bluuebunny/crossref_metadata_2025 huggingface dataset:
On the mathematical theory of risk
Authors: Lukacs Eugene
Published: August 2016

Although the first essay on the theory of risk (41) was published in 1786, this theory has been for the most part developed during this century. Moreover, the original presentation was rather difficult and the formulae inconvenient for the practical computer. Only recently has the classical theory of risk attained a satisfactory and seemingly final form. Few text-books, none of them in the English language, discuss these developments; it may therefore be useful to give an exposition of these results. As a rule no proofs will be given, instead reference will be made to the relevant literature.

This survey will be restricted to the classical theory of risk, which deals essentially with the individual insurance. It is possible to approach the problem of risk from an entirely different angle, considering not the individual insurance but all the policies in force. This leads to the collective theory of risk (27, 29, 15, 40), which is based upon the theory of homogeneous random processes. Only the classical theory will be considered here, the inclusion of the collective theory of risk would considerably extend the scope of this paper, and in any case many of the relevant papers are in English.
The use of normal significance limits when the parent population is of Laplace form
Authors: Edwards L.
Published: August 2016

The present note is contributed, not because the numerical results obtained will be of use to actuaries, but in the belief that the methods adopted may be of interest to students as illustrating the application of the concepts of theoretical statistics to a problem which arose in practice.

The theory and technique of statistical Quality Control have been described by H. C. H. Carpenter inJ.S.S.Vol. v, 1946, p. 207, and it is shown there how the control lines inserted on the charts are based on the assumption of a normal distribution.
Factor analysis and its application in aptitude testing.
Authors: Edwards D.M.
Published: August 2016

It has long been the desire of administrators, particularly those concerned with personnel selection problems, to find an objective method of dividing people into types. So far, the accepted method of obtaining data to achieve this object has been to submit the individuals to some form of testing procedure. Although the objective type of test, scored quite independently of the opinion of the marker, has done much to dispense with criticisms against the examination system, the interpretation of the results is obviously of little value unless it is known precisely what the tests are measuring. It is, for instance, obvious that the score in a test, ostensibly of mathematical ability, in general depends to some extent on the ability of the candidate to read, and, in fact, all tests probably measure several aspects of attainment. For this reason it is evidently desirable that some method should be found of separating test scores into components which can be ascribed to specific attainments, and the process of doing this is calledFactor Analysis.
Annuities certain at linearly decreasing rates of interest
Authors: Beard R. E.
Published: August 2016

The problem considered by Mr E. M. Thomas on pp. 253-4 ofJ.S.S.Vol. VII can be approached analytically as follows:

Consider the ratiowhereand

. This is a function ofhand may be expanded in a Taylor series

The first term on the right-hand side is unity and it is easy to show that the second term is

wherev= (I +i)−1.
Medical examination for contingent assurances
Authors: Nagler H.
Published: August 2016

The object of medical examination in life assurance is to guard the insurer against financial loss which might occur if the life assured suffered a heavier mortality than that underlying the premium calculation. Such a loss would occur under a whole-life assurance; on the other hand, if the sum assured became payable on the death of A provided B survived him, then the higher the mortality of B the greater the profit of the insurer.

There are, however, more complex types of assurances for which it is less easy to say whether a higher mortality in a particular life will produce a profit or loss to the insurer. Examples will be given below of assurances under which an increase in mortality will produce a profit or loss according to the age of the life in question. It is therefore necessary to give a rule to settle this point, and with it the question whether medical examination is required or not.
The treatment of income tax and expenses in the analysis of surplus
Authors: Dyson E. J. W.
Published: August 2016

These notes are intended to elucidate the treatment of income tax and expenses in the analysis of surplus of a commission-paying office transacting ordinary life assurance and annuity business in the United Kingdom only. The Office is assumed to make an annual valuation for internal purposes, but not necessarily to distribute surplus yearly.

It may first be remarked that the analysis of surplus forms both a check on the accuracy of the valuation and a guide to the amounts and relative importance of the various sources of profit and loss. We are here not concerned directly with the first of these functions and only with two items of the second. It must be realized, however, that the analysis is related to the valuation bases, which may depart materially from the bases underlying the office premiums, particularly at a time when conditions are changing rapidly, or if there is a substantial proportion of very old business on the books.
The analysis of surplus disclosed by a bonus reserve valuation
Authors: Rose D. S.
Published: August 2016

1. The analysis of the surplus of a life office disclosed by a bonus reserve valuation does not differ in principle from the analysis of the results of a valuation on a net premium basis, but the treatment of bonus requires special consideration. A method of analysis appropriate to a uniform compound reversionary bonus is discussed in the following paragraphs, and a numerical example is given by way of illustration.

