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: 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.

Description: Often an investor is offered an annuity for a fixed purchase price. The computation of the yield rate implied by this transaction must presently be computed by an iteration scheme, usually on a computer. With reasonable parameters, the problem of determining the yield rate can be readily solved with a desk calculator. From the Actuarial Research Clearing House 1982, Vol.1.

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: 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 is a presentation of recursive APL programs for Steffenson's and Romberg's algorithms. The programs call themselves repeatedly until terminating conditions are reached. From the Actuarial Research Clearing House ARCH 1987 Vol. 1.

Description: In computing actuarial measurements, such as the moments of present value functions for insurance and annuities, the stochastic nature of the interest rate is commonly ignored. This paper treats the interest rate as a normal random variable and presents general formulas for the mean and variance of the present value function for insurance and annuities. An example demonstrating these formulas is presented. It is found that taking the force of interest to be fixed at a mean value results in slightly underestimating the actuarial present value along with the variance for both insurance and annuities.

Description: This paper presents an additional view of estimating parameters of the force of mortality using Bayesian methods. Some examples are provided. From Actuarial Research Clearing House 1993 VOL. 1.

Description: Mortality rates for a local community are desired in conjunction with the calculation of health-adjusted life expectancy HALE, an indicator of population health.

Description: This paper studies the joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at ruin. The classical model is generalized by discounting with respect to the time of ruin. The authors show how to calculate an expected discounted penalty, which is due at ruin, and may depend on the deficit at ruin and the surplus immediately before ruin.