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 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.