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. 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.

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.

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.