In England and Wales prior to 1956 annual estimates for the infant mortality rate q0 were obtained as the quotient of an observed number of deaths and an exposure calculated by reference to the related births. Since 1956, however, infant mortality rates have been measured as the ratio of the numbers of deaths and births in a given calendar year (cf. reference 4, Part I, supplement to Table 24).

Various definitions of mathematical probability are described and commented upon: (i) the classical formulation, based on the ratio of favourable to total “equally likely” aspects of a system; (ii) formulations based on relative frequency in a sequence of trials, or on the limit of relative frequency as the number of trials is increased indefinitely; (iii) von Mises' refinement of this, in which the sequences obey special postulates ensuring “randomness”; (iv) modern revisions of the classical definition, “equally likely” aspects being replaced by an aggregate, and ratio of aspects by relative measure of a sub-aggregate; (v) the approach of Keynes, in which probability is the “logic of uncertain inference,” developed by a symbolic algebra; (vi) the approach of Jeffreys, by axioms and conventions of procedure, based on the principle of indifference and the use of the rule of inverse probability. It is suggested that, whereas in formulations based on relative frequency, frequency cannot be held to afford any explanation of the facts of frequency, in the a priori formulations, on the other hand, any postulates put forward are still very far from explaining to inquiring minds the commonly observed phenomena of so-called chance. It is further suggested that in actuarial applications the nexus between axioms of probability and causes of mortality is especially obscure, with consequent need of caution in adopting and interpreting the more refined modern methods.

This paper has the strictly practical objective of devising procedures for managing Equity portfolios to the best advantage.

First, Modern Portfolio Theory, (MPT) which has been developed over the last 35 years with just this objective, is critically examined; from a study of the history of MPT and of its philosophy, principles and practices, the authors conclude that this discipline makes no contribution whatever to improving the performance.

Few who are engaged in the practice of Life Assurance will deny that the prevailing restrictions imposed on, and charges made for foreign travelling and residence are unsatisfactory to all parties concerned. A considerable and increasing portion of the public whose pursuits or inclinations, especially in early life, take them to different parts of the world, are deterred from effecting life assurances on this account. The value of policies as securities is diminished owing to the uncertainty of the extra premiums which may at any time be imposed, and the risk of the assurances being forfeited altogether by causes over which mortgagees have no control. And actuaries feel that this subject is the opprobrium of their profession; for as in general no sufficient data exist whereby the risks incurred may be measured, the extra charges are therefore arbitrary and unscientific, for the most part little better than random guesses made on no intelligible principles. For these reasons it is hoped that any suggestions on the subject, however imperfect, may not be unacceptable, and may be the means of eliciting some useful discussion.

The purpose of this paper is to provide an opportunity for discussion within our profession of ‘the use of an actuarial approach and actuarial evidence’ in the assessment of damages arising out of personal injury and fatal accident litigation. The need for such a paper was intimated in the pages of our Journal by William Phillips in his Review of Principles of the Law of Damages by Professor Harry Street. Since the publication of what Phillips described as ‘from the actuarial point of view…the most important legal textbook which has been published in the last 50 years’ the employment of actuaries in this field has been widely discussed within the legal profession. The most important recent development has been the inclusion of personal injury litigation as Item VI of the first programme of the Law Commission set up by the Law Commission Act, 1965. The words quoted in the first sentence above are taken from the list of ‘Questions for Examination’ under (b) of Item VI, ‘Assessment of Damages’. The current examination being conducted by the Law Commission makes this a particularly appropriate time for a sessional meeting on this subject. The writer has had the advantage of a sight of a preliminary Working Paper prepared by the Law Commission and will be quoting certain extracts from that paper below. It must however be stressed that the Working Paper is a preliminary one which attempts to do no more than canvass views: it in no way sets out the conclusions of the Law Commission on the matters discussed.

On the occasion of the bicentenary of the foundation of scientific life assurance, it was thought fitting that a work should be prepared in which the development of some aspect of the subject might be discussed. The authors undertook some research on the origins and disposal of surplus and the results are set out in a book entitled Surplus in British Life Assurance—Actuarial Control over its Emergence and Distribution during 200 Years. The following pages convey some of the impressions formed in the course of its preparation. Much of the later part of the paper consists, in fact, of extracts from the text of the book. The introductory sections present a short outline of the book as a whole.

