1.1. As every actuarial student is taught:

“Pay-as-you-go is acceptable for a State pension scheme because the State is, for practical purposes, assured of a continuing existence”.

However:

“The position is quite different in the case of an occupational scheme, since an employer's business may cease to exist”.

In the following pages we give a description of the method pursued in an investigation into the Mortality Rates of the combined populations of New South Wales and Victoria, also tabular statements of the results at which we arrived. We offer no apology for trespassing on the courtesy of the Institute and asking their attention to a paper on such a well-worn subject as mortality rates, inasmuch as the rates of mortality being experienced by persons living in different parts of the world, are in themselves of more than passing interest. Moreover, where the population under consideration has been largely transplanted from a home on one side of the globe to a new land on the other, amidst new surroundings, experiencing a new climate, and cultivating almost virgin soil, its progress in the social scale will probably attract more than usual attention. The Australian Colonies afford an excellent example of such a new nation, and their rapid development makes their experience in mortality a subject of more than usual moment, both to themselves and to the mother country. Not only is there the desire to compare their present mortality rates with those prevailing in the mother land but there is the additional incentive to enquiry as to whether their own present experience is varying from that of their earlier days. To those engaged in the conduct of Industrial Business, rates of mortality, derived from the statistics of the general population, are an absolute necessity; and as industrial assurance is now making rapid strides in the Australian Colonies, a paper dealing with Australian mortality should be welcomed by those most closely associated with that class of business.

As the published facts concerning the rate of mortality in tropical Africa are very scanty, and Insurance Offices are therefore often compelled to fix the extra premiums for African risks in an almost purely arbitrary manner, I venture to lay the following investigation before the members of the Institute as a contribution to our knowledge of the subject. So far as I am aware, the only publications dealing with the subject are a note by my father, Dr. T. B. Sprague, on the Rate of Mortality on the Congo (J.I.A. xxv, 437); a note read by myself before the Actuarial Society of Edinburgh on the Rate of Mortality in Sierra Leone (Transactions, iii, 365); a paper by Mr. J. R. Hart on the Mortality on the West Coast of Africa, which appeared in the Insurance Record of 2 October 1896; and a paper by Dr. T. Glover Lyon on the Mortality amongst Europeans in certain Unhealthy Districts (J.I.A., xxix, 541).

The climate of any place is the result of the various phenomena regulating the natural order of the universe, as these are modified by circumstances affecting the particular locality. Climate has been concisely defined by Humboldt to signify all those states and changes of the atmosphere which sensibly affect our organs,—temperature, humidity, weight, agitation, electric tension, purity, and transparency. If we would correctly consider the climate of any place, it is accordingly necessary to give some consideration to every one of these phenomena. Temperature alone, if that be held to signify the mean annual temperature, gives a very imperfect idea of climate. It no doubt forms a most important element, but it must be considered with reference to its range, and that not only the minimum and maximum temperatures of the year, or the average daily temperature of the various months of the year, but it is also essentially necessary to know the daily range of the thermometer throughout the year, and during a series of years. The suddenness of the variations of the temperature is a most important element in judging of climate, and it is also important to understand the causes of the daily extremes of heat and cold, and the accompanying force and direction of wind during these extremes. Very intense heat and very severe cold may be borne without uneasiness, or even without much discomfort, provided these are unaccompanied by wind.

The first life table was a brilliant ‘guesstimate’ by John Graunt (1662) based on mortality data analysed by cause of death but not by age or sex. It was over thirty years before Halley (1693) constructed a table to show “the odds that there is, that a Person of that [any] Age does not die in a Year”. In the meantime several writers tried to use Graunt's figures to make deductions about probabilities of death. This note is a description of these efforts.

The paper considers systems of payments which are not fully funded, i.e partially funded or fully unfunded. Generally, the objective is to be able to establish a premium formula which is consistent with long term planning as to e.g. a target rate of funding, limited variation in premiums from year to year, etc. The premium formulas considered are those which relate premiums to prior years' premiums, claims experience and accumulated funds. These questions are reviewed in Section 1 which suggests the use of control theory. Section 2 formulates and provides a formal solution to the problem.

Section 3 provides a couple of results which relate premiums to targeting of accumulated funds.

Subsequent sections consider the construction of premium formulas. It is emphasized that the intention is not to supply a definitive set of instructions as to how the premium formula might be constructed, but rather to illustrate some of the principles relevant to it.

In particular, two numerical examples are provided in § 6.2. Premium formulas are constructed which appear to respond reasonably satisfactorily to simulated claims experience.

It is found that accurate prediction of future claims escalation is crucial to the operation of formulas of the linear control theory type (§ 6.2.1). Brief comment on possible further research aimed at dealing with this aspect of the question is given in Section 7.

In submitting to the Institute the results of our investigation into the subject of masculinity, we are aware that this theme is somewhat outside the ordinary discussions of the Institute, and we only propose to deal with certain aspects of the question. It may therefore be well to begin by defining the term masculinity, which is simply a convenient expression for stating in one word the proportion of the sexes at birth. The choice of this word has been determined by the fact that male births generally predominate in number over female births. According to the extent of this predominance, masculinity may be described as high or low. The usual practice is to state the number of male births to 1,000 females. When the male births are fewer than the female births the masculinity is said to be negative, the representative figure being then below 1,000.