2. It is assumed that the valuation formula is

where (S + B) represents the sum assured and existing bonuses,

P is the office premium,

k is the proportion of premium reserved for expenses,

x is the present age nearest birthday,

n is the curtate duration to maturity,

b is the rate of bonus for which a specific reserve is made.
On finding the rate of interest on an annuity-certain by inverse interpolation with a calculating machine.
Authors: Packer L. R.
Published: August 2016

In his lecture ‘Computing methods’ (J.S.S. Vol. VIII, pp. 76-7), D. H. Sadler describes a method of inverse interpolation invented by Dr Comrie. This note shows how the method may be used to solve for i the equation = K. The solution of this equation to a sufficient degree of accuracy is a minor but troublesome problem of office practice, and the writer hopes that the method here described will be of practical value. In addition to its simplicity and directness it has the considerable merit that it makes full use of what a calculating machine can do, and, in consequence, requires from the computer very little calculation. It will be seen that, apart from the making of a short difference table, the whole of the work is done on the machine.
The examination of equity stocks
Authors: Weaver D.
Published: August 2016

Although ordinary shares have for many years now been accepted by the actuarial profession as suitable investments for a portion of the assets of insurance companies and pension funds there is very little in the journals of the Institute or of the Society that will help students to discover the methods by which the merits of individual shares are judged. There are indeed papers dealing generally with ordinary shares [e.g. H. E. Raynes: ‘The place of ordinary stocks and shares (as distinct from fixed interest-bearing securities) in the investment of life assurance funds’, J.I.A. Vol. LIX]; but apart from these the only one dealing with methods is that by the late R. B. Gough in J.S.S. Vol. v, No. 1. This has become a little out of date especially since the new Companies Act which followed the report of the Cohen Committee. I therefore propose to set out the methods which I believe are now generally accepted for the preliminary examination of the record of a company, and then to indicate lines upon which further investigations might be made.
The method for the expression of multiple-life contingencies in terms of last survivor statuses.
Authors: Damle S. C.
Published: August 2016

The student is familiar with the Z formulae for the expression of certain multiple-life contingencies in terms of symmetrical combinations of the component joint-life statuses. The present note develops an analogous method based upon last survivor statuses. In certain circumstances this latter type of expression may be the more convenient for practical use.

Consider a set of m lives. Then in the notation followed by E. F. Spurgeon, in his book, Life Contingencies, Zr
represents the sum of the probabilities of r lives surviving a given period for all combinations of r lives that can be made out of the set of m lives. The number of combinations of r lives that can be formed out of the set of m lives is .
Time series
Authors: Johnson N. L.
Published: August 2016

The object of this note is to provide an introduction to methods used in time-series analysis, together with a general appraisal of their usefulness. The treatment is purely expository and, of necessity, rather condensed. Nothing more than a broad survey of the subject is attempted; those interested in the technical details of theory and application should consult the references given at the end.

The termtime seriesis applied to any series of observed values of some character when theorderof the items in the series, as well as their actual magnitudes, is of importance. Examples of such series are common in statistical practice, and the following may be cited in illustration: economic series such as weekly, monthly or annual production figures, prices or index numbers; series of results of routine inspection and testing of successive batches of manufactured product; continuous blood-pressure records; results of psychological fatigue tests expressed as the rate of working on some standard task in successive 5 sec. intervals. In all these examples the factor which determines the order of the observations istime. The study of ordered series of observations is entitled ‘Time Series’ because in a large proportion of applications time is the ordering factor. Nevertheless, it is not necessary that the series be ordered according to time.
The decline in spinsterhood
Authors: Hocking W. S.
Published: August 2016

A Great deal of ink has been spilt during recent yearsonthe subject of the trend of the birth-rate and whether the population of this country will be maintained or will decline. Relatively little attention has, however, been paid to one of the factors that has a great deal to do with the course of births, viz. the supply of potential parents of both sexes. It is sometimes assumed that the position in this respect remains ‘normal’, whereas rather startling changes have occurred in recent years in the size of the reservoir of unmarried adults from which marriages are drawn, and it may be concluded from these that a considerable fall in the number of marriages, to be followed by a consequential fall in the number of births, is almost inevitable during the next few years.
The distribution of the sum of n rectangular variates. I
Authors: Packer L. R.
Published: August 2016

The purpose of this note is to establish, by finite difference methods, some of the properties of two probability distributions: (1) the distribution of the sum ofnindependent variates, for each of which every value in the interval (0, 1) is equally probable; and (2) the distribution of the sum ofnindependent variates, each of which must take one offequally probable values, 0, 1, 2, …,f–1. For brevity we shall refer to these distributions as (1) the continuous case and (2) the discrete case. The continuous case is important because it gives a solution to a problem that often arises in practical computing: ‘Ifnnumbers, which are all “rounded-off’ at the same [decimal] place, are added together, what is the chance that the total will be the correct (rounded-off) total, or will be 1, 2, etc., different in the last place from this correct (rounded-off) total?’ (Forster, 1947).

