Although actuaries have been connected with life insurance business for more than 100 years, it is only more recently that actuarial activities in the non-life branches have taken place.

The problem of calculating level premiums for the steadily increasing risk in life insurance immediately calls for mathematical ability. The need for mathematically trained specialists is not so easily seen when the problem is to calculate premium rates for fire and casualty insurances. The premium rates in this field have to a great extent been fixed by persons with none or very little knowledge in mathematics and mathematical statistics. When the market conditions allow for considerable margins this arrangement works out very well. The statistical investigation needed later on for controlling the premium rates is not very complicated, and the premium rates can if necessary be changed on short notice. A mistake made in the premium stipulation, will generally not have a lasting effect. In life insurance on the other hand, the contracts often stretch over many years and a mistake in the premium stipulation cannot easily be corrected. These circumstances explain the reason why actuaries have been more often engaged in life insurance than in the fire and casualty branches.

But a closer study shows that from a mathematical point of view, the proper fixing of premium rates is often more complicated in the fire and casualty branches than in life. In the fire and casualty field a steady changing of market conditions seems to take place. The competition grows keener and keener, and the margins are cut down. Sooner or later we reach a point where it is of vital importance to know as exactly as possible where we stand. This means that we have to study the risk premium, the security loading and the expense loading separately, and to estimate these quantities with the highest efficiency.

Thank you, Mr. Masterson, Sir George and friends. Mr. Masterson told you that Mr. Longley-Cook was going to give this report originally. Since he can't, he has turned it over to me, and I shall deliver it practically the way he has written it.

The profession of actuary originating in the need for a scientific approach to the problems of early life insurance companies, has broadened its scope over the years, and many actuaries now provide valuable contributions to the scientific study of problems in insurance, commerce and industry which are completely unrelated to life insurance. Because a large majority of actuaries are concerned, however, with problems of life insurance and pension plans, those outside these fields have felt the need for an association which is concerned with their special interests.

I feel most honoured to take part in the birth of Astin, an association for the study of insurance problems outside of the life insurance field. It was most wise that Astin has been formed as a section of the International Congress and not as an independent organization because, although our problems may be different, we will gain much in our mutual association.

A specialist should not, in his devotion to his particular line of study, lose touch with the broader and more general developments of science. Cross-fertilization of ideas can, on many occasions, prove invaluable. It was over 48 years ago that Mr. Stanley Otis and others suggested that a society of actuaries and statisticians of liability companies be formed. Some five years later, the Casualty Actuarial and Statistical Society of America—later to be known by the shorter title of Casualty Actuarial Society—was inaugurated.

The following comments on the papers written in English, French and German under Subject IVA and published in Trans. XVth. International Congress of Actuaries 1957, formed the basis of an address by Mr. C. Philipson, Sweden, on Thursday 17th October, to the members of Astin in New York.

Let sn be the maximum value of si and tn the minimum value of the angular coefficient of the straight line connecting the point (si, Ai) with point (1, 1), when i takes the values 1, 2 … n and the point (si, Ai) is taken to mean the vertex of the convex curve representing the generating function of the ith favourable risk. In a portfolio of m + n independent risks—where m are unfavourable and n favourable—Franckx finds that the superior limit of the probability that the aggregate amount of claims shall not exceed k can be written

, where Im is taken to mean the product of the generating functions for the m unfavourable risks.

Speaking of the theory of risk as first given by Filip Lundberg and developed by Cramér and the Scandinavian School he writes:

“Cela n'empêche qu'il y a encore un monde entre la théorie et la pratique et que les actuaires n'auront la partie gagnée que dans la mesure ou leurs travaux seront suffissamment simples que pour qu'ils soient et compréhensibles et directement utilisables”.