Two persons turn up cards alternately, each starting with a similar, but differently shuffled, pack of n cards. What is the probability that before all the cards have been dealt two identical cards are showing at the same time?

If the two players deal simultaneously the answer is unity minus the probability that none of the n pairs of cards is an identical pair. The problem is thus reduced to the calculation of the number of ways in which n letters can be put into n addressed envelopes without any letter going to the correct addressee. This is the classical example of derangements, and the solution can be found in Chap, IV of Whitworth's Choice and Chance, viz.

This paper finds a strong size effect for the total business of 106 U.K. life companies from the 1981–82 Insurance Directory and Year Book.

The industry is regulated by the 1982 Insurance Companies Act which consolidated earlier legislation. This does not control output or prices of firms but many other items including investment. The industry is not highly concentrated with the five largest firms in 1980 with 30% of premiums. In 1980, total ordinary branch premiums amounted to £5.8 billion.

Section 2 surveys briefly some relevant research, while §3 discusses the data and size and other economic factors for life assurance firms. Section 4 discusses the empirical results while §5 has a brief conclusion.

This paper sets out the working party’s view that for a defined benefit pension scheme’s commutation rate the appropriate starting point should be to set it in line with the scheme’s cash equivalent transfer value basis. We recognise that there may be several reasons why an actuary in their advice may deviate from that starting point and we explore these in detail, giving our views on when deviation is and is not justified, noting that many common reasons used such as selection risk are often used without (in our view) adequate justification. We also cover frequency of review – our view is that commutation rates should be reviewed at least every 3 years and actuaries should consider performing a high-level review of commutation rates annually. We suggest that actuaries should consider proposing market-related commutation rates especially in periods of volatile market conditions. In terms of timing, there are good arguments to review commutation terms either following or during a valuation. Finally, we set out some considerations on how actuaries should present their advice, such as clearly setting out all the information required to take key decisions, following up with any actuarial certification in writing (if necessary) and illustrating the impact on members for changing commutation rates.

There has been no more valuable improvement in the science of Assurance calculations than that effected by the invention of the Commutation or D and N System of calculation;—a method which, as is now universally known through the writings of Baily, Professor De Morgan and Mr. Gray, we owe, in this country, to the genius of Mr. George Barrett, of Petworth, Sussex. It appeared at first in an incomplete and rather inconvenient form, but various important modifications and extensions of the principle of the method were some time afterwards made; and it was practically applied to the calculation of Life Contingencies by the late eminent actuary Mr. Griffith Davies, with whose name it is now generally associated.

Before proceeding to describe the mortality experiences made use of in this investigation, I will first of all discuss the various materials that have been used in investigations into the mortality among assured lives, the methods of arranging those materials in order to deduce the rate of mortality, and the method of graduation best adapted for the adjustment of the rate of mortality among recently-selected lives, pointing out the advantages and disadvantages of each, and stating which I have adopted. This will necessarily partake more or less of the nature of an historical sketch; but I think it will conduce to clearness, and will, I trust, prove interesting as well as instructive. I have also thought it desirable to state somewhat fully the information on which I have based my conclusions, in order that my readers may be in a position to exercise an independent judgment.

The mortality, according to age, of the general population of England in all localities, was first satisfactorily determined for the period of seven years, ending with the year 1844. The observations and results were published by the Registrar-General in the year 1849; and in the following year I was allowed the opportunity of exhibiting in The Lancet (vol. i. 1850, pp. 297–330) the principal results in new combinations, with my conclusions therefrom. The knowledge thus obtained of the mortality of the general population (with distinction of town from country districts) is valuable for testing the correctness of independent observations made on the mortality of classes of the labouring population, such as are contained in “Friendly Societies,” whose mortality and sickness it is now proposed to discuss.

The Friendly Societies, which are sometimes called Benefit Clubs, have for many hundred years been highly popular in England; not merely because they supplied one of the principal wants of the working classes—namely, relief in sickness or accidents which disable them from obtaining their usual wages—but because, by mutual association, they afforded some scope for the talents and sagacity of some of the members to be recognised and appreciated by others. But by the very nature of their composition they were deficient in the element of stability ; and notwithstanding the best intentions of the members, the Societies have been constantly broken up and reformed.

Actuaries have become increasingly involved in general insurance, and in particular, in the London Market. This paper examines the management of the pricing process in the context of the London Market, and deals with concepts such as profit testing, risk and reward, and setting underwriting targets. The key area covered is the communication of a strategy in a meaningful way that can be controlled at the operating level.