. Climate change-related disclosures and reporting are important tools and allow stakeholders to understand climate-related risks a company is facing and help various stakeholders to take informed decisions.

The landscape for climate change-related reporting requirements is ever evolving, with a trend from voluntary to mandatory, with many global disclosure standards and requirements influencing local requirements and other related standards.

This paper explores these ideas further, giving a general background to disclosure requirements, discusses greenwashing, details disclosure organisations including TCFD and the ISSB, and provides details on a country level including green taxonomies.

Parametric mortality models permit detailed analysis of risk factors for actuarial work. However, finite data volumes lead to uncertainty over parameter estimates, which in turn gives rise to mis-estimation risk of financial liabilities. Mis-estimation risk can be assessed on a run-off basis by valuing the liabilities with alternative parameter vectors consistent with the covariance matrix. This run-off approach is especially suitable for tasks like pricing portfolio transactions, such as bulk annuities, longevity swaps or reinsurance treaties. However, a run-off approach does not fully meet the requirements of regulatory regimes that view capital requirements through the prism of a finite horizon, such as Solvency II’s one-year approach. This paper presents a methodology for viewing mis-estimation risk over a fixed time frame, and results are given for a specimen portfolio. As expected, we find that time-limited mis-estimation capital requirements increase as the horizon is lengthened or the discount rate is reduced. However, we find that much of the so-called mis-estimation risk in a one-year value-at-risk assessment can actually be driven by idiosyncratic variation, rather than parameter uncertainty. This counter-intuitive result stems from trying to view a long-term risk through a short-term window. As a result, value-at-risk mis-estimation reserves are strongly correlated with idiosyncratic risk. We also find that parsimonious models tend to produce lower mis-estimation risk than less-parsimonious ones.