P. 299, §2 line 5: ‘Duvillar’ should read ‘Duvillard’.

P. 302, line 5: –dy–sdxnm should read –dy–sdx/nm

P. 304, Note below Table 2: 7.4.1. should read 714, 1.

1.1 Following the thalidomide tragedy, a Royal Commission was set up in March 1973 to examine and report on the circumstances in which anyone suffering personal injury should be entitled to compensation and on the amount, the form and the source of such compensation. The Commission also considered the extent to which dependants should be compensated for losses which they incurred arising from the injury or death of a victim. The Commission, whose chairman was Lord Pearson, took written evidence from 766 organizations or persons and oral evidence from 113. The Report of the Commission, published in March 1978, was in three volumes comprising in all 1,084 pages. Volume 2 (259 pages) contained detailed statistical information which had been produced from various sources. It is known that in many cases information had to be assembled from inadequate data, and the Commission pointed out that many of the figures were a matter of judgment. They ascribed degrees of reliability to each table, but in some cases they were probably over-optimistic. Volume 3 (280 pages) reported on practice overseas.

1.1. This is intended as a discussion paper or a working paper. It does present new data; but that is not its main purpose. Its aim is to stimulate thinking about possible techniques for studying mortality through morbidity, rather than to produce results. The Secretary of the International Union for the Scientific Study of Population when outlining the purpose of a new committee of the I.U.S.S.P. on “factors affecting mortality and the length of life” stated that “it is a common feeling that the traditional demographic and actuarial approach to mortality produces diminishing returns. It is also a common feeling that closer links with other biomedical disciplines, with genetics or biology, are essential if we wish as demographers to improve our contribution to the study of mortality.”(1) The formation of that Committee was a major factor prompting me to set down some views which I have long held on the subject of mortality studies.

1.l. The aim of this paper is to examine a number of issues that arise in decision-making. In particular it seeks to explore the relevance to decision-making of the commonly made polarization as between the so-called objective and subjective approaches to probability. The paper is in three parts. The first concerns utility, and the second various aspects of probability. The third and final part looks at the interplay between these two concepts. Whilst a number of the comments and illustrations refer specifically to the insurance industry, the concepts discussed are broadly set in the wider context of business and commerce as a whole. It is hoped that the paper will thereby provide a basis for discussion on a topic that has acquired increasing importance in recent years.

1.1. Consider the situation where a party, in return for a capital outflow of c at a given time (which will be taken as the time-origin), is entitled to subsequent cash flow. This subsequent cash flow may contain positive and/or negative elements of inflow.

The development of a ‘law of mortality’, a mathematical expression for the graduation of the age pattern of mortality, has been of interest since the development of the first life tables by John Graunt (1662) and Edmund Halley (1693). Although Abraham De Moivre proposed a very simple law as early as 1725 the best known early contribution is probably that of Benjamin Gompertz (1825). Since World War II mathematical formulae have been used to graduate sections of the English Life Tables, as well as assured lives mortality, and pensioner and annuitant mortality. Reviews of attempts at finding the ‘law of mortality’ have been given by Elston and Benjamin and Haycocks.

1.1. In 1968 the government of the day set up a committee under Lord Crowther to carry out a wide-ranging review of consumer credit. At that time only a few aspects of this complex field were covered by legislation and there was a minimal degree of control and consumer protection. The Crowther Committee reported in March 1971 with a fairly voluminous report, making extensive recommendations for changes in the law and for greatly increased control of this increasingly important area of consumer affairs.

1.1. In the education and training of actuaries, Life Contingencies (or the Mathematical Basis of Life Assurance) has been taught traditionally as a deterministic branch of applied mathematics. There are many justifications for this practice. Three are given below:

1.1.1. Actuaries in life assurance practice deal with problems concerning population groups of large numbers of homogeneous lives. Then, regarding, for example, a life table function as only an estimate (in the strict statistical sense) of an unknown population parameter adds little to the practical value of the theory as the variances of such estimates would be negligible.

1.1. This paper is intended as a tribute to a man who died at the age of 49 just over 200 years ago having made material contributions to what is now regarded as actuarial science, as well as to many other branches of science, but whose work has largely been overlooked.

1.2. Johann Heinrich Lambert was born in Mulhouse, Alsace on 26 August 1728 and died in Berlin on 25 September 1777. He was largely self-taught, having had to leave school at the age of 12 to help his father in his tailor's shop. At the age of 20 he became tutor to the children of a noble Swiss family; this ended 10 years later when he had taken the children on an educational tour of Europe during which he was able to meet eminent scientists of the time and go to lectures at universities and learned societies. Eventually, in 1765, he obtained a post at the Royal Academy of Sciences in Berlin where he stayed until his death.

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.

A mathematical model of the dynamic behaviour of an insurance system with delayed profit/loss sharing feedback is developed. The model is then subjected to a disturbance input consisting of an isolated group of unpredicted claims and the dynamic responses of cash flow and accumulated cash flow determined. Increasing delays are seen to lead first to undesirable oscillatory responses and eventually to instability. where the responses become unbounded. Such behaviour is noted to be independent of the type of business and to be a property of the feedback mechanism and not related to the type of disturbance input.