Description: This paper investigates the use of models of dependent mortality for determining annuity values. We discuss a broad class of parametric models using a bivariate survivorship function called a copula. Using data from a large insurance company to illustrate our methods, we calculate maximum likelihood estimates to calibrate the rnodel.

Description: The projection methods used by the Social Security Administration's Office of the Chief Actuary are important. The resulting projections are cited regularly by policy-makers, academics and others interested in the long-term financial solvency of the OASDI system. However, a complete description of this projection methodology that is vital for serious policy discussions is not available to the general public. This summary was constructed in connection with the Social Security Advisory Board's 1999 Technical Panel on Methods and Assumptions. A goal of the Methods and Modeling working group of the Technical Panel was to 'work to ensure that the projection methods used by the Office of the Chief Actuary become more public.' From Actuarial Research Clearing House 2000, Vol. 1.

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 introduces density estimation for functions of observations. The nonparametric density estimates are introduced and certain computational issues are discussed and a central limit theorem for the estimator is provided. From Actuarial Research Clearing House 1993, VOL. 1.

Description: This paper focuses on the fact that life and annuity reserves that are determined from discounted case flows mask the dynamic nature of interest rates. To study this effect in a stochastic interest environment, the authors look at a change in discounted reserves. By looking at the appropriate measure of change, the paper explores potential short-term consequences of changes in the interest environment.

Description: Actuaries and other managers of risk identify factors in modeling insurance risks because [i] they feel that these factors may cause the outcome of a risk, or [ii] that the factors can be managed, thus allowing analysts a degree of control over the system risk. The purpose of this paper is to propose a framework for quantifying the relative importance of a source of risk. The intent is that, with a quantitative measure of relative importance, risk managers will be able to sharpen their intuition about the relative importance of risks and be better custodians of financial security systems. This paper proposes a measure of relative importance that has its roots in both the statistics and economics literatures. The measure is intuitively appealing when assessing the effectiveness of basic risk management techniques including risk exchange, pooling and financial risk management. The risk measure is also shown to be useful in multivariate situations where several factors affect a risk simultaneously. The paper illustrates this usefulness by considering a pool of policies that is subject to mortality, the risk of a disaster that is common to all policies, and to a common investment environment.

Description: In a product warranty, the renewal function is the expected number of failures in a specific warranty duration. To estimate the renewal function, cross-sectional regression data is assumed to be available and the data is assumed to be semiparametric. In this article, the observations are a11owed to be residuals from a complex regression model. It is observed that estimation can be accomplished using reasonable models for the contracts and data collection. From Actuarial Research Clearing House 1992, VOL. 2.