Laplace (1776) gave a proof of the continuous case; and later (1812) gave a proof of the discrete case, from which, by a limiting process, he derived the result for the continuous case. The result for the discrete case had, however, been published much earlier by de Moivre (1711), and proofs had been published by de Montmort (1713) and de Moivre (1730). Laplace's proofs are long and difficult to follow; but, as far as I can discover, no later alternative proofs were put forward until Rietz (1924) gave a much simpler proof of the continuous case. Irwin (1927) used characteristic functions to prove the continuous case; and Hall (1927) gave a remarkable geometrical proof of the continuous case and derived a general expression for its moments.
The Division of A Trust Fund Between Life Tenant and Reversioner and the Incidence Of Estate Duty
Authors: Hayes L. T.
Published: August 2016

Heavy taxation by Estate Duty and Income Tax has recently led to a serious consideration of the avoidance of this onerous liability by means of gifts made by a donor in his lifetime and, in the case of a settled fund, of an exchange of benefits where the Beneficiaries can come together and bring the trusts to an end.

If, in the case of a Settlement, Life Tenant and Reversioner can by mutual agreement arrange to divide the Fund between them, the Life Tenant may benefit considerably by realizing a sum in excess of the market value of his interest and using it to provide as much or more spendable money than before. He may also promote a smaller liability to Sur-Tax. The Reversioner may succeed in securing a cash sum larger than he could expect at a future date on the death of the Life Tenant reduced as it would be by Estate Duty at the aggregable rate applicable to the Life Tenant.
Life Office Accounts
Authors: Lawton J. W.
Published: August 2016

The actual system of book-keeping used by an office will depend on many factors, such as the volume of business transacted, the departments into which the office is divided and the scope of their work, and the information required to be produced. This paper deals mainly with premium income accounts, as the production of the revenue account figure for premiums is more complex than that of other revenue items, and as more departments in an office are concerned with premiums in one connexion or another than with the other revenue items. The object of the paper is, therefore, to show the relationship between the requirements of various departments, i.e. the accountants, the valuation (Actuarial) department, the departments concerned with issuing policies, with collecting renewal premiums and with settling claims and surrenders, etc., and the different aspects peculiar to each. For instance, the accountants require premiums to be classified according to funds, e.g. Life, Annuity or Capital Redemption, whereas the department concerned with the collection of premiums requires them to be classified according to the method of renewal, e.g. monthly or non-monthly, or terms of non-forfeiture. The actual books of account will not be described in great detail but only the principal objects that are required of each book, which would be ruled to suit the workings of the office; and the specimen headings given in the Appendices to the paper are merely to illustrate the system of book-keeping being described, which relates to an Ordinary Life Office.
The Wider Field
Authors: Spratling F. H.
Published: August 2016

‘Extending the scope of the profession’ is such a well-worn cliché that one could define the wider field effectively, if ungrammatically, as the place professional scope extends or can extend into.

F. A. A. Menzler raised the matter to the level of public importance at the Annual General Meeting of the Institute in 1924, exercising the Fellow's democratic right of intervention. At the invitation of the Council, he developed his ideas in a paper submitted to a Special General Meeting of members on 26 October 1925. He drew attention to the growing importance and recognition of statistics as a tool of government and of management. He claimed that the actuary was ipso facto a trained statistician, and that actuaries might reasonably expect to fill the increasing number of statistical posts then becoming available. Menzler also showed that the membership of the Institute had grown substantially in numbers during the preceding twenty years.
The Practice of Industrial Assurance
Authors: Allaway G. W. E.
Published: August 2016

The aim of this paper is to illustrate the background of Industrial Assurance. The paper therefore contains as little technical detail as possible. Industrial Assurance is fundamentally similar to Ordinary Assurance, but the organization and administration of Industrial business varies from that of Ordinary business partly as a result of special legislation applicable to Industrial Assurance and partly as a result of the frequent collection of premiums at the home of the policyholder.

The technical and legal side of the business has been dealt with in various papers given before the Institute and the Students' Society. Little has been written of a descriptive character, and it is thought that an appreciation of the nature and day-to-day conduct of the business might help the student to get the technical side more easily into perspective. A problem in Industrial Assurance cannot be tackled from the point of view of Ordinary Assurance.
Annuity and Cash Options.
Authors: Blunt R. H.
Published: August 2016

In several recent papers given to the Institute and Faculty of Actuaries attention has been focused on options in both the assets and the liabilities of a life office. The warnings that have been given about the concealed danger of options and the desirability which has been stressed of making adequate, if not severe, charges therefor are, it is hoped, sufficient justification for introducing a paper confined to the subject of annuity and cash options. The paper is limited to the development of the theory and to supplying tables to assist in the calculation of option costs in practice; questions of policy are considered to be beyond the scope of the paper.
The Actuary in Canada
Authors: Suttie T. R.
Published: August 2016

I Shall not try in this paper to give a complete picture of the actuary in Canada, nor of the Canadian life insurance business. I have neither the space nor qualifications to attempt such a task.

