Description: Shiu derives two formulas for calculating the probability of eventual ruin in a collective risk model. This paper implements one of the formulas by incorporating an algorithm to reduce round-off error due to convolution. It gives the results of the programs for some claim distributions.

Description: Six methods are presented for calculating the probability of ultimate ruin where the waiting times between claims are independent and identically distributed. Three of the six use Monte Carlo techniques. From Actuarial Research Clearing House 1993, VOL. 1

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: This paper studies a smoothing spline Poisson regression model for the analysis of mortality data. From Actuarial Research Clearing House 2006, Vol. 1.

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: 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 Product Development Section, the Financial Reporting Section, the Modeling Section and the Committee on Life Insurance Research are pleased to present new research on modeling and forecasting cause-of-death mortality. Authored by a Milliman team led by Alexandre Boumezoued, the report develops a framework for forecasting cause specific death rates. Included also is a Cause of Deaths Forecasting Tool and a user guide for the tool.

Description: The dependent relationship between two lives is readily analyzed within the context of probability theory. This paper presents useful relationships between certain actuarial and probability functions and then explores measures of dependence. From Transactions of Society of Actuaries 1986, Vol. 38.

Description: This paper describes how Markov chain Monte Carlo and related methods recently presented in the statistical literature can be used to quickly and efficiently simulate random draws from distributions with log-concave or nearly log-concave densities. From Transactions of Society of Actuaries 1995, Vol. 47.

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