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: An updated and expanded translation of the 1863 Theory of Life Insurance Premium Reserves by Dr. August Zillmer, Stettin, Prussia. This is a seminal paper for the life insurance reserve method used extensively in Europe.

Description: This presentation provides evidence that a decline in interest rates in the negative interest rate environment produces a much more serious consequence on life insurers than that in the positive interest rate environment.

Description: This paper develops a theory for the valuation of some kinds of interest sensitive cash flows. A process is derived which takes as input, assumptions about the capital markets and policy holder behaviour, and produces as output interest and decrement assumptions which can be used for conventional actuarial discounting. The methodology is illustrated using some idealized, but tractable, models of conventional non-par whole life insurance. The method is also applied to a simple Universal Life plan. The paper concludes by considering some of the problems encountered when applying the ideas to more practical problems.

Description: This paper uses a hypothetical game to illustrate issues facing the life insurance industry, specifically distribution costs.

Description: We present a method to calculate the percentile of the distribution of the present value of the death benefit for a continuous deferred whole life Insurance.

Description: This presentation focuses on IBNR in life settlements.

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: The problem of estimation of a tabular survival model from complete samples is considered from a Bayesian approach. If a life test involves a large cohort group, then data is typically given as a grouped data set. The survival function St is usually estimated by the moment estimator. We approximate the joint prior distribution of the unknown unconditional failure probabilities by a Dirichlet distribution, and then use a linear relationship between St and the conditional survival probabilities to obtain a Bayes estimator of St.

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.