I have always had a healthy and perhaps wary respect for actuaries since I was interviewed by the ‘Scottish Widows’ in Edinburgh after finishing my studies at Edinburgh University in 1949. During this interview, people were pointed out to me who were still trying to pass their examinations after 19 years and, when I saw what the examination syllabus included, reason took over and I decided to go down the easier path of accountancy.

1.1. The concept of the matching of assets to liabilities is fundamental in matters of finance. In its broadest sense matching is relevant both to the investment of life office and pension funds and to actuarial calculations in relation to those funds.

1.2. Matching is inherently connected with the uncertainty of future conditions, as measured by such indicators as rates of interest, inflation and currency exchange. It is when conditions do not work out as hoped for or expected that the risks associated with mis-matching can materialize. Whether considering investment policy or an actuarial calculation it is important that the nature of a portfolio which minimizes these risks be appreciated, and yet it is often difficult to specify such a portfolio with precision. This may not be a source of difficulty in practice when the judgement of the actuary is applied to the problem in hand, but there is evident scope for refinement of the concepts.

Royal Charters incorporating academic and professional bodies have usually been granted as soon as the organization could prove itself worthy of the honour. Why, then did it take the Institute nearly 40 years to acquire its charter? The story has been told in R.C. Simmonds's The Institute of Actuaries 1848–1948 but bears retelling here.

The initial object of this paper was to make general observations on the draft Insurance Companies (Winding-Up) Rules 1983 which were circulated for comment and would be made under Section 59 of the Insurance Companies Act 1982. They concern the identification of general and long-term assets and liabilities, and the evaluation of policyholders' claims, in a winding-up. The wider objective is to review insolvency law generally in relation to long-term insurers and in particular the interaction between the general law concerning companies and the specific law relating to insurance companies. This review leads the authors to set out the case for a radical new approach.

These notes discuss the Proposal by the Commission of the European Communities for a Council Directive “On the implementation of the principle of equal treatment for men and women in occupational social security schemes”. Article 6, §§ 1(h) and (i) of the proposed Directive state that it would be contrary to the principle of equal treatment to provide for benefits whose level or amount differ or to set contributions at different rates, “by taking into account different factors of calculation, actuarial or otherwise, with regard to the phenomena of ill health, mortality or life expectancy”. These notes concentrate on this proposal, which is of considerable actuarial importance. Actuaries take into account different factors of calculation with regard to these phenomena, not simply by convention or through unjustifiable prejudice, but because of a sincere respect for the truth. To attempt to ignore the truth may have dangerous consequences, which are discussed.

1.1. Since its formation in 1974 the General Insurance Study Group has been considering various aspects of the solvency of general insurance companies and a number of papers have been produced for discussion at GISG Seminars. These have been deposited in the library at Staple Inn but have not been presented or made available to a wider audience in the profession.

1.2. At the Dublin Seminar in October 1981, three working parties reported on different aspects of solvency: technical risks, investment risks and reinsurance. These papers covered a wide field but lacked a coherent theme. During 1982 some work was set in hand to draw the threads together. This was not completed for the Stratford Seminar in November 1982 but there was by that time much interest in the Finnish solvency study which had recently been presented to the ASTIN Colloquium in Liège.

1.1. An earlier paper by the author has attempted to describe the theories of multi-state life tables and inhomogeneous Markov chains in their application to the study of morbidity as introduced by Pollard. It is the purpose of this paper to extend the model to describe the relationship between the incidence and prevalence of a disease. The implications of certain assumptions about the presence of mortality and of differentials in the level of mortality are also discussed.

0.1. Since the concept of immunization was introduced in Redington (1952) many new ideas have been advanced in connexion with the pricing of government securities. It is shown in Bierwag (1977) for example, that the applicability of an immunization strategy depends on the form of movements assumed possible in the yield curve.

0.2. Much of this earlier work has been framed in deterministic terms, where prices or yields are assumed to be known in advance, and uncertainty has been introduced via arbitrary instantaneous changes in those yields. It is easily shown that portfolios of securities with a given mean term or duration are immune (in the sense of yielding the same return at the required realization date) to certain forms of instantaneous change.

