1.1.— Under Subject 4 at this Congress we have discussed the practical application of modern statistical techniques in different branches of insurance. During the last decades, there has been an almost explosive development in theoretical statistics and related branches of mathematics. I think it has been very useful to survey the techniques, which have been developed, and find out if they can be used in insurance.

1.2. — There may, however, be some danger in this approach. When new means become available, we should of course have an open mind, and examine these means in order to see if they can serve our ends. We should, however, not get so excited over the power of new techniques, that we distort our ends just for the sake of being able to apply the means.

Linear programming, to take an example, is a powerful tool, which has proved extremeiy useful in many, apparently very different fields. There is, however, little point in using this technique in insurance, unless we have problems which consist of determining the maximum of a linear expression, subject to linear restraints. If there are problems in insurance which can be cast in this form, with sufficient approximation, then linear programming is obviously useful. If, however, we lose something essential by reformulating our problems in this way, linear programming may become a dangerous temptation, which we should resist.