It is a characteristic of motor insurance data that policies can be classified by many different factors, for example age of policyholder, No Claims Discount (N.C.D.), status, amount of voluntary excess and so on. The most ‘complete’ data on the experience of a portfolio would be a classification of each policy by the various rating factors, and by the number of claims which occur on that policy in the period of exposure. It will be shown that provided certain conditions are fulfilled, useful results can be obtained with far less information.

The model selected assumes that the claim frequency of a policy (that is, the average number of claims per year) is of the form

where α, β, γ,.. are rating factors (age of policyholder, N.C.D., status, etc.) and the subscripts range over the different values of the factor (e.g. if N.C.D. has five levels, the subscript of that factor can take five levels). The μ in the formula is a parameter whose use will be explained later.

In February of this year (1970) the Inland Revenue published a memorandum giving details of changes they propose to make in the tax treatment of occupational pension schemes. Although these proposals in certam instances were dependent on the existence of the previous Government's National Superannuation Scheme, the Finance Act, 1970, in which the legislation to introduce the changes was incorporated, contains no reference to this Scheme. In the Finance Act, the conditions for automatic Inland Revenue approval are more severe than those announced in the February memorandum The Act does, however, give the Inland Revenue wide discretion to relax these stringent conditions. The Inland Revenue have indicated that they will use these powers of discretion to implement all the proposals in their February memorandum ignoring any reference to the now defunct National Superannuation Scheme.

This paper has been based on the Finance Act, 1970 and the Inland Revenue memorandum. However, these documents do not clarify all the points involved and, until the Inland Revenue issue their practice notes, as they intend to shortly, we cannot be certain how the changes will apply in all cases.

This paper has been written as an ‘Expository Article’ and, as such, is not meant to be complete. Its main object is to describe useful concepts and methods that are not covered by the standard reading for the Institute's examinations. As the title of the paper implies not all of these concepts are new. Some, in fact, are first principles which are particularly useful when performing an actuarial valuation using a computer. The title also suggests that the paper is confined to Ordinary Life business. However, much of what is said could also be applied to Industrial or even Non-life business.