The level of benefits paid to members of occupational superannuation schemes will depend on the level of contributions made by the employer and employee, the investment earnings received by the accumulated assets and the expenses incurred in the management of the scheme. However, this third factor has been ignored by previous studies into occupational superannuation, even though higher expense levels will naturally cause reduced benefits for a given level of contributions and investment return. In this respect, cost efficiency within the superannuation industry is an important criterion in assessing the efficacy of employer-sponsored occupational superannuation.

This paper is largely based on a Ph.D. thesis (Coutts (1983)) and provides an actuarial approach to the technical aspects of motor insurance premium rating, where equal weights are given to both the practical and statistical elements of the problem. The methods described are applicable to the competitive United Kingdom motor insurance premium market. However, it is also contended that in countries where motor rating tariffs are in operation, the analyses proposed are still necessary for management to judge where in the portfolio the business is potentially unprofitable.

By the definition of generalized assurances and annuities, the relation 1 = Ās + δās is shown to be the simplest member of a family of relations in which the present value of the capital and interest repayments is equated to the original amount of a loan. When the force of interest is constant over time, the relation takes the simple form above, but when the force is a polynomial in time, the interest payments become a series of annuities, the payments on which increase over time at different rates.

The data presented in C.M.I.R. (1979) and (1984) on the Sickness Experience for Individual PHI Policies contain duplicate policies. In dealing with these data it is therefore necessary to be able to take account of the effect of duplicates on the variance of sickness claim inceptions and of weeks of sickness claims.

1. The rise in the general level of prices that has occurred in Britain at varying speeds over the last half century has caused many investments to appreciate considerably in money terms, but without this necessarily representing any increase in the purchasing power of the monetary proceeds. It has for some time been desirable to adjust for changes in the general purchasing power of money, and to calculate returns on investment ‘in real terms’. The issue by the British Government of Index Linked Treasury Stocks provides investments whose future return is defined in terms of the Retail Prices Index (R.P.I.), and it is desirable to calculate ‘real’ redemption yields on these stocks. There has been some discussion about how such real yields should be calculated, and, as will be seen, it is necessary to make certain assumptions in order to produce explicit results. The Joint Investment and Index Committee of the Institute of Actuaries and the Faculty of Actuaries has asked me to prepare this note in order to explain the details of how real yields should be calculated, and what assumptions need to be made and stated. I am very grateful to the members of the Committee, particularly the Chairman, R. H. Pain, for their assistance in its preparation.

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.

This paper deals with life assurance policies where the death benefit is the maximum of a fixed sum assured and a return of the gross premiums paid. The gross premium is then the solution of an implicit equation. The conditions for the uniqueness and existence of a solution are discussed.

1.1. This paper is supplementary to another by the same author on the subject of matching. It describes the mathematical analysis of the following problem.

1.2. We are given:

1. a pattern of expected future cash flows under a pension scheme or insurance contract;

2. a set of investments available for purchase; and

3. a model of the future behaviour of investment conditions.

What set or sets of available investments would provide the best match against the given liabilities in order to minimize any likely surplus or deficiency on completion of the liability cash flows?

In Australia, the Insurance Acts 1973 introduced the formal requirement of a solvency margin. The solvency margin required by Statute is a proportion (15% in fact) of net premium written in the last completed financial year. Since then, there has been a certain amount of discussion on the means of funding that margin under expansionary conditions.

The vicissitudes of the discussion in Australia and the United Kingdom have been as follows.

At first, it appeared unquestioned that increases in solvency margin must be financed effectively by premium loadings. For example, Loader and Ryder (1976) state flatly that “The increase in solvency margin must be met from profit earnings”. The ideas of Loader and Ryder were adopted as a point of departure by Cooper and Long (1977). Basically the same theme was presented by Eriksen and Jones (1977).

This note continues an annual series on mortality rates in Great Britain; the previous note in the series appeared in J.I.A. 109, 447 and dealt with mortality in 1980. Table 1, below, shows central death-rates for Great Britain for the year 1981, together with the ratios of these rates to the corresponding average rates for the 3 years 1970–72, which have been taken as a standard. Death rates in this form for the years from 1966 to 1979 were published in J.I.A. 108, 413. The rates for 1981 have been calculated using the deaths recorded as occurring in Great Britain in 1981 and the ‘home’ population at 30 June 1981, i.e. the number of people actually in the country at the time, as estimated by the Registrars General of England and Wales and of Scotland.