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 presentation of the simplex algorithm in 'A Study Manual For Operations Research' [edited by Eugene A. Narragon] is difficult to follow. The purpose of this note is to show that a better understanding can be obtained by means of a geometric interpretation and the exchange method.

Description: This is a study note that supplements material contained in the book, 'Actuarial Mathematics,' 2nd edition, by N. L. Bowers, Jr., H.U. Gerber, J.C. Hickman, D.A. Jones and C.J. Nesbitt. The topics covered include integer functions, uniform distribution of deaths throughout each year of age, and annuity coefficients.

Description: In problem 24, Chapter 5, of Kellison's 'Fundamentals of Numerical Analysis' it is indicated how a divided difference can be expressed as a ratio of two determinants. This study note shows that this method works well also in the case where some of the arguments of collocation coincide. The rule is: If an argument occurs k times, the derivatives of the corresponding row up to order k-1 should be used in numerator and denominator.

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 note points out that the non-linear parameter estimation technique presented in the Part 5 Study Note is in fact the Gauss - Newton method for the non-linear least-square problem.