The main object of my paper on the Error introduced into Mortality Tables by Summation Formulas of Graduation, published at page 54 of the present volume of the Journal, has already been to a large extent fulfilled; and the admirable papers which it has called forth from Messrs. Lidstone and Spencer are a liberal reward for my labours. That object was, to show that the theoretical error in question is so small as to be quite insignificant; and thereby to bring summation formulas up again for discussion, with a view to ascertain which of them are the best as means of graduation pure and simple, and how they can be used most effectively.

In the concluding sentences of the paper I spoke of a graduation by summation, to be followed, in order to gain smoothness, by one by the graphic method; and in the reply to the discussion I casually threw out the idea of correcting the theoretical error by means of the fourth central difference; but these suggestions were only concessions to the misgivings of weaker brethren, and were not put forward seriously as being in my own opinion either necessary or desirable. I am convinced that we have now summation formulas which give as smooth graduations as need be desired, and the results of which conform with close accuracy to the original facts; and, emphasizing what has already been said, my own view is that the theoretical error they introduce is so minute as to be unworthy of consideration for a moment.

Actuarial practice has been changing rapidly over recent decades, and this speed of change is likely to continue. The actuary of the future will face challenges from many quarters, including the need to communicate with multi-disciplinary teams of competing professionals, and to live in an increasingly multi-national and cross-border environment. The discussion paper reviews such trends and challenges, both national and international, and seeks to stimulate a discussion of key issues, including supply and demand, expanding the scope of actuarial work, the role of the consultant, training implications and the development of a more international profession.

The publication of the Sickness and Mortality Experience of Registered Friendly Societies, the work of our late distinguished member, Mr. W. Sutton, has directed the serious attention of the Manchester Unity of Oddfellows to the question of the continued reliability of the Tables on which the Society has been accustomed to base its financial estimates, and as the result of the interest thus awakened, the Actuaries of the Order have been instructed to make a complete investigation of its experience during the five years 1893–97. From the immensity of the data to be handled in this investigation (these being contributed by about 3,500 branches and comprising, inter alia, some three million years of life and 40,000 deaths) it has been necessary, at the outset, to closely consider the methods of tabulation and classification to be adopted, and preliminary experiments on a somewhat elaborate scale have accordingly been required. The results of these experiments appear to possess a definite value in relation to the subject of friendly society experience, and I am emboldened on this account to offer the following notes respecting them for the consideration of this meeting.

This Presidential Address considers what needs to be done to enable the United Kingdom actuarial profession to flourish in a more competitive environment. It addresses the need for continued modernisation of the actuarial skill-set, and the need to pay greater attention to the way we communicate our findings. The Address briefly reviews some of the recent changes to the regulation of life assurance in the U.K. before considering the role and structure of the professional body in the post-Morris era. It ends with some thoughts on developments in education and CPD.

This Presidential Address is a call to arms for the profession. It outlines many areas in which we could be major contributors if we are prepared to undertake the necessary research, discussion and seminar work. In covering the historical landscape of actuarial work, emphasis is placed on looking to the future in life assurance, pensions and investment. Education, public interest and marketing are all covered in the context of what we need to do and the need to get it done sooner rather than later. Our future, and that of the Faculty, is again opened up for debate to ensure that we remain objectively focussed.

This paper takes a broad look at tax in general and some of the tax issues peculiar to life offices. A theoretical model for the taxation of life offices and their policyholders is then developed. Moving from theory to practice, the paper then offers its own solution to the ‘puzzle’. Appended by way of background reading are brief histories and summaries of life office tax in the UK, New Zealand, USA and Canada.

This paper focuses on Enterprise Risk Management (ERM) and strategic business management for health insurance companies in our world of ‘unknown unknowns’ and the emergence of unexpected risks over time. It illustrates how Chief Risk Officers (CROs) can focus on ‘risk and opportunity management’ through an ERM framework, and thereby balance risks against opportunities, whilst being resilient against ‘unknown unknowns’ and their emergence over time as ‘known unknowns’ and ‘known knowns’. The paper has been designed to meet the broad requirements of health insurers that would like to implement an ERM framework for the effective risk management of their health insurance lines of business. Risk management for health insurers in the context of Solvency II and broader European Commission regulatory requirements is also discussed. The authors discuss how insurers can develop and apply risk management to build resilience in the face of the storms and shocks that may lie ahead.

The recent financial crisis has raised challenges to market-consistent valuation, both in its implementation and application. These include both commercial and technical challenges. The whole concept of mark-to-market accounting has been questioned in some quarters.

There have been commercial challenges in deciding how to assess business strategies given recent volatile market-consistent results, including the implications for ALM and new business pricing. Industry-wide, macroeconomic concerns have been raised regarding procyclicality.

This paper recognises these commercial challenges and highlights how a combination of different forms of management information covering both market-consistent and other measures can help in making decisions. This paper sets out some possible approaches to mitigate procyclicality.

There have been technical challenges in:

• – assessing how to value instruments in markets which are or have become illiquid

• – selecting an appropriate ‘risk-free’ or reference rate

• – deciding whether and how to make additional allowance for the liquidity premium or own credit risk

• – the calibration of stochastic models used to value embedded financial options and guarantees

• – assessing an appropriate allowance for non-hedgeable risk.

This paper discusses these technical challenges. The paper proposes a way forward in some areas, taking into account the recent dislocation of the financial markets and drawing on recent Solvency II, IASB, FASB and MCEV developments.