Analytical Expressions of risks Involved in General Insurance

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†.