Description: The use of Gompertz's law to describe mortality between the ages of 30 and 90 is discussed in this paper. A further use of Gompertz's law, as a tool in comparing mortality tables, is presented for thirty-three modern tables. From Transactions of Society of Actuaries 1981, Vol. 33.

Description: The objective of this paper from the Transactions of Society of Actuaries 1964, Vol. 16, Pt. 1, No. 44 AB, is to illustrate some of the alternative approaches to making approximate probability statements about the present value of life annuities assuming a specified distribution of the random variable, time until death, and a fixed interest rate.

Description: This paper discusses the Whittaker-Henderson graduation method. From Transactions of Society of Actuaries 1984, Vol. 36.

Description: This paper derives formulas for obtaining the ruin function and the distribution of total claims of collective risk theory. From Transactions of Society of Actuaries 1968, Vol. 20, Pt. 1, No. 57.

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.

Description: This paper presents a statistical and mathematical method to calculate Stop-Loss Premiums. It also includes a discussion of the paper. From Transactions of Society of Actuaries 1976, Vol. 28.

Description: Shiu derives two formulas for calculating the probability of eventual ruin in a collective risk model. This paper implements one of the formulas by incorporating an algorithm to reduce round-off error due to convolution. It gives the results of the programs for some claim distributions.

Description: The dependent relationship between two lives is readily analyzed within the context of probability theory. This paper presents useful relationships between certain actuarial and probability functions and then explores measures of dependence. From Transactions of Society of Actuaries 1986, Vol. 38.

Description: This paper describes how Markov chain Monte Carlo and related methods recently presented in the statistical literature can be used to quickly and efficiently simulate random draws from distributions with log-concave or nearly log-concave densities. From Transactions of Society of Actuaries 1995, Vol. 47.

Description: This paper derives a formula for approximating the ruin function of collective risk theory. Use of the ruin function to determine the amount of initial capital needed for a new line of business is discussed. From Transactions of Society of Actuaries 1969, Vol. 21, Pt. 1, No. 59 AB.