Description: This is Mr. Hilary L. Seal's response letter to Editor Arnold F. Shapiro in regards to the 1983.1 ARCH's document on number of deaths observed in a mortality study.

Description: Actuarial literature in the twenty-five years includes discussions of a well known inequality. Among the recent papers on various aspects of this classic result are those by Berin 1970, Olson 1975 and Sarason 1960. A standard method for achieving this inequality uses Jensen's inequality. This is the method used by Bowers, et al 1983. We will also employ this method in an attempt to learn about it.

Description: This note is labeled actuarial because it deals extensively with the force of interest, a concept which is characteristically of concern to the actuarial community. The authors’ personal point of view is that we should modify the basic definition of the compound interest.

Description: This is a letter to readers of The Actuary from Arnold Dicke and Walter Lowrie to solicit opinions on the problem which seems to crop up each time an examination is to be set.

Description: This is a proof on Lidstone's theorem. It contains formulas for calculating policy dividends.

Description: The yield rate is that effective rate of interest at which the present value of his expenditures is equal to the present value of his returns. This paper encourages students of Theory of Interest class to try to approach yield rate problems by starting with the definition of yield found in Steve Kellison's text.

Description: While we agree with the conclusions expressed by Silver and Hedges The Classical Definition of Compound Interest is Adequate by Murray Silver and Bob Hedges, ARCH 1981.2, we do not believe the theorem follows from the stated Axiom. We present an alternative proof which uses only the accumulation function and not the force of interest.

Description: This is a letter from Jan M. Hoem to Arnold F. Shapiro about Exposed-to-risk considerations based on the Balducci assumption and other assumptions in the analysis of mortality.

Description: The paper gives two criteria for fit and uses two different criteria to transform an initial graduation into one with better fit. It is shown that the two sets of criteria give the same transformation. The mathematical relationships between the two sets of criteria are then derived. It is clear from those relationships that when one set of criteria is small, the other set is small [but reasonably the same]. Some general comments on various measures of fit are made.

Description: This is a letter from F.G. Reynolds, University of Waterloo, to Mr. C. Smith, Cologne Life Reinsurance Co. As an assignment the author had the students in his Risk Theory class extend the method of Trobliger to three levels of risk. Both the data of Trobliger and the data of Thyrion, which can be found on pages 27 and 16 of Seal's Stochastic Theory of a Risk Business, were fitted.