I shall, however, try to bring out the differences in these fields which would be most noticeable to a United Kingdom trained actuary coming to live and work in Canada. I have, I think, advantages in attempting to do this. I have not been in Canada for so long that I have forgotten the contrasts which struck me most forcibly, but on the other hand, after almost six years, I can hope to be a reasonably accurate guide and in some cases at least suggest an explanation for the differences.
Some Legal Points Affecting Investments
Authors: Swift T. F.
Published: August 2016

Members of this Society and of the parent Institute have considered, from time to time, questions affecting the investment of life insurance funds. In the early days ‘Bailey's Canons’ were propounded, and comparatively recently J. B. H. Pegler's ‘Actuarial Principles of Investment’ and H. G. Clarke's ‘Broad Analysis of the Problem’ have been discussed. Also, the more practical aspects of the subject have received due consideration: notably Stock Exchange Investments by A. S. Holness, Loans and Mortgages by W. Murray Simpson and Real Property by G. B. Lane, F.S.I., and W. A. Leach, F.S.I., in 1944, and further by A. C. Wheeler and K. A. C. Wheeler in 1953.

My purpose is to present certain legal points affecting these investments. I hope my remarks may to some extent be supplementary to these previous contributions on the subject of investments, and I shall try to avoid covering the same ground.
The Analysis of Surplus of an Annuity Fund
Authors: Prevett J. H.
Published: August 2016

1. The subject of analysis of surplus has been given much study by actuaries both for the intellectual satisfaction it affords and for the practical value of the results of such inquiry. One of the earliest papers in our literature is that of G. H. Ryan in 1892 (J.I.A. 30), the first half of which was entitled ‘On a Method for determining the Gain or Loss from Mortality in an Annuity Company’. Since that date, however, attention has been devoted almost entirely to the analysis of surplus of a life fund, in view of the problems involved in its distribution, and Ryan's restricted treatment remains the only reference for students with regard to the analysis of surplus of an annuity fund. The purpose of the following notes, therefore, is to illustrate symbolically a full analysis of such a fund comprising immediate, deferred and contingent annuities, obtaining a complete reconciliation, and at the same time to indicate briefly the practical difficulties and the consequent steps in the analysis at which curtailment would be necessary in practice. Discussion of the relative importance of sources of surplus is outside the scope of these notes.
Bias of the Census Method.
Authors: Stevens W. L.
Published: August 2016

Two conditions have been proposed (Anderson & Dow, 1948) for the census method of constructing a mortality table to be ‘strictly correct’: (1) that at the beginning and end of the investigation, ages of lives are evenly spread over the year of age x to x + 1, or (2) that numbers and distributions of ages are the same at beginning and end.

In effect, these alternative conditions are proposed to insure that the approximate formula for the total period of exposure to risk, derived from annual census,

shall be reasonably correct. It is, however, of interest to examine the method more closely, under the hypothesis that the total period of exposure to risk can be determined with negligible error, as would theoretically be possible by holding censuses with sufficient frequency.
Population Data of the Classical World
Authors: Green P. J. H.
Published: August 2016

Current interest in world population and resources has resulted in the publication of several books in which the increase in world population over the last two thousand years has been traced or at least referred to. It may therefore be of interest to summarize some of the population statistics available for Greek and Roman times and the methods which have been used to obtain estimates of totals from them.

It is known that in many of the provinces of the Roman Empire a census was taken every 14 years which compares favourably in accuracy and completeness with those of modern times. Individual census returns have survived which show that in Egypt in the first two centuries A.D. the whole population was enumerated by households and by age, sex and occupation, but the only record of totals which have been preserved is a statement in Josephus's Jewish Wars to the effect that the population of Egypt excluding Alexandria was, according to the census returns, 7,500,000.
Some aspects of Policy Reserves and Premiums under the New Mortality Tables
Authors: Thomas E. M.
Published: August 2016

In the course of the discussion at the meeting at Staple Inn last October one speaker regretted the absence of any reserve figures from the notes then under discussion. This comparison of reserves under a new table with those under a table to which we have become accustomed is something of a habit which we tend to do perhaps without asking ourselves why we do it. What does a comparison between A1924–29 and A1949–52 reserve values tell us? Does it really tell us what change to expect in our liability as a result of a change of valuation basis or are these figures merely calculated as a matter of interest, serving in practice no useful purpose?

