Description: This article investigates the properties of the Gompertz distribution function. Explicit formulas for continuous life insurances and annuities are given in terms of the left-truncated gamma function. Moreover, approximations for the mean, variance, skewness and kurtosis of the Gompertz distribution are also given. Finally, the article shows that using a Gompertz assumption at fractional ages produces better a approximation than the usual UDD assumption.

Description: Deferred term, pure endowment and endowment life contingency functions and their derivatives are discussed in general and some familiar formulas are derived in particular.

Description: This article analyzes a fixed premium interest sensitive life contract with the objectives of developing an approach to estimating its market value and assessing various notions of its duration. The results of these analyses have implications for market value accounting of life insurance liabilities and for life company portfolio management.

Description: This paper consists of two parts. The first concerns the financing of public systems, the second is a challenging introduction to variances encountered in life insurance and life annuity theory. The first part emerges from work by some actuarial students and faculty at the University of Michigan during the past five years. The second part was stimulated by some developments in the preparation of the second edition of Actuarial Mathematics.

Description: Study of the Pareto distribution and its affect on life contingencies. Includes examples of the mortality model, actuarial present values, and whole life premiums.