1. The object of this paper is to look at the two principal types of unit-linked contracts that are now being offered with reference to the actuarial problems that they raise. In particular the calculation of premium rates, valuation, analysis of surplus and investment problems are discussed.

2. In looking at the policies that are currently offered in the unit-linked field there are two broad groupings into which most fall. These are the ‘Decreasing Term Assurance’ group and the ‘Endowment Assurance’ group. There are of course variations within each group. The main difference between the groups is that there is virtually no investment risk to the office in the Decreasing Term Assurance group but there is an investment risk in the Endowment Assurance group.

3. Because these two groups of contracts are very different and raise different actuarial problems, it is convenient to sub-divide this Paper and deal with the two groups separately.

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.

1. In the past, concepts of funding and methods of costing have frequently been discussed in papers submitted to the Institute and the Students' Society usually with particular emphasis on selfadministered funds. There is still scope for further thought on the subject of funding methods and it is hoped that this paper will provide an opportunity for further discussion with particular reference to insured schemes. Life offices are not in the same position as consulting actuaries since their basic function is to insure the benefits required rather than to give professional advice. At the same time they have a responsibility to ensure that their costing methods are basically sound and that the issues involved are not misrepresented to their prospective and current policyholders. In recent years there has been a tremendous demand for final salary arrangements using the controlled funding system of administration but little attempt has been made to codify the principles which ought to be followed in making cost estimates.

1. In this note we shall try to unravel a puzzle. It is hoped that the triviality of the subject-matter will not persuade the reader that it is unworthy of his attention; our excuse for offering it is that the underlying principle turns out to be applicable to some very practical situations. In many of these we experience no problem and seem to be on firm ground, as may a man who on a winter's day strays from the common on to the pond, until the ice breaks.

2. By repeatedly presenting theorems that appear intuitively to be unacceptable, a mathematical training is apt to engender distrust in the conclusions of common sense. When the mind has learned to convince itself of the truth of a host of astonishing facts, it hesitates to reject a fresh one however improbable it may seem. This reluctance has an unfortunate consequence, in that the more often the validity of such results is demonstrated, the less the urge is felt to scrutinize a new proof before entering yet another black mark upon the long crime sheet of intuition. Thus, paradoxically, the highly trained expert may sometimes be deceived into accepting a false statement that would be instantly denied by a layman incapable of following its supporting argument. ‘You can't fool me’, boasts the novice, ‘I'm too ignorant.’

An Organization & Methods department is essentially advisory and should not have authority to make other departments adopt its recommendations. It is also consultative and cannot investigate any field of activity without an express invitation from whoever is responsible for that activity. It can of course always ask to be invited!

Organization and Methods is basically an examination into all aspects of a clerical organization, its methods and procedures and related activities.

‘Organization and Methods’ can be applied to:

Office equipment: Studying the machines and equipment available, and advising on equipment most suitable.

Office accommodation: Considering requirements for accommodation and how the best use can be made of the space available according to the nature of the work of individuals.

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.

The subject of reinsurance has received relatively little treatment in our actuarial literature and indeed the definitive paper on the subject was written by G. T. Foster in 1945. This paper is still the recommended reading for the subject in the Final Examination. Non-proportional reinsurance finds its usual place in the fire and accident departments but for reasons which I hope will become apparent later it is much less common in life assurance. It seems to me that the reason for this is that it is a form of cover unattractive to both parties since it is essentially short term, whereas life assurance offices are concerned with long term liabilities. Nevertheless, since some actuaries may be unfamiliar with the subject chosen for this meeting, I felt that the ground might be better prepared if the subject of life assurance were treated first.

Definitions

It is usual to start with a definition and in this case it is easier to define what is meant by proportional reinsurance, since this is the type of reinsurance most commonly encountered by actuaries.

It may be stated as follows: When a claim arises, the shares of the reinsurer and ceding company are paid in proportions which were fixed in advance. This is a simple and rather obvious statement, and for this very reason it is often overlooked.

Most statistical techniques are based on a sample of fixed size n. This may be because n is chosen beforehand or because it is dictated by the circumstances. Sometimes, however, the members of the sample occur one after the other and we can then use sequential methods.

A sequential sampling scheme gives us a ‘stopping rule’ for deciding, after observing each successive member of the sample, whether we can stop sampling and reach a decision or whether we must examine another member.

As an example take the problem of deciding between hypotheses H0 and H1 that a parameter θ takes one of two values θ0 and θ1 respectively, using Wald's Sequential Probability Ratio (SPR) test.

Actuaries often need to construct a mathematical model, representing the expected future experience of a group of risks, where the data available from the group are not large enough to provide results which are sufficient for this purpose. A wider experience derived from risks, which have some features in common with the group's risks, must be combined with that of the group in such a way that the weight attached to the group's experience in the combination corresponds with its value for rating purposes.

Fire insurance, which often includes cover for flood, riot, earthquake and storm, can be divided into four classes:

1. P.D.H.—Private dwelling house.

2. Householder's Comprehensive—In addition to providing the cover as for P.D.H. this also includes other ancillary risks many of which are optional, including those for burglary and personal accident.

3. Industrial Fire—Risks range from farms and small shops to vast industrial complexes. The insurance is against damage to property and contents.

4. Consequential Loss of Profits—Over and above the material damage sustained, there is in most cases a loss of profit arising out of the interruption and a need to go on paying various standing charges, despite the fact that there may be no income. This type of cover, which is usually ‘tailor-made’ to fit the precise requirements, is intended to provide for any additional loss arising out of a fire or the occurrence of any other insured peril.