The answer to that must depend, at least as far as reserves under the main classes are concerned, on the extent to which we use a true net premium valuation. Interesting information is to be found in the paper recently given to the Faculty by J. M. Beattie.
Economic Policy
Authors: Cottrell H. C.
Published: August 2016

This paper sets out those considerations which appear to the author to be of major importance in the formulation of economic policy and some of the history of the development of thought on these matters. It should be emphasized at once that it represents the knowledge acquired by an actuary, with no formal training in economics, in the course of attempting to appraise the policies actually adopted in recent years, and that it is addressed primarily to those setting out with the same equipment on the same path.

The only other introductory remark necessary is that, inter alia, considerations of space prevent any lengthy discussion of non-economic factors which influence economic policy. This does not imply that technological, moral or social problems may be ignored, but that, for this purpose, they are regarded as parameters in the economic equation.
The Practical Application of Statistics in the Business World—How Much Mathematics does it Require?
Authors: Ramm B. T.
Published: August 2016

In recent years there have been a number of papers read to statistical societies and much written on the place of the statistician in business. In the fields of quality control and operational research the position of the mathematical statistician is unchallenged. That of the statistician employed in the day-to-day running of a business is, however, very different. He may have had a mathematical training but is more likely to be an accountant or an economist. This has tempted the author to analyse the extent to which he, as a statistician in business, makes use of his mathematical and actuarial training and employs the mathematical techniques of the statistical textbook. Most of the energies of such a statistician are employed in the collection and tabulation of data; in the main his especial skills are based on an intimate knowledge of the sources of his information (which range from the firm's accounting system for internal statistics to the almost newspaper reporter tactics needed by the market intelligence statistician) and on a familiarity with the needs of the users of the figures (psychology can play its part too in their presentation).
Valuation of Pension Fund Assets
Authors: Gilley D. F. , Funnell D.
Published: August 2016

It has been remarked on many occasions that whilst there is a plethora of material which has been contributed to the Institute and the Students' Society on the actuarial valuation of liabilities, the subject of valuation of assets seems to have been consistently overlooked by all save one or two authors. We believe that a compelling reason for this apparent indifference to the subject may be found in the trend of interest rates within the experience of the actuaries who introduced the valuation techniques which a student may now tend to take for granted.

Consider Table 1, compiled from information given in a paper by C. M. Douglas, F.F.A., on ‘The Statistical Groundwork of Investment Policy’. During the period 1833–1912 the average annual rate neither exceeded £3. 11s. od.% nor fell below £2. 9sod.%, and in general the yield drifted slowly downwards.
The Budget and the National Economy
Authors: Weaver D.
Published: August 2016

In working his way through the Institute syllabus the student deals in Section C with subjects rather baldly described as ‘Sources of National Income and Expenditure’, ‘Introduction to Government Finance’, and at a later stage, with the money market and banking and financial institutions. What disciplines these impose on the student I have only a vague idea for I am now a ‘vintage’ actuary in the sense that this is used as being synonymous with ‘old crock’. However, I see from theYear Bookthat ‘members of the profession are recognized as especially competent to advise on financial problems’ and I take it that the purpose of this meeting is to help newly qualified actuaries towards the attainment of this special competence.

My subject tonight is the budget, and although it is given to few actuaries to advise on the making of the budget we must all know how to discuss it intelligently, for clearly our judgment of the national economy underlies our reading of nearly all other financial problems.
The Administration of a Private Pension Fund
Authors: Haigh J. R.
Published: August 2016

This paper attempts to set out some of the points of detail in the administration of a privately administered pension fund based on the practical experience of a large fund. The solutions offered to the problems arising have necessarily been reached in the context of a particular fund and do not claim to be the only, or even the best, answers for other funds; indeed the very problems may be different in other funds, particularly in smaller ones.

It seems essential, therefore, to describe the main features of the fund in question.
Consulting Practice
Authors: Bradley J. R. , Coutts A. H.
Published: August 2016

The original purpose of this paper was to help students working for Parts IIIC and IVB of the Institute examinations and the equivalent sections of the Faculty examinations. The large majority of students have never been inside a consultant's office, have little or no practical experience of the subjects involved and seem to find these parts of the examinations extremely difficult because of their lack of practical knowledge. The paper does, however, seem to have expanded beyond its original aim into a general discussion of the practice and organization of a consultant's office, but it is hoped that at least part of the original intention has been fulfilled. It is written largely from the point of view of the staff carrying out the technical work in such an office. Perhaps it should be stated at the outset that it also refers mainly to one particular firm of consultants. The first part of the paper is concerned with a broad description of the services provided by a full-time consulting actuary and the necessary office organization and the remainder describes the particular features of the various types of work undertaken.
Controlled Funding Methods for Group Pension Schemes
Authors: Lyon C. S. S.
Published: August 2016

