Pension fund is created for what it will do while in full operation—not for what will emerge when it is wound up nor for what it might provide for members during their employment. Nevertheless, the dissolution provisions are important: they may reflect the philosophy on which, or the limitations within which, the fund is financed but it is of paramount importance that they should make llowance for the considerable problems that can and do arise on a dissolution acutally taking place.

A great deal of theoretical and empirical work has been carried out in recent years, particularly in the United States, on the use of mathematical models as an aid to the selection of investment portfolios containing equities. The present paper attempts to survey some of the more important advances that have been made, and to assess them in relation to the problems that managers face in the running of a portfolio.

The development of sickness insurance of the type dealt with in this paper has been a long process, commencing in a tentative fashion, probably a century ago, in Europe. In 1900, E. Hamza, at that time actuary of a Russian insurance company, contributed to the Third International Congress a paper of interesting historical significance which is clearly based on long experience in Germany. In his paper he developed an approach fundamentally different from the traditional British approach. British methods—which can be described with complete adequacy at this stage as a continuation of Friendly Society actuarial technique—have stood the test of time for at least 150 years and it is the purpose of this paper to analyse the two lines of development; to pose the question of their efficacy in the future; and to outline alternative methods depending on modern mathematical techniques.

The authors have advised on the level of motor vehicle (third party risks) insurance rates of premium in the circumstances under which that business is written in New Zealand and this paper records the approach taken. It has been prepared in the hope that, as no difficult mathematics are involved, the basic ideas may appeal both to actuaries and to persons other than actuaries who are interested in the transaction of non-life insurance. They are relevant not merely to third party motor insurance but also to non-life insurance generally in a situation where insurance is compulsory and the rates of premium are centrally controlled. In those circumstances more sophisticated techniques of deriving premium rates are less necessary.

Pollard and Pollard pointed out that, while it has been conventional to refer to Ax, as ‘the present value of an assurance of one on a life aged x’, this value is a random variable (denoted by Ãx) with mean Ax.