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: This paper presents a stochastic model in continuous time to characterize the ultimate benefit to be derived by a group of similar workers from their career membership in pension plans. This characterization is in terms of termination rates, vesting rules, plan types and periods of employment. The employment termination pattern is represented by a renewal process and a reward function is introduced to unify different plan types. A number of basic functions are then deduced to represent termination benefits, retirement benefits and the loss due to delayed vesting. An analysis of these functions lead to a number of conclusions regarding the comparative effects of delayed vesting in different plans. From Actuarial Research Clearing House 1981, Vol. 1.

Description: This paper attempts to quantify the benefits to the purchaser of a non-qualified variable annuity as compared to an investment in a mutual fund. From Actuarial Research Clearing House 1991, VOL. 3.

Description: Editor's Comments from Actuarial Research Clearing House Paper 1979

Description: Table Of Contents for all ARCH research done in 1978.

Description: This paper was motivated in part by a desire to use, in a variety of classroom situations, some of the readily available statistics on mortality and related factors. A second aim was to illustrate certain statistical ideas, such as the relative merits of means and medians. However, the subject of racial differentials in mortality rates is of considerable intrinsic interest, which the analysis presented here only begins to address.

Description: Using data from a large insurance company, we construct a parametric model for the joint survival function based on a Hougaard copula function.

Description: This paper introduces actuaries to the concept of 'copulas,' a tool for understanding relationships among multivariate outcomes. A copula is a function that links univariate marginals to their full multivariate distribution. Recently, there has been a rapidly developing literature on the statistical properties and applications of copulas. This paper explores some of these practical applications, including estimation of joint life mortality and multidecrement models. In addition, the paper describes basic properties of copulas, their relationships to measures of dependence and several families of copulas that have appeared in the literature. This paper will also be useful to those who wish to use copulas for statistical inference. Statistical inference procedures are illustrated using insurance company data on losses and expenses. For this data, the paper shows how to fit copulas and describes their usefulness by pricing a reinsurance contract and estimating expenses for pre-specified losses.

Description: This paper addresses various modifications of the Kimeldorf-Jones Bayesian graduation method. These enhancements entail the use of time series and eigenvalue decomposition. By augmenting the existing method one can empirically smooth the Kimeldorf-Jones technique. From Actuarial Research Clearing House 1991, VOL. 1.

Description: The differences between select and ultimate insurance mortality are usually explained in terms of: 1. deterioration of a person's physical condition which occurs due to aging, and 2. anti-selection which occurs as some policyholders allow their coverage to lapse [i.e., those policyholders who find their health has become poor keep their coverage, while those who remain healthy discontinue their insurance]. This paper explores the differences in mortality between companies related to the differences in lapse rates of the companies.