This paper surveys some statistical models of survival data. A basic model of a random lifetime is defined, and censoring is introduced. Methods based on observations of small segments of lifetimes are compared. Markov and semi-Markov (multiple state) models are recommended as well-understood and flexible models well suited to actuarial data. A Poisson model is discussed as an approximation to a two state model, while traditional Binomial-type models are shown to be more restricted and less tractable than multiple state models.

The honour I have received by the invitation of the President and members for organising the Fourth Session of the International Statistical Congress, to be held daring the week commencing the 16th July instant, which the state of my health prevents me having the satisfaction to attend, induces me to offer to the notice of the distinguished members some observations which, I think, may be considered of some importance in connexion with the objects of the Congress; having for many years paid attention to the subject of vital statistics, and to the mode of rendering the information derivable from its pursuit interesting, beneficially and scientifically, to the public, who may gain consoling pecuniary advantage from it, and to the student, who may enjoy the contemplation of the paths of science; because the services which have been obtained by the public from Assurance Societies, and from the proper management of Friendly Societies, have been obtained by the attentive and philanthropic study of the subject, and the mode of pursuing that study depends on statistical inquiries, and, I may say, on deep mathematical reflection,—a reflection which, whilst it may and has been of important service to society at large, may offer many new views in philosophical and mathematical branches of enquiry even quite unconnected with statistics or its objects.

The authors' purpose in this paper is to analyse the financial structure of a life office and, in particular, the relationship between the assets and liabilities of a life assurance fund. This analysis is based upon the principle that the guarantees of future capital security and of long-term interest yield involved in the contracts issued by a life office should be backed either by “matched assets” providing equivalent guarantees of capital and interest or by sufficient free reserves to cover the possible adverse effects of departure from the “matched assets” position.

In Parts I and II of the paper, the principle of “matched assets” is studied in relation to three model offices representing stationary and increasing funds operating under idealised conditions. For each model office the “standard” date-distribution of assets is determined–the distribution which, so far as possible, will insulate the fund from the effects of fluctuations in the market rate of interest upon existing assets and liabilities. The profit or loss resulting from “going long” or “going short”, as compared with the standard asset distribution, is then investigated against the background of a rise or a fall in the general level of interest rates.

Data held within administration records of occupational pension schemes yield a rich source of information on mortality rates and the statistical predictors (covariates) of longevity. In this paper we provide, for the first time, a multivariable analysis of post-retirement mortality using the detailed information held within occupational pension scheme records.

Using the extensive dataset of over one million living pensioners and dependants and 530,000 historic deaths collected by Club Vita, we investigate the importance of factors including gender, affluence and lifestyle on the observed period life expectancy of individuals. We describe one approach to constructing a multivariable model for pensioner baseline mortality, showing how such factors explain a variation in observed period life expectancy in excess of ten years. The relative importance of each factor on mortality is analysed and we describe the interactions between these factors and age, answering questions such as whether the impact of a healthy lifestyle or affluence attenuates with age. Further, we highlight the importance of the choice of affluence measure in analysing mortality, and show that the salary at retirement is a better predictor of longevity than the pension amount for male pensioners.

The results of this paper are directly relevant to any pensions actuary advising on an appropriate baseline assumption (i.e. current mortality rates) for use with occupational pension schemes.

1.1 My paper entitled ‘The Matching of Assets to Liabilities’ described a new study of the subject of matching. The paper outlined the mathematical framework, showed some calculations, and suggested various applications in the field of actuarial valuation.

1.2 Subsequently A. D. Wilkie published a note entitled ‘Portfolio Selection in the Presence of Fixed Liabilities: a Comment on “The Matching of Assets to Liabilities”’. Wilkie's note appears to represent a new extension of portfolio selection theory which enables him to encompass the conventional portfolio theory and to show where my approach to matching fits into the picture.

1.3 This paper is in the nature of a reply to that of Wilkie. My objective at the stage of the first draft was to re-examine the matching portfolio, as defined in relation to specified liabilities, in view of the wide range of alternative portfolios which Wilkie has described. The scope of this work progressed well beyond my original plans when I found a most interesting mathematical relationship between the ‘matching portfolios’ described in my earlier paper and the ‘efficient portfolios’ described in Wilkie's.

