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 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: 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: 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.

Description: This paper is written totally under present Indian conditions, but keeping an eye on the future, when there will be number of insurers, and this model can be applied to any condition where a number of insurers already exist. The purpose of this paper is to attempt to measure, from the point of view of a potential life insurance policyholder, the quality of the insurers and the variability between them so that it will be helpful for potential policyholders to choose their insurers according to their requirements.

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: Mr. Robert L. Brown's response to previously published solutions 14.6 and 15.3 of the New Life Contingencies. Also mentioned is the new Canadian reserve standard.

Description: The analytical laws of mortality such as Gompertz and Makeham are often used by actuaries to describe the survival distributions. Numerical approaches to evaluate features such as mean and variance of these distributions may be very difficult not to mention the characteristics of their life contingent functions.