Description: This paper presents an introduction to collective risk theory. In collective risk theory one seeks to investigate directly the risk enterprise as a whole. Primary interest is focused not upon the gains, losses, or claims from individual policies but upon the amount of total claims or the total gain arising from all the policies in the portfolio considered. Followed by several discussion papers submitted.

Description: From the 1960 Transactions Vol. 12 No. 32, this article is a discussion of the paper ‘Introduction to Nonproportional Reinsurance,’ by Herbert L. Feay, which also appears in this volume of the Transactions. The contributors to the discussion provide their comments with respect to the author’s paper, raising some questions, but generally finding the paper an excellent introduction to a complex and not well explored field, at least from the perspective of life actuaries. The author, in his reply to the discussion, emphasizes that the paper was meant as an introduction to stimulate further work in this field.

Description: From the 1960 Transactions Vol. 12 No. 32, this paper provides a comprehensive introduction to nonproportional reinsurance and its application in life and health insurance, and employee benefit plans. The author defines the various types of reinsurance and notes that to date nonproportional reinsurance has not been widely used in the U.S. for life insurance, and explores areas for possible application. Theoretical aspects such as formulas for premium determination are also discussed.

Description: In calculations involving the distribution of total claims in a risk theory setting, several authors have found it desirable to approximate a risk-theoretic distribution by use of the incomplete gamma function. A recent paper evaluated an excess loss ratio premium by use of a gamma distribution whose first and second moments agreed with those of the risk-theoretic loss distribution. A discussion of that paper pointed out that a translated gamma distribution allowed one to make the approximate distribution agree with the risk-theoretic distribution as far as the first three moments are concerned. The method presented in this paper allows one to make as many moments of the approximate distribution as desired agree with those of the risk-theoretic loss distribution. From Transactions of Society of Actuaries 1966, Vol. 18, Pt. 1, No. 52.