This paper derives second moments of estimates of the parameters in the chain ladder model. Thus, the so-called link ratios, and proportions of ultimate claims for each development year are considered. This enables confidence statements about the chain ladder parameters to be made with statistical rigour. The methods are illustrated using 6 sets of real data taken from the DTI returns.

In 1969, A. H. Pollard and J. H. Pollard published a paper in which they treated actuarial functions as random variables, the randomness being caused only by variations in the age at death. In 1971, J. H. Pollard took this one step further by allowing the rate of interest as well as the age at death to vary and used these results to determine premium loadings for non-profit assurances.

There has recently been some debate about the usefulness of financial economics to the actuarial profession. The consensus appears to be that the techniques are potentially valuable, but the published material is not quite ‘oven ready’. Some development work is required before the material can be applied.

The author has carried out much of the necessary development work on behalf of various clients over the last few years. On some occasions the results have conflicted with more conventional actuarial methods. The main aim of the paper is to bring the new techniques into the public domain so that they can be properly discussed by the profession, and adopted more widely if appropriate.

The paper contains a number of worked examples using techniques developed by financial economists. The author has listed the computer code which generated the examples and deposited copies on the Internet, so that others can explore the issues with a minimal development overhead.

Recent developments which affect the financing of occupational pension schemes in the U.K. arc reviewed. These point to the need for realistic bases, and an approach to finding a ‘best estimate’ is described. It is suggested that typical bases contain significant margins and the long-term dangers of using bases which contain margins are illustrated using a model fund. A review of funding methods suggests that the projected unit and entry age methods should be used for normal purposes in conjunction with a discounted income approach to the valuation of assets. Suggestions are made as to the degree of prudence appropriate for funding purposes.

This survey continues a series of international mortality comparisons, of which the most recent were Giles & Wilkie (1973) and Wilkie (1976). The first part of the paper is a descriptive survey of mortality data from United Nations sources over the period 1970-90. The second part is based on short reports prepared by contributors from the actuarial associations in various countries, and aims in particular to provide a comprehensive bibliography.

1.1. Multiple state life tables can be considered a natural generalization of multiple decrement tables in the same way as the latter can be considered a natural generalization of the ordinary mortality table. The essential difference between a multiple state model and a multiple decrement model is that the former allows for transitions in both directions between at least two of the states, see for example Haberman (1983, Fig. 2). whereas in the latter, transitions between any pair of states can be in one direction only, if they are possible at all; see for example Haberman (1983, Fig. 1). Multiple state life tables, unlike mortality tables and multiple decrement tables, are not included in the professional actuarial examination syllabuses in Britain and have only rarely been mentioned in the British actuarial literature, one example being C.M.I.R. (1979, Appendix 2). Despite this, such models have been included in the actuarial examination syllabuses of other countries for several years, for example Denmark, and would appear to have obvious actuarial applications, for example sickness insurance. Dr Haberman's paper (J.I.A. 110) on the subject of multiple state models is to be welcomed since it provides both an introduction to this subject and an interesting application. The approach to the study of multiple state models put forward by Haberman (1983, §3) is characterized by the use of flow, orientation and integration equations. For brevity we shall refer to this as the FOI-approach to multiple state models. The purpose of the present paper is to put forward an alternative approach to multiple state models. This approach uses the forces of transition, or transition intensities, between states as the fundamental quantities of the model. For brevity we shall refer to this as the TI-approach.

The aim of this research was to look at the emergence of wearable technology and the internet of things (IoT) and their current and potential use in the health and care area. There is a wide and ever-expanding range of wearables, devices, apps, data aggregators and platforms allowing the measurement, tracking and aggregation of a multitude of health and lifestyle measures, information and behaviours. The use and application of such technology and the corresponding richness of data that it can provide bring the health and care insurance market both potential opportunities and challenges. Insurers across a range of fields are already engaging with this type of technology in their proposition designs in areas such as customer engagement, marketing and underwriting. However, it seems like we are just at the start of the journey, on a learning curve to find the optimal practical applications of such technology with many aspects as yet untried, tested or indeed backed up with quantifiable evidence. It is clear though that technology is only part of the solution, on its own it will not engage or change behaviours and insurers will need to consider this in terms of implementation and goals. In the first weeks of forming this working party, it became evident that the potential scope of this technology, the information already out there and the pace of development of it, is almost overwhelming. With many yet-unanswered questions the paper focuses on pulling together in one place relevant information for the consideration of the health and care actuary, and also to open the reader’s eyes to potential future innovations by drawing on use of the technology in other markets and spheres, and the “science fiction–like” new technology that is just around the corner. The paper explores:

• an overview of wearables and IoT and available measures,

• examples of how this technology is currently being used,

• data considerations,

• risks and challenges,

• future technology developments and

• what this may mean for the future of insurance.