Solvency II is currently one of the most sophisticated insurance regulatory regimes in the world. It is built around the principles of market consistency and embedding strong risk management and governance within insurance companies. For business with long-term guarantees, the original basis produced outcomes that were unacceptable to the member states. The original design was amended through Omnibus II. The working party has looked back at the outcome of the final regulation and comments on how well Solvency II has fared, principally from a UK perspective, relative to its initial goals of improved consumer protection, harmonisation, effective risk management and financial stability. We review Pillar 1’s market consistent valuation (including the risk margin and transitional measures) as well as the capital requirements (including internal models). We look at the impact this has on asset and liability management, pro-cyclicality and product design. We look at Pillars 2 and 3 in respect of the Own Risk and Solvency Assessment, liquidity and disclosure. Finally, we stand back and look at harmonisation and the implications of Brexit. In summary we conclude that Solvency II represents a huge improvement over Solvency I although it has not fully achieved the goals it aspired to. There are acknowledged shortfalls and imperfections where adjustments to Solvency II are likely. There remain other concerns around pro-cyclicality, and the appropriateness of market consistency is still open to criticism. It is hoped that the paper and the discussion that goes with it provide an insight into where Solvency II has taken European Insurance regulation and the directions in which it could evolve.

This paper reviews the United Kingdom stochastic asset model developed by Wilkie (1995b). Certain aspects of the methodology used to develop this model could be problematic. Moreover, Wilkie (1995b) did not provide a complete evaluation of his model; certain economic theories and the constancy of the model's parameter values did not appear to have been specifically considered. This paper attempts to provide a comprehensive review of Wilkie's model.

This paper discusses possible approaches to the construction of gilt yield indices published by the Financial Times. The existing method, described by Dobbie & Wilkie (1978) splits bonds into high, medium and low-coupon bands and fits separate yield curves to each. This method has been identified as susceptible to ‘catastrophic’ jumps when the least-squares fit jumps from one set of parameters to another set of quite different values. This problem is a result of non-linearities in the least-squares formula which can give rise to more than one local minimum. A desire to remove the risk of catastrophic changes prompted this research, which is being carried out as part of the work of the Fixed Interest Working Group.

Recent changes in the taxation of bonds has, further, prompted the need for a review of the yield indices. Significantly, since the announcement of the new tax regime, the old coupon effect has been removed. This has made the use of a single forward-rate curve appropriate for the first time.

A particular form of forward-rate curve is proposed as the basis for a revision of the gilt yield indices. This curve appears to give a significantly better fit than the present yield–curve model. It is also argued that the risk of catastrophic jumps has been reduced significantly.

Rapid developments in genetic science have been accompanied by confusion regarding the predictive power of DNA-based tests and in the impact of such tests on the insurance industry. The United Kingdom actuarial profession has begun to engage in the associated social policy issues and to try to throw some light on the issues through quantitative research and objective analysis. At the same time, many insurance industry actuaries have been involved in work on behalf of the insurance industry to develop a sound basis for permission to be sought to make use of the results of certain predictive genetic tests. This paper briefly outlines some of the history of the development of the debate in the U.K. and draws together some of the debates and discussions which have taken place within the Genetics Group of the Social Policy Board of the U.K. actuarial profession, as well as providing some pointers to the directions which the debate might take in the future, with some important potential consequences for the insurance industry and for actuaries.

The modelling of extreme events is becoming of increased importance to actuaries. This paper outlines the various theories. It outlines the consistent theory underlying many of the differing approaches and gives examples of the analysis of models. A review of non-standard extreme events is given, and issues of public policy are outlined.

