1. 1. It must, of course, be understood that a considerable part of the paper consists in a recapitulation of the work of previous authors. Explicit references will, however, only exceptionally be given. The reader may be referred to the following works, where extensive references will be found to the literature on the subject: G. Bohlmann, Die Theorie des mittleren Risikos, VI Intern. Kongr. F. Vers.-Wiss., Wien 1909, Bd I
2. 2. A. Berger, Lebensversicherungstechnik, Bd 2, Berlin 1925. Cf also the forthcoming Transactions of the ninth Intern. Congress of Actuaries, Stockholm 1930, Subject D.
3. Verhandlungen d. VI. Intern. Kongr. f. Vers.-Wiss., Wien 1909, Bd I, p. 962. Cf also Berger’s comments on Altenburger’s paper, l. c., p. 3.
4. F. Lundberg, Über die Wahrscheinlichkeitsfunktion einer Risikenmasse, Skandinavisk Aktuarietidskrift 1930. In this paper, references are given to the earlier papers by Lundberg bearing on the subject. Cf also a Review by the present writer in Skandinavisk Aktuarietidskrift 1926, and the work by I. Laurin: An Introduction into Lundberg’s Theory of Risk, Skandinavisk Aktuarietidskrift 1930. By the kindness of Dr. Lundberg and Dr. Laurin, I have been allowed to read their recent works here quoted in manuscript.
5. Cf Lévy, Calcul des probabilityés, Paris 1925, p. 166.