This paper considers a general framework for the selection of assets to meet the liabilities of a life insurance or pension fund. This general framework contains the mean-variance efficient portfolios of modern portfolio theory as a special case. The paper also demonstrates how the portfolio selection and matching approach of Wise (1984a, 1984b, 1987a, 1987b) and Wilkie (1985) fits into this general framework. The matching portfolio is derived as a special case, and is also shown to have implications for determining the central value of the liabilities.

Although equity release market sales have been flat since 2003, the market has seen significant developments in terms of product flexibility, with greater levels of guarantees and drawdown schemes, in particular, leading to the reduction in average case sizes. All things being equal, products should have become more expensive for consumers, but the competitive environment which has driven product innovation has also resulted in lower product margins. This is all good for the consumer, but it is increasingly difficult for providers to reach target returns on capital, and this is deterring some prospective new entrants. One of the purposes of this paper is to investigate the profitability of typical schemes in the market at present, and so to address the question of whether competition has forced the market to function at non-profitable levels. In doing this, the paper also provides a benchmark for existing providers and potential new entrants, against which they can check the reasonableness of their own assumptions. We will aim to provide a rational pricing methodology, which can be adopted by any organisation active in the market, and we hope that this can support the market as it expands over the coming years. In order to produce a set of cohesive results, we have modelled a range of potential outcomes using a pricing basis which we consider to be broadly ‘average’. While we would encourage providers to compare our results with their own pricing assumptions, and to ensure that they are satisfied as to the reasons for any differences, there is a health warning, as our results should only be used as a check in this regard. If our ‘averages’ are suitable for use by some providers, then this is just co-incidence. In practice providers should adapt the assumptions made to suit their own product features, target market, expense profile and appetite for risk.

A project to develop an Accounting Standard for Insurance, with the aim of enhancing understandability, relevance, reliability and comparability of general purpose financial reporting for insurance worldwide, is being progressed by the International Accounting Standards Board. The basis of the proposals is that assets and liabilities be shown at fair values (market values for quoted instruments). This paper, prepared by a Working Party established by the Life Board of the United Kingdom actuarial profession, summarises and comments upon a number of the principal features of the proposals, as they have emerged up to September 2001. The paper goes on to consider how a system of reporting for prudential regulatory purposes might be built upon a fair value general reporting base, summarising the thinking of a number of other bodies, proposing certain principles and suggesting lines of development. The appendices to the paper discuss a number of issues in further depth and present some illustrative results of some investigations into applying fair value methods in practice. The emphasis of the paper is on reporting for life assurance business, although many of the principles apply equally to general insurance.

Insurance industry practitioners have deep knowledge of their industry, but there is a lack of a simple-to-understand, practical blueprint on applying distributed ledger technology solutions, including blockchain. This paper provides a practical guide for actuaries, risk professionals, insurance companies and their Boards on blockchain, including an education piece to provide an understanding of the technology. Examples of real-world applications and use cases in insurance are provided to illustrate the capability of the technology. The current risks and challenges in adopting the technology are also considered. Finally, a checklist of issues to consider in adopting a blockchain solution for insurance business problems is provided.

Several important classes of liability are sensitive to the direction of future mortality trends, and this paper presents some recent developments in fitting smooth models to historical mortality-experience data. We demonstrate the impact these models have on mortality projections, and the resulting impact which these projections have on financial products. We base our work round the Lee-Carter family of models. We find that each model fit, while using the same data and staying within the Lee-Carter family, can change the direction of the mortality projections. The main focus of the paper is to demonstrate the impact of these projections on various financial calculations, and we provide a number of ways of quantifying, both graphically and numerically, the model risk in such calculations. We conclude that the impact of our modelling assumptions is financially material. In short, there is a need for awareness of model risk when assessing longevity-related liabilities, especially for annuities and pensions.