Personal finance is a challenging topic which can benefit from a scientific approach to individual financial planning. This paper presents an individual asset liability management (iALM) model for life cycle planning which uses the methodology of dynamic stochastic optimisation and incorporates ideas from both classical and behavioural finance. Its implementation is in the form of a decision support tool for use by financial advisers or wealth managers. The investment universe is given by a set of indices for major asset classes and their returns are simulated forward over the lifetime of a household. On the liability side the foreseen cash flows of incomes and outgoings are simulated and punctuated by life events such as illness and death. The household's utility function is constructed for each time period over a range of monetary values in terms of household financial goals and preferences. Taxes and pension savings are treated using the tax shielded saving accounts specific to a national jurisdiction in terms of constraints in the optimisation sub-models. The paper goes on to present an analysis of iALM model recommendations for a representative UK household, together with an evaluation of the sensitivity of the financial plan generated to changes in market environments such as the 2007–9 crisis. The promise of this new technology is to bring modern decision support tools to individual investors in order to facilitate custom designed consumption, savings and investment policies.

Assumptions about future mortality are more important than those for factors such as fertility, migration, disability trends or real interest rates for cost projections of the U.S. Old Age, Survivors, Disability and Health Insurance scheme. Recently, one factor has been assumed to be the key driver of future mortality in both official British population projections and actuarial ones: a ‘cohort effect’ associated with a group who were born in a period centred on the early 1930s who have been identified as having experienced particularly rapid improvements in mortality rates and are often referred to as the ‘golden generations’ or ‘golden cohorts’. The concept of ‘cohort effects’ is discussed; limitations of national-level cohort data considered; and methods for identifying such effects are reviewed. Particular attention is given to the analysis of populations which have been identified as having clear cut cohort effects; those of Britain and Sweden in the later part of the nineteenth century and early twentieth century, as well as the contemporary British population. The likely magnitude of such effects is discussed using a stylised model to assess the extent to which members of the ‘golden generations’ are especially privileged.

The determination of the probable effect, upon the increase of population, of the extinction of small pox, is a problem which has been discussed at some length by three of the great continental mathematicians of the last century, namely, D. Bernouilli, D'Alembert, and Laplace. I propose, first, to solve the problem by what may be termed the theory of the composition of decremental forces, and then to reproduce (by way of comparison) from Mr. Todhunter's History of the Theory of Probabilities, the solutions given by the three eminent mathematicians in question.

The search for functions which describe how mortality varies with age is an old one. Over the past two decades demographers have developed model life tables based on the structure of relations among mortalities in different populations rather than explicit expressions of age. The earlier work was analytic and empirical using techniques of statistical regression but more recently functional models have been constructed. These developments are described with particular concentration on the logit relation families of curves.

Some uses of the model life tables in demography are examined such as mortality projections, the dynamics of age structure and estimation from the limited data of developing countries. The implications of the logit system for certain of the “classic” speculations are considered—the span of life, whether a generation carries its own mortality with it and the accumulation of the unhealthy at older ages with saving of life at the younger.

This report presents the results of an investigation into the mortality of impaired assured lives during the period 1947-63. A preliminary account, outlining the nature of the investigation, was given by the first author in his Presidential Address to the Assurance Medical Society in 1955, and a report on the results up to the end of 1958 was given in a paper by the second author, which was presented to both the Institute and the Faculty of Actuaries in 1961 (J.I.A. 87, 196, and T.F.A. 27, 20). Earlier this year the first author read a paper to the Assurance Medical Society which gave the statistical results up to the end of 1963. These same statistics form the basis of the present paper, but the text has been revised and expanded. Certain passages in the present paper, notably §§ 7, 8, 9 and 11 which describe the recording and tabulation of data, have been reproduced from Clarke's 1961 paper.

Investment efficiency is a function of the risk, return and total cost of an investment management structure, subject to the fiduciary and other constraints within which investors must operate. Institutional investors implement their investment policies through investment management structures. In this paper the aim is to enhance the investment management structure by broadening the financial objectives, by recognising the effect of behavioural issues and by incorporating governance constraints. We therefore suggest that investment efficiency should be considered as a combination of financial efficiency and non-financial efficiency.

Modern portfolio theory had a revolutionary effect on portfolio construction. In the same way, we believe that investment management structures should be constructed in a more disciplined and quantitative manner. In this paper we outline the quantitative and qualitative methods by which these structures can be developed. The proposed new framework for designing investment management structures seeks to optimise net information ratios while simultaneously recognising the level of regret risk facing fiduciaries, minimising non-financially-productive behavioural biases and taking account of the resources available to the fiduciary to monitor these structures.