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: In this paper the author shows that the aggregate claims distribution of a portfolio modeled by a mix of the individual and collective models can be obtained with a single recursion under some conditions. He discusses why the collective model is not necessarily an approximation of the individual model in the context of pension funds, for example. An application to a Swiss pension fund is presented. From Actuarial Research Clearing House 2003, Vol. 1.

Description: Table of Contents

Description: This paper presents a model of the progression of the Acquired Immunodeficiency Syndrome [AIDS] epidemic in the United States. From Transactions of Society of Actuaries 1989, Vol. 41.

Description: This paper reviews recursive formulas for aggregate claim distributions. Followed by a submitted discussion paper

Description: Authored by a MIB Solutions team of Tom Rhodes, Stuart Klugman, Marianne Purushotham and Stacy Gill, the report summarizes the results of a study on the application and adoption of credibility theory within the life insurance and annuity industry. In addition to the report, numerical examples related to the application of credibility to company mortality and lapse data are provided in the four Excel files. This excel spreadsheet is a numerical example relating to the application of Credibility for mortality - Limited Fluctuation Method. Please see the SOA website research section for the full report on Credibity Theory Practices.

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: In this paper two theorems concerning the optimality of the perfect-fit and perfect-smoothness graduations are proved. Two examples are presented and some difficulties with regard to computational feasibility are reviewed. A discussion of the paper follows. From Transactions of Society of Actuaries 1978, Vol. 30.

Description: A presentation of a mathematics/statistics based approach for determining credibility factors for possible use in group health insurance premium rate setting and experience refund setting. Includes supporting mathematical proofs of approach. Followed by discussions submitted by several people

Description: This is a discussion about computer models and simulation tools for life insurance companies. From Transactions of Society of Actuaries 1969, Vol. 21, No. 59AB