1.1. This paper is concerned with claim reserves in general insurance. General, or non-Life, insurance may be taken to include such classes of business as Motor, Liability, Property, etc., and the claim reserves with which the paper is concerned are usually described as ‘outstanding claims reserves’ or ‘reserves for claims incurred but not reported’ (I.B.N.R.). Each of these reserves falls under the heading of ‘technical reserves’, and may be referred to as ‘provisions’ by the accountancy profession. Such reserves are intended in some sense to represent the liability of the insurer arising from events which have occurred within the scope of, and during the period of currency of, the insurance. It is implicit in the definition of such reserves that there is defined a specific date, which will be referred to in this paper as the accounting date, to which the reserves relate. The need for outstanding claim reserves arises from the separation in time of the reporting of a claim to an insurer from the subsequent settlement of that claim, whether this settlement involves the payment of a positive sum by the insurer, or whether, in the event, no payment is made.

1.1. The distribution of personal sector wealth between individuals is far more unequal than the distribution of incomes of individuals. Whereas in 1974 the wealthiest 5% owned 47% of all marketable wealth of the personal sector in this country, the share of the top 5% of incomes was much lower at about 20% of total incomes from all sources (before tax). Life-cycle factors would have contributed to this difference because those nearing retirement have had more opportunity to accumulate savings than those early in their careers. But, as will be seen later, such factors provide only a partial explanation and it has become apparent that the greater inequality in the distribution of wealth is due largely to the incidence of other sources of wealth, such as inheritances. In order to throw more light on the processes which have led to the present distribution of wealth it is necessary to consider models of the build-up of savings out of earnings and, also, methods of estimating the overall size and distribution of inherited wealth. These are the main purposes of this paper.

1.1. The purpose of this paper is to survey some new results concerning the term structure of interest rates and discuss actuarial applications. The term structure of interest rates exhibits the relationship among the yields on default free debt instruments of different maturities. Although there is a considerable volume of literature dealing with the determinants of the term structure the analysis has until recently been presented for the most part in a deterministic (i.e. non-stochastic) framework. This constrasts with the treatment of capital assets where equilibrium prices have been obtained under the assumption that returns on these assets are random variables.

In 1969, A. H. Pollard and J. H. Pollard published a paper in which they treated actuarial functions as random variables, the randomness being caused only by variations in the age at death. In 1971, J. H. Pollard took this one step further by allowing the rate of interest as well as the age at death to vary and used these results to determine premium loadings for non-profit assurances.