Description: The purpose of this paper is to provide a method for calculating special contingency reserves for investment losses. The method is derived by first building a stochastic investment model and then utilizing its probabilistic structure. From Transactions of Society of Actuaries 1980, Vol. 32.

Description: This paper presents a few formulaic examples displaying the advantages of geometric methods over arithmetic methods and provides some theorems proving the increased accuracy geometric methods can provide for interpolation or extrapolation

Description: This paper uses operations research to develop the answer to a question concerning the optimal size of a debit, which is a defined geographical area for an agent to sell and service business as part of a 'combination company' operation. From Transactions of Society of Actuaries 1968, Vol. 20, Pt. 1, No. 57.

Description: This is a discussion of the paper, New Possibilities in Graduation by Kingsland Camp. From Transactions of Society of Actuaries 1955, Vol. 7, No. 19.

Description: This paper shows how actuarial pricing based on the mathematical concept of present value can be formulated and solved using Markov chains and an approach borrowed from engineering mathematics called ballistic control theory.

Description: This paper considers the distribution of aggregate claims of an insurer. The general form of the distribution is considered initially, and, after a few mild restrictions are imposed, it is characterized as being a compound distribution. Followed by one submitted discussion paper.

Description: In this paper, the coefficients of the minimum-Rz moving-weighted-average formulas are derived using matrix algebra and the method of Lagrange multipliers. Reviewer's note: This mathematics can be useful in the graduation process of mortality and morbidity table construction

Description: Discussion of how to obtain tight upper and lower bounds on E[hX] for a given function h, and a random variable X with three known moments.

Description: It is well accepted that, for ages 30 and above, human mortality rates increase with age, yet no established graduation method makes direct use of this knowledge. Such a method is offered in this paper.

Description: The objectives of this paper are: 1. To show why scientific laws of mortality are preferable to the continued use of graduation techniques on mortality tables. 2. To develop a new theory leading to a new mathematical law of mortality that reduces to Gompertz's law as a first approximation. 3. To demonstrate an understanding of select mortality and produce a simple formula that is reasonably consistent with it. 4. To develop methods to test this and other similar formulas on various bodies of data to establish their validity and usefulness. 5. To discuss the meaning of the results and provide some examples of the use of the formula for purposes other than graduation. 6. To discuss extensions of the models. From Transactions of Society of Actuaries 1980, Vol. 32.