The origin of savings connected with human life was not a particularly happy one in France. A certain Neapolitan named Lorenzo Tonti submitted to Mazarin, the Finance Minister of ‘Sun King’ Louis XIV, a savings plan, the profits from which would help to replenish the sadly depleted royal coffers of this grandiose monarch. The plan was called a ‘Tontine’ after its originator and provided for a lump sum to be divided amongst the survivors of those who had contributed after a period of say 10 to 15 years. The ‘sales psychology’ was good as the individual is normally of the opinion that he will outlive his contemporaries. Unfortunately the results were disastrous as Parliament refused to ratify the royal edict of 1653 and Mr Tonti was clapped in the Bastille.

British life offices transacting life assurance outside the United Kingdom have until now confined themselves almost entirely to the countries of the British Commonwealth—because among the countries with stable currencies the members of the Commonwealth have in the main been the ones with which we have had the largest numbers of other business contacts. Another influence has been the absence of a language barrier. Before the 1914–18 War some offices transacted business on the Continent of Europe but thereafter most of them pulled out; today as far as I know only one British office transacts life assurance in France, one in Germany and none in Italy.

One might be forgiven therefore for thinking that actuaries handling life office affairs need not concern themselves with life business on the Continent of Europe—particularly as, at the beginning of last year, the negotiations for Britain's entry into the European Common Market broke down.

This paper arose from a report prepared by a working party set up under the auspices of the Research Committee. The views in the paper are my own but they are, to a considerable extent, based upon work done by Messrs J. K. W. Davies and P. N. S. Clark. I am also indebted to Mr R. T. Foster of the Government Actuary's Department for clarifying points arising from the current Regulations.

2. The paper is concerned with the Returns made by Life Offices to the Department of Trade and Industry in accordance with The Insurance Companies (Accounts and Forms) Regulations 1968. The aims of this paper are:

(i) to discuss the objectives of the Returns,

(ii) to discuss whether the questions asked by the present Regulations and the answers currently being given in the Returns achieve these objectives,

(iii) to discuss possible changes in the Regulations, and

(iv) to discuss the role of the actuary in relation to the Returns and also in relation to the auditor.

Nearly twenty-two years have elapsed since the masterly essay of our President gave to the institute an opportunity for comprehensive examination of the British friendly society system. During the intervening period, phases of the subject have been occasionally before the Institute, but the period has been one of great activity amongst the friendly societies, and developments of interest to actuaries culminating, it may be suggested, in the co-operation of the State and the societies proposed by the Chancellor of the Exchequer, have emerged. In the circumstances it has seemed to me that the Institute might again survey this wide field of provident effort with interest to its members and profit to the community.

I propose accordingly to examine the more important groups of societies, paying particular regard in respect of the leading affiliated orders to the machinery by which it is sought to equip the constituent parts for the effective recognition of their duties; thence passing to some questions of special interest to ourselves. For the purpose of connected description it will be necessary to mention particular organizations, but I trust that nothing of what I have written may seem to depart from the excellent custom of neutrality which governs our debates. I venture indeed to say that so far from being unduly sensitive, all the societies which are striving for improvement (and I think this may be said of most of them) are receptive towards the stimulus of informed criticism.

The Institute of Actuaries has always been ready to welcome contributions from members able to give information regarding the mortality found to prevail among special classes of lives, and among lives resident in other parts of the world than Great Britain. The authors of the present paper having had occasion to look closely into the subject of West Indian mortality, chiefly in connection with the financial affairs of the Barbados Mutual Life Assurance Society, have therefore willingly responded to an invitation to lay before the members of the Institute some account of the statistics which they have been able to gather, and of the conclusions at which they have arrived. They desire, in the first place, to express their thanks to the directors of the Barbados Mutual Society for permitting them to publish the results of the society's mortality experience, and to Mr. Spencer C. Thomson, the manager of the Standard Life Office, for some valuable statistics relating to the experience of that office regarding West Indian mortality.