As reports on work done on subjects discussed at earlier colloquia and on new lines of investigation 6 papers have been laid down on my table (To be exact, 5 on my table and the last one on my chair at the beginning of this colloquium on Wednesday morning).

Four of them deal with problems concerning the estimation of reserves. These are the papers by Beard, Molinaro, Benedikt and Hovinen.

The other two papers, each of which has two authors, namely Kauppi and Ojantakanen and van Klinken and Groenenberg deal with mathematical questions of more general interest.

I can repeat what my colleagues have said this week:

Although the number of the papers is rather small, the importance and the quality of them seem to me to be very great.

The paper of R. E. Beard concerns the studies he has made on the data provided by the 6th Conference of European Insurance Supervisory Services. Suitable statistics of motor insurance on which to experiment have been made available relating to 28 European insurance companies. Beard has made certain preliminary studies of these statistics. His paper has been written against the background of these studies. Although only the broadest indications of numerical values are given, since the detailed statistics are confidential, nevertheless the comments made are based on the studies of the figures. Therefore these comments have a considerable practical utility.

As a basic principle on which to build calculations of technical reserves it is assumed that the claim frequency rate will be constant and that the distribution of claims by amount will be stable, both apart from random fluctuations. Although it is hardly possible to prove the validity of these assumptions, there could be no basis for calculation if these principles were not true.