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.

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.

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.

Simulation is the technique of examining a problem by playing it through like a game. Usually the problem involves probabilities and these are modelled in the game by a random element introduced by throwing a die, picking numbered counters from a bag or generating random numbers on a computer. Usually the probabilities of interest are estimated by playing through the game a large number of times. It is the speed of the modern computer which has turned the technique from an interesting toy into a powerful tool.

As an example suppose we have a problem involving a payment if a life aged x dies before age x+1 and we are given qx = ·024, say. If we have a bag with counters numbered 1, 2,… 1,000 and pick one at random then the probability that the number drawn is less than or equal to 24 is just ·024. Hence it will be convenient to invent the ‘rule’ that at that point in the game if the number drawn is less than or equal to 24 then x dies and the payment is made, otherwise he lives and no payment is made.

1. A great deal of time and energy has been spent over the last twelve months or so on the Government's proposed 1972 State scheme. And rightly so, for the financial implications are substantial while the problems of advising employers and trustees on how or to what extent to adjust their occupational schemes, and on how to operate them thereafter, are formidable.

2. As a result, however, there is perhaps a danger of not enough attention being paid to the proposed simultaneous legislation for the preservation of pension rights. The object of this paper is to air some of the problems related to pension preservation and its implications.

Some definitions

3. The Department of Health and Social Security's latest summary of the Government's three 1969 Social Security White Papers (Cmmd. 3883, 4124 and 4195) were, I suspect, prepared primarily for the benefit of members of the two Houses of Parliament. It seems that many of them have had some difficulty in understanding the complexities of the new earnings related pension proposals. Certainly the Government's spokesman in the House of Lords found quite a few difficulties in presenting the White Paper on abatement to that body.