The costing technique known variously as Controlled Funding, Stabilized Costing and Aggregate Costing, is a comparatively recent development in the field of Life Office group pension schemes. Before explaining and discussing the methods used, it may be helpful to outline the principal types of Life Office group pension scheme, and to examine the more traditional methods of costing employed. It should be made clear at the outset that the term ‘group pension scheme’ relates to schemes insured by means of group deferred annuity contracts and approved under section 388(1) or section 379(3) of the Income Tax Act, 1952—endowment assurance schemes and group life assurance schemes are not within the scope of this paper.
A Note on Some Elementary Derangement and Allied Problems
Authors: Bizley M. T. L.
Published: August 2016

The following method of solving a certain type of problem in permutations and combinations, and in probability, is so simple that it must have been used before. On the other hand, the writer has never seen it expounded in the following form, and it does not seem to be well known to students. Whilst, therefore, no originality is claimed, this note may be found of interest to readers; and they may care to compare the length of the solutions to the examples below with those to be found in the text-books employing more conventional methods.
An Address Given to the Faculty of Actuaries Students' Society on 10 October 1960
Authors: Ross A. F.
Published: August 2016

When your invitation came I thought what better subject is there to discuss than the problems facing our own institutions and in particular the problems that are likely to be left to your generation to solve or to suffer under. I therefore intend to deal in this address with one or two of the more controversial issues of the present time—issues which I feel will leave their mark on our business and our profession.

At the end of the 1914–18 War, Life Offices pondered and considered how they could regain their strength. Not only had war claims been heavy but they had suffered severe depreciation on their investments, due to the increase in the market rate of interest. The solution that the great majority found to this problem of regaining strength was to pass their bonus.
The Impact of National Insurance Act, 1959, on Private Pension Schemes
Authors: Beech T. Hugh
Published: August 2016

Can the National Pension Scheme as a whole now be expected to maintain solvency? On what lines may the Scheme be expected to develop in the future? Should contracting out not have been permitted?

The temptation to go into these and other fascinating questions will be resisted as far as possible; it is proposed instead to confine the subject matter of this paper reasonably closely within the area implied in the title. In order to establish the context in which the present situation has arisen, it is appropriate, however, to begin with a very brief survey of the more recent history of national and private pensions in Britain before the passing of the National Insurance Act 1959, which will be referred to henceforward simply as ‘the Act’; the situation before the Act comes into operation will similarly be referred to as ‘pre-Act’. When the Act comes into operation two new situations will arise; ‘Contracted-in’ and ‘Contracted-out’. There are thus three conditions to consider, and as far as possible when using expressions in connexion with contracting out such as saving, extra cost, etc., it will be stated whether these are by comparison with the contracted-in or pre-Act position, lack of clarity on this point having been a source of confusion in some of the literature on the subject.
The Extra Premium for a Premium Rebate Benefit in Recurrent Single Premium Group Life Assurance.
Authors: Madders P. M.
Published: August 2016

1. Consider the question: Given the group life assurance premium for death benefits, what extra should be charged for a premium rebate on the basis that the cost of the rebate must be covered by the extra? Assume no additional administrative costs are involved.

2. Let the rebate be a proportion s of the excess of a fraction a of the total office premiumP′ over the total claimCin a year. The rebate is thens(αP′–C). Usually the benefit is more complicated, but as explained in §8, the extra premium for the more complex benefit is related in a simple manner to the extras for the benefit described. In order to avoid scale constants the average sum assured per life is taken as unity.
The Census.
Authors: Johnston E. A.
Published: August 2016

The census taken in this country last April will still be fresh in everybody's minds, so that the present time seems very suitable for a discussion on census-taking. The subject is of particular interest, as considerable developments have taken place throughout the world in the 16 years since the war ended, and more developments are likely in the years to come. In these notes, therefore, I have tried to set the British census against the background of census-taking as it is practised in the rest of the world at the present time.
An Introduction to Boolean Algebra
Authors: Squires R. J.
Published: August 2016

At the Annual General Meeting of the Students' Society in 1961, a motion was passed that articles of a less serious nature than those normally published in the past be accepted by the Editors ofJ.S.S.It is in the spirit of this motion that this article is offered. It does not pretend to advance actuarial science in any way, and its only purpose is to introduce members of the profession to a technique which is interesting in that it is different from our normal techniques and to show that it has possibilities in the actuarial field by demonstrating its applications in other fields.

