Description: The objective of this paper is to present and to apply a numerical method in the calculation of the minimal and maximal ultimate ruin probabilities in two risk models given some moment constraints on the individual claimsize distribution. An application of this optimization problem is to find the extremal lower and upper bounds of the ultimate ruin probabilities given those constraints. The paper considers the classical risk models with constant and variable premiums.

Description: This paper compares percentile estimates of a large number of cash flow testing scenarios, where only a very small number fall in the ruin tail, by parametric and non-parametric methods.

Description: Table of Contents

Description: This paper provides a method for estimating long-tailed unpaid losses from paid loss development using trended generalized bondy development. From Actuarial Research Clearing House 1993, VOL. 3.

Description: The method described in this paper is to allocate surplus to each category of business and reserves in proportion to its estimated effect on an insurer's surplus variation. Risk load for each category of business is then selected so that the return on allocated surplus for each category is equal to the overall return on surplus. From Actuarial Research Clearing House 1993, VOL. 3.

Description: In Gary Venter's paper on Credibility in Foundations Of Casualty Actuarial Science, he suggeted that estimating the variance of the estimated least squares credibility Z would help provide an understanding of the accuracy of the calculation. This paper examines this suggestion. From Actuarial Research Clearing House 1994, VOL. 1.

Description: In the paper, the authors implement the empirical version of a robust Kalman filter credibility estimator with a data set, and compare its sensitivity to large claims with that of other credibility estimators in the literature.

Description: This paper examines the pricing of catastrophe risk bonds. Catastrophe risk cannot be hedged by traditional securities. Therefore the pricing of catastrophe risk bonds requires an incomplete markets setting and this creates special difficulties in the pricing methodology. The paper briefly discusses the theory of equilibrium pricing and its relationship to the standard arbitrage-free valuation framework. Equilibrium pricing theory is used to develop a pricing method based on a model of the term structure of interest rates and a probability structure for the catastrophe risk. This pricing methodology can be used to assess the default spread on catastrophe risk bonds relative to traditional defaultable securities.

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: In this paper the author shows that the aggregate claims distribution of a portfolio modeled by a mix of the individual and collective models can be obtained with a single recursion under some conditions. He discusses why the collective model is not necessarily an approximation of the individual model in the context of pension funds, for example. An application to a Swiss pension fund is presented. From Actuarial Research Clearing House 2003, Vol. 1.