The trustees and sponsors of defined benefit schemes rely on the advice of the Scheme Actuary to make important decisions concerning the funding of the scheme, the investment of its assets, and the use of surplus assets to improve benefits. These decisions have to be made in the face of considerable uncertainty about financial and demographic factors that will affect the future experience of the scheme and its success in meeting various objectives.

The traditional actuarial valuation combined with actuarial judgement has played an important role in guiding decision making; but we argue that stochastic methods can add value in certain crucial areas, in particular the financial risk management of defined benefit schemes. Rather than dealing with risk by incorporating margins in the valuation basis, a stochastic approach allows the actuary to evaluate specific and quantifiable risk and performance measures for alternative funding and investment strategies.

This paper recommends a framework that, when combined with a suitable stochastic model, measures the risks inherent in contribution rate and asset allocation decisions, allowing better decisions to be made. In doing this, we suggest and apply various risk and performance measures that may be thought appropriate, although our intention is to illustrate their use rather than prescribe them as objective standards. The framework provides the means to explore the trade-offs involved in possible contribution and asset allocation decisions, and points to decision strategies expected to give improved outcomes for the same level of risk. A feature of the approach that marks it out from current asset/liability techniques is that it examines the funding and investment decisions together. It does not derive a contribution rate in the traditional way, but leaves this as free variable, in the same way that the investment decision is taken to be a free variable. Another distinctive feature of our framework is that it is based on projection rather than on valuation, involving stochastic simulation of the experience of the scheme over a time horizon reflecting the concerns of the trustees and the sponsoring employer.

The paper provides a case study (based on a model final salary pension scheme) showing the advantages of the framework, and goes on to explain how the results may practically be communicated to trustees and scheme sponsors.

This paper describes current asset share techniques, examines alternative asset share philosophies and discusses practical issues associated with the calculations. Alternative approaches to smoothing payouts using asset shares are examined. A financial management framework is described which provides information on the financial position of a with-profits fund. A central part of the framework is the concept of risk-based capital. The factors to be considered in determining risk-based capital are described and examples given of the possible capital needs of with-profits business.

Data have been generously supplied by the Faculty of Actuaries Withdrawals Research Group. These data cover the lapse or withdrawal experience for the calendar year 1976 of seven Scottish life offices. An extensive analysis has been published by the Research Group although, for reasons we shall discuss later, we believe that the approach outlined here is better able to describe the structure of the data than the detailed (and somewhat pedestrian) tabulations of this earlier paper.

1.1. This paper is concerned with claim reserves in general insurance. General, or non-Life, insurance may be taken to include such classes of business as Motor, Liability, Property, etc., and the claim reserves with which the paper is concerned are usually described as ‘outstanding claims reserves’ or ‘reserves for claims incurred but not reported’ (I.B.N.R.). Each of these reserves falls under the heading of ‘technical reserves’, and may be referred to as ‘provisions’ by the accountancy profession. Such reserves are intended in some sense to represent the liability of the insurer arising from events which have occurred within the scope of, and during the period of currency of, the insurance. It is implicit in the definition of such reserves that there is defined a specific date, which will be referred to in this paper as the accounting date, to which the reserves relate. The need for outstanding claim reserves arises from the separation in time of the reporting of a claim to an insurer from the subsequent settlement of that claim, whether this settlement involves the payment of a positive sum by the insurer, or whether, in the event, no payment is made.

Previous investigation

A previous investigation into the mortality of diabetics was made by A. J. Steeds following the analysis of data based upon a large London clinic. The present paper is based on data derived more recently from the experience of the patients attending a large Birmingham clinic.

Diabetes mellitus

2. Diabetes mellitus is a very ancient disease which may be described as a disturbance of the normal insulin mechanism of the body. The pancreas is a gland which secretes insulin for the purpose of converting sugar and starches into the energy forms required by the body (the metabolism of carbohydrates) and disturbance in this metabolism is accompanied by an abnormality in the breakdown of fats. Apart from physical damage to the pancreas the causes of diabetes are various and obscure (although they are thought to include heredity, overweight and, in females, a high level of childbearing). It is generally accepted that diabetes in young lives is a more severe form associated with insulin deficiency, whereas in older lives the disease is of a milder type, but there are many exceptions to this broad division.

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.

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.