This is not the first time that the subject has been written about in an actuarial journal. Edmund C. Berkeley (1937) wrote a paper for the American Institute of Actuaries going into the subject in some detail, and it is from this paper that I have taken my examples of applications to life office practice.
An Application of Computer Techniques to Mortality Graduation.
Authors: Lloyd R. C.
Published: August 2016

1. S. Benjamin (J.S.S.17, 93) advocates a re-examination of actuarial methods with a view to taking advantage of the capabilities of electronic computers. A somewhat specialized field of actuarial work where such a re-examination is profitable is mortality graduation by means of curve fitting. This field is a specialized one because, in practical actuarial work, graduation can usually be done adequately by straightforward means—for example, a graphic graduation of withdrawal rates for a pension scheme valuation. Full-scale curve fitting is usually reserved for the graduation of assured lives mortality experiences.
The Calculation of Premium Rates for Decreasing Temporary Assurances
Authors: Thomas E. M.
Published: August 2016

In their text book,The Practice of Life Assurance, published in 1952, Coe and Ogborn devoted less than four pages to the methods of calculating premiums for varying temporary assurances, including family income policies. At that time decreasing temporary assurances were relatively uncommon except for a block of single-premium policies transacted mainly by a small number of offices which specialized in them.

Since that date, however, the transaction of this type of policy on an annual-premium basis has assumed very substantial proportions, particularly in connexion with mortgages, and the cover provided varies considerably among different offices. Some are prepared to go to considerable lengths to provide exact cover, whereas others appear reluctant to go into any great refinements. This is understandable as the calculation of premium rates is quite a formidable task whichever of the known methods is used. The not infrequent changes in building societies' interest rates add considerably to the difficulties.
Motor Insurance Statistics
Authors: Scurfield H. H.
Published: August 2016

The object of this paper is to look at some of the practical problems which have to be faced in an analysis of motor insurance statistics and to point towards some of the solutions. In order to cover the ground, it has not been possible to examine any of the issues in any great depth and only private car insurance is considered. Much of the theoretical background to the subject has already been very ably put to this Society—in particular in papers by R. E. Beard and P. D. Johnson—with the result that a certain element of repetition has been inevitable, but this paper is in no way intended to be a complete theoretical treatise. The intention has been to consider various problems, discuss some actual statistics and their implications and then to continue. It is hoped that this may lead to a better understanding of the practical issues involved and at the same time may encourage others to delve into a quite entrancing subject which offers considerable scope for useful research.
IV Simulation
Authors: Benjamin S.
Published: August 2016

Simulation is the technique of examining a problem by playing it through like a game. Usually the problem involves probabilities and these are modelled in the game by a random element introduced by throwing a die, picking numbered counters from a bag or generating random numbers on a computer. Usually the probabilities of interest are estimated by playing through the game a large number of times. It is the speed of the modern computer which has turned the technique from an interesting toy into a powerful tool.

As an example suppose we have a problem involving a payment if a life agedxdies before agex+1 and we are givenqx= ·024, say. If we have a bag with counters numbered 1, 2,… 1,000 and pick one at random then the probability that the number drawn is less than or equal to 24 is just ·024. Hence it will be convenient to invent the ‘rule’ that at that point in the game if the number drawn is less than or equal to 24 thenxdies and the payment is made, otherwise he lives and no payment is made.
Claim Frequency analysis in Motor Insurance
Authors: Grimes T.
Published: August 2016

It is a characteristic of motor insurance data that policies can be classified by many different factors, for example age of policyholder, No Claims Discount (N.C.D.), status, amount of voluntary excess and so on. The most ‘complete’ data on the experience of a portfolio would be a classification of each policy by the various rating factors, and by the number of claims which occur on that policy in the period of exposure. It will be shown that provided certain conditions are fulfilled, useful results can be obtained with far less information.

The model selected assumes that the claim frequency of a policy (that is, the average number of claims per year) is of the form

where α, β, γ,.. are rating factors (age of policyholder, N.C.D., status, etc.) and the subscripts range over the different values of the factor (e.g. if N.C.D. has five levels, the subscript of that factor can take five levels). The μ in the formula is a parameter whose use will be explained later.
The Taxation of Life Assurance Companies in the United Kingdom
Authors: Stewart H. M. , Brocksom C. J.
Published: August 2016

When we were asked to present a paper to the Students' Society we were asked to bear in mind the need of the actuarial student for a simple up-to-date paper on this subject. The impossibility of this task hit us immediately—the subject is not itself simple and the currency of the paper is dependent on the whims of Government. However, we write of the current situation as we see it and we shall try to bring out the basic facts of life office taxation whilst at the same time giving, for the benefit of those without first-hand experience, some feeling for the practical as well as the theoretical aspects of the subject.

