There are so many phases of the problem of blood pressure that I shall limit myself to dealing with a recent investigation of the mortality on lives accepted as “standard risks” by the New York Life Insurance Company.

The experience investigated was that of new policies issued from 1925 to 1936, inclusive, observed from entry until the anniversaries of the policies in 1937. The investigation was by policies and was divided into two groups, (a) those in which there was no impairment, and (b) those in which there appeared minor impairments but not of sufficient moment to place the policyholders in a substandard group. The expected deaths were obtained according to the company's standard experience for the same years of issue and exposure. The total number of policies emerging by death was 9552.

The approaches to liability valuation, assessment of prudential capital and measurement of profit for life offices are undergoing radical change. A common thread runs through all of these proposed changes — each change represents a move away from traditional actuarial approaches towards a more economically coherent, market-consistent approach. These changes should encourage a general improvement in the life industry's risk management processes. However, they will come at a cost. The measurement of the economic risks generated by the complex guarantees written by life offices is far more difficult than applying the latest resilience test equity fall. This will require a step change in the sophistication of life offices' risk and capital measurement and management know-how. The measurement of value, risk and capital will soon demand the application of ‘stochastic’ modelling tools. In this paper, we explore some of the issues raised by the application of these approaches to the valuation and risk management of with-profits business.

Actuarial practice as regards mortality analysis and projection is changing rapidly. This paper provides a short introduction to some of the limitations and risks in using trends in cause of death as a means for projecting future mortality rates. It also covers recent developments in analysing the mortality of smaller populations, including survival models and “piggyback” models.

With the increasing use of complex quantitative models in applications throughout the financial world, model risk has become a major concern. Such risk is generated by the potential inaccuracy and inappropriate use of models in business applications, which can lead to substantial financial losses and reputational damage. In this paper, we deal with the management and measurement of model risk. First, a model risk framework is developed, adapting concepts such as risk appetite, monitoring, and mitigation to the particular case of model risk. The usefulness of such a framework for preventing losses associated with model risk is demonstrated through case studies. Second, we investigate the ways in which different ways of using and perceiving models within an organisation both lead to different model risks. We identify four distinct model cultures and argue that in conditions of deep model uncertainty, each of those cultures makes a valuable contribution to model risk governance. Thus, the space of legitimate challenges to models is expanded, such that, in addition to a technical critique, operational and commercial concerns are also addressed. Third, we discuss through the examples of proxy modelling, longevity risk, and investment advice, common methods and challenges for quantifying model risk. Difficulties arise in mapping model errors to actual financial impact. In the case of irreducible model uncertainty, it is necessary to employ a variety of measurement approaches, based on statistical inference, fitting multiple models, and stress and scenario analysis.

After reviewing some general issues concerning solvency and the problems associated with establishing the financial strength of a general insurance company using the traditional balance sheet concept, the authors put forward an emerging costs approach for examining the strength of a company. This enables the true nature of the assets and liabilities to be taken into account, including their essential variability. Simulation is suggested as a powerful tool for use in examining the financial strength of a company and in exploring the impact of alternative scenarios. A particular example of such a simulation model is then presented and used to explore the resilience of a company's financial position to variations in a wide variety of parameters. The model enables the user to quantify the probability that the assets will prove adequate to meet the liabilities with or without an assumption of continuing business. This in turn permits an appropriate asset margin to be assessed individually for any particular company in the light of the strategy that the company intends to follow. Some of the implications of this approach for the management and supervision of general insurance companies are explored. The suggestion is made that the effectiveness of statutory supervision based on the balance sheet and a crude solvency margin requirement is limited, since it cannot have proper regard to the risk profile of individual companies. More responsibility should be placed on an actuary or other suitably qualified professional individual to report on the overall financial strength of the company, both to management and to the supervisory authorities.

The classical approach to actuarial problems has been deterministic. That is, the assumption has been made that the number of policies in force is large, that chance fluctuations are unimportant, and that the use of mean values is adequate. The actual cost to a company of an annuity, for example, may in fact vary from nothing (if the annuitant dies immediately) to a large amount (if he lives to be a nonogenarian). On average, the cost will be ax, and for many purposes, this value is good enough.

In this paper we adopt the multiple time-series modelling approach suggested by Tiao & Box (1981) to construct a stochastic investment model for price inflation, share dividends, share dividend yields and long-term interest rates in the United Kingdom. This method has the advantage of being direct and transparent. The sequential and iterative steps of tentative specification, estimation and diagnostic checking parallel those of the well-known Box-Jenkins method in the univariate time-series analysis. It is not required to specify any a priori causality as compared to some other stochastic asset models in the literature.

At first sight one might perhaps be loth to admit that a very close analogy can be drawn between the insurance of under-average lives and the investment of life assurance funds. It seems to me, however, that in some important respects the two operations are comparable.

I think it must be admitted that practically any life, however bad, would be insurable provided the risk to be run could be accurately assessed and the requisite premium charged. Similarly, almost any investment would be worth buying provided that the risk of the loss of capital could be accurately gauged and the rate of interest was sufficiently large to pay what may be called an investment rate and to provide a sufficient margin to cover the risk of loss of capital.

