Description: This article shows a different form of the Black-Scholes formula for European calls and puts under risk-neutral assumptions, that permits a comfortable verbal interpretation. The derivation of this alternative form appears at the end of the article.

Description: The two-parameter Pareto distribution is a commonly used model in reliability and risk modeling. Minimum variance unbiased estimates of the parameters of Pareto distribution are not known. In this paper, we propose and investigate a method of estimation of the parameters of the Pareto distribution. This method is based on minimization of the Kolmogorov-Smirnov distance between the empirical cumulative distribution function [cdf] and the cdf of the Pareto distribution.

Description: This paper develops credibility using a longitudinal data framework. In a longitudinal data framework, one might encounter data from a cross-section of risk classes towns with a history of insurance claims available for each risk class. For the marginal claims distributions, we use generalized linear models, an extension of linear regression that also encompasses Weibull and Gamma regressions. Copulas are used to model the dependencies over time specifically, this paper is the first to propose using a t-copula in the context of generalized linear models. The t-copula is the copula associated with the multivariate t-distribution like univariate t-distributions, it seems especially suitable for empirical work. Moreover, we show that the t-copula gives rise to easily computable predictive distributions that we use to generate credibility predictors. Like Bayesian methods, our copula credibility prediction methods allow us to provide an entire distribution of predicted claims, not just a point prediction.

Description: This is a stochastic model used to find the distribution of the discounted value of all future cash-flows.

Description: Appendix to the Critical Review of Stochastic Simulation Literature and Applications for Health Actuaries. The Development of a Simulation Model of Primary Prevention Strategies for Coronary Heart Disease

Description: Summary of all issue articles, with theme of recognizing limits of classical actuarial methods.

Description: This paper presents a statistical methodology based upon information theory, for adjusting mortality tables to obtain exactly some known individual characteristics, while obtaining a table that is as close as possible to a standard one. Followed by a discussion paper submitted

Description: In this paper, we introduce a family of leptokurtic symmetric distributions represented by the difference of two gamma variates. Properties of this family are discussed. The Laplace, sums of Laplace and normal distributions all arise as special cases of this family. We propose a two-step method for fitting data to this family. We develop a statistical test for goodness-of-fit and introduce a test of normality of the data. A simulation study is provided to illustrate the theory.

Description: This article is a book review of “Two Stochastic Processes,” by John A. Beekman. The author of this article notes that the two stochastic processes referred to in the book are the Gaussian Markov and the collective risk stochastic processes, and that both the theory and applications are examined. Note: a more detailed review of this book will appear in the Transactions.

Description: This paper is from the Transactions of Society of Actuaries 1956 Volume 8, Number 20. It was presented at the 1956 Spring Meetings of the Society of Actuaries for discussion. The author presents an outline of how difficulties in the determination of a frequency distribution of the expected costs may be overcome by, in part, applying the concept of using a series of random numbers with a view of making mortality studies for each life in a group of annuitants. The paper also presents the results of some experiments which were designed to discover whether or not the concept could be conducted on an IBM 650 electronic data processing machine.