We shall in sections 1–11 of the paper take the reader through the main points concerning the computations of tax for a proprietary life office, then in sections 12–18 give brief notes about some of the complications and finally in an Appendix give a simplified computation.
Some Experiments with the Emerging Costs of a Hypothetical Pension Fund
Authors: Loades D. H.
Published: August 2016

1.1. In text-books concerned with the study of pension funds the space devoted to the calculation of emerging costs is usually small and this is probably in keeping with the number of occasions when such estimates are necessary.

If, however, it is accepted that the purpose is to produce the best estimate of the emerging costs, the calculations become interesting and consideration of the appropriate bases provides a useful background to the selection of a suitable basis for valuing the capital liabilities of the fund.

1.2. This paper develops some ideas generated while preparing detailed estimates of the emerging costs of several immature pension schemes with high rates of turnover of staff. A computer model is described which at the moment is in the early stage of development. Having outlined the pattern of costs derived from the model, the paper considers the effects of simplifying the original assumptions and in particular compares the results of using a traditional valuation basis.
The Actuary in South Africa (1973).
Authors: Barke P. W.
Published: August 2016

1.1. It is over 17 years since the paper ‘The Actuary in South Africa’ (1) was discussed. In South Africa as elsewhere great changes have taken place and it was felt appropriate to bring the position up to date. Nevertheless those interested are recommended to refer to the 1957 paper and not least to Mr R. G. Mallett's introduction to the discussion. Since the decision was taken to write this paper, Mr Spedding's paper ‘The Actuary in Australia’ (2) has been presented and to facilitate comparison, I have followed the general outline of that paper.

1.2. The South African currency is Rands and cents (100 cents equals one Rand). Since South Africa did not follow the United Kingdom devaluation of 1967 the parity was R. 12 equals £7 sterling but South Africa devalued at the end of 1971 and then R. 2 was almost the same as £1. At the time of writing the pound is roughly equivalent to 1·5 Rand.
Paleobiology of Early Cretaceous protocardiids, Caribbean Province
Authors: Scott R. W.
Published: August 2016

The Protocardiinae is represented by 11 valid species of Protocardia and one species of Nemocardium in the Lower Cretaceous of the Gulf of Mexico. These taxa appeared in the Caribbean Province through a combination of immigration and evolution from the local stock. One species group, Protocardia texana-Protocardia salinaensis-Protocardia subspinigera, developed as geographically and environmentally distinct populations that migrated in space and time. Another group, Protocardia roanokensis-Protocardia prosogyrata-Protocardia nutans-Protocardia denisonensis, differentiated through time by dichotomous branching. These species occupied sand to mud substrates. The coarseness of their shell ornament is positively related to substrate grain size. The geographic and stratigraphic distributions of these species illustrate that diversity is positively correlated with the extent of distribution and that endemism develops during transgression.
On the Cretaceous Echinoid Physaster Pomel, 1883
Authors: Stokes Robert B.
Published: August 2016

The genus Physaster was erected by Pomel (1883, p. 47) for Holaster inflatus of Agassiz and Desor (1847, p. 28) which d'Orbigny had first (1854, p. 89, Pl. 814, figs. 4, 5) maintained in Holaster but later (1855, p. 171, Pl. 903, figs. 1–8) transferred to Echinospatangus. Physaster inflatus (Agassiz and Desor) is the type species by monotypy. Inflataster Anthula, 1899, is an objective junior synonym derived tautologically from the same type species.
Salamander tracks (Ambystomichnus?) from the Cathedral Bluffs tongue of the Wasatch Formation (Eocene), northeastern Green River Basin, Wyoming
Authors: Foster John R.
Published: August 2016

Vertebrate tracks are comparatively rare in Tertiary deposits of the western United States. Unlike the deposits of the Mesozoic in this region, in which each formation often has several dozen known tracksites, there are only a few known sites in Paleocene units of the region (Lockley and Hunt, 1995), and though the Eocene Green River Formation contains relatively numerous tracks, especially those of birds, there are only a few taxa represented. The occurrence of amphibian tracks in the Eocene Wasatch Formation is therefore of interest, not only in that it adds to the known ichnological record of the Tertiary of the western United States but also in that the tracks indicate the presence of an otherwise under-represented member of the vertebrate paleofauna of the time. Skeletal remains of amphibians are present but not common in many Tertiary formations of the western United States, and remains of large salamanders are rare. Only the large caudate Piceoerpeton is known from the Tiffanian and Clarkforkian of Montana and Wyoming (Naylor and Krause, 1981), and its only Wasatchian occurrence is at Ellesmere Island, north of the Arctic Circle. The tracks described here appear to represent a nearly Piceoerpeton-sized salamander in the lacustrine shoreline deposits of the early Eocene Wasatch Formation of southwestern Wyoming.