Description: Summary of the SOA's Annuity Valuation with Dependent Mortality research report which examines the standard industry practice of assuming independent lives for insurance products that cover multiple lives.

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: Presented at October 1986 Annual Meeting. This session discussion is about the use of simulation, or Monte Carlo, techniques to analyze complex insurance models such as estimating reserves, solvency considerations, and estimation of mortality and distribution of aggregate losses with the aid of a computer program

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: This paper addresses the extension of the theory of life contingencies to a stochastic interest environment and its application to solvency valuation and surplus. A discussion of the paper follows. From Transactions of Society of Actuaries 1990, Vol. 42.

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.

Description: In this paper we use expectations of different random variables to define the notions of retrospective, prospective, individual, and aggregate net premiums for plans with contingent obligations.

Description: This summary is intended to provide the pension actuary with guidance in interpreting and using the termination and retirement information in the 2003 SOA Pension Plan Termination and Retirement Study. The tables in the study were developed based on 1.7 million life years of data from 112 plans collected primarily from actuarial consulting firms for the period 1995 – 2000.

Description: This article discusses Jed Frees’ book in progress, “Regression Modeling with Actuarial and Financial Applications” which offers a synthesized introduction to regression and time series.