It is now some sixteen years since Sir David Cox (1972) published his epoch making paper in which he incorporated regression type arguments into life-table analysis. Central to the method was the introduction of the multiplicative hazard

with vector of covariates z, unknown regression parameters β, and so-called base-line hazard λ*(t) = λ (t, 0). Applications of the method, based on the conditional likelihood argument expounded by Cox in which the base-line hazard λ* is unknown, have proliferated in the intervening years, largely in the field of medical statistics. There have been relatively few applications in which the base-line hazard is assumed known at the outset. Specific cases include Breslow et al. (1983), Berry (1983) and Hill et al. (1985).

The paper considers a number of methods of estimating the work time lost due to sickness, unemployment and stoppages. The most satisfactory approach suggested is based on a multiple state working life table. Numerical examples of the measurement of work time lost are provided for particular application to the actuarial assessment of damages (arising out of personal injury or fatal accident). Other applications, including the pricing of unemployment insurance, are also discussed.

This is not so much a paper as a series of loosely-connected essays and it requires explanation.

For some years I have felt that my generation had an unusual duty to the history of the profession. The first 180 years of actuarial history no doubt seemed eventful enough at the time but they took place against a stable background when interest rates were seldom outside the range 3% to 5%. But since 1945, say, a turbulence undreamed of in those earlier days has become the commonplace of our activities.

The theoretical basis for, and practical application of, the discounted income method for valuing UK pension fund assets is discussed, with particular reference to the widely adopted application to variable income (equity type) assets, as proposed by Day & McKelvey (1964), in the context of both the management and compliance objectives of pension fund valuation. An alternative methodology is proposed in which consistency with assets, liabilities, and market values is demanded, with smoothing of the valuation result achieved on an explicit rather than implicit basis. It is then demonstrated that the explicit smoothing parameter can be set so as to achieve the historic smoothness framework for establishing pension fund investment policy.

In conclusion the paper suggests greater emphasis on market-related methodologies for compliance valuations and leaves open the choice of methodology for management valuations and monitoring purposes, on the grounds that there is a large subjective element in any realistic basis. However, it is demonstrated that while smoother than unadjusted market-related methods, other aspects of the dynamics of the funding level under the method of Day & McKelvey can be perverse and it is suggested that this method should not be allowed to dictate investment decisions.

1. Before dealing with the question of mortality in Australia it will perhaps be well to indicate briefly what is meant by “Australia,” since the name is used with different significance in different cases. At an early stage of Australian history the name was restricted to the island continent itself, and what is now known as the Commonwealth of Australia was generally spoken of as Australia and Tasmania, in somewhat the same way as the homeland pair is spoken of as Great Britain and Ireland. With the advent of Federation, however, this mode of reference became less usual and has now practically disappeared.

The relationship of the chain ladder method to mathematical statistics has long been debated in actuarial science. During the 1990s it became clear that the originally deterministic chain ladder can be seen as an autoregressive time series or as a multiplicative Poisson model. This paper draws on recent research and concludes that chain ladder can be seen as a structured histogram. This gives a direct link between classical aggregate methods and continuous granular methods. When the histogram is replaced by a smooth counterpart, we have a continuous chain ladder model. Re-inventing classical chain ladder via double chain ladder and its extensions introduces statistically solid approaches of combining paid and incurred data with direct link to granular data approaches. This paper goes through some of the extensions of double chain ladder and introduces new approaches to incorporating and modelling incurred data.

I propose in this paper to deal with a question which has an important bearing upon those calculations as to deathrates, which are now so widely circulated and so generally felt to possess interest.

It has occurred to the Registrar-General, and, as I believe, to other inquirers, to remark that the mortality happening in London is diminished, “because domestic servants, shopwomen and milliners, “who have come from the country, retire when health fails them “to their native air.”

There is currently no international standard for profit reporting in life insurance companies. The paper sets out the issues which an international standard for life companies will need to address, bearing in mind compatibility with existing International Accounting Standards, in particular IAS 32 Financial Instruments: disclosure and presentation, IAS Exposure Draft E62 (now IAS 39); Financial instruments; recognition and measurement and the discussion paper of March 1997 prepared by the Steering Committee on Financial Instruments entitled ‘Accounting for Financial Assets and Financial Liabilities’. The paper discusses possible approaches to the issues which arise and comments on each, ending with some final conclusions.

This paper focusses on some practical issues that can arise when developing methodologies for calculating benchmark figures for extreme market events, particularly in the context of the Financial Services Authority's ICAS regime. The paper limits discussion to equity and interest rate risks. Whilst not intended to constitute formal guidance, it is hoped that the material contained within the paper will be useful to practitioners. The paper acknowledges the role of prior beliefs in the choice of data to be used for modelling and its influence upon the ensuing results.

Of the many valuable contributions by which the transactions of this Institute have been enriched by the labours of Mr. Samuel Brown, not the least interesting is the paper on the investments of Assurance Companies, read before the Institute on the 25th January, 1858. I feel much diffidence in again reverting to this question; but as Mr. Brown, at the outset of his paper, admits that the subject is too extensive to be exhausted by a single discussion, it has occurred to me that an attempt to arrive at some general principles on which the funds of Life Assurance Societies should be invested, and to consider how such principles can best be reduced to practice, might, perhaps, be the means of exciting some useful discussion.