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 the abstract for the research paper on a hierarchial model for micro-level stochastic loss.

Description: This is the abstract for the paper on a household's life insurance demand - a multivariate two parts model.

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.

Description: Full version of Pension Section News, March 2000, Issue No. 42.

Description: The 1999 Technical Panel on Assumptions and Methods by Edward W. Frees from Pension Section News, March 2000, Issue No. 42.

Description: This presentation develops a micro–level stochastic model for the run–off of automobile insurance claims. The analysis uses policy exposure, claims and payments experience data from vehicle insurance portfolios obtained from a major general insurance company in Singapore. The data are from the General Insurance Association 'GIA' of Singapore, an organization comprising most of the general insurers in Singapore. Modelling the run–off of individual Reported But Not Settled [RBNS] claims is the very aim of the work. The presenters focus on the following components of the development process: the time to an event, the conditional event type, the conditional payment type if any, and the conditional severity if any. They distinguish three types of events: settlement without any payments made during development, settlement with a payment and a payment without settlement. Given that a payment is to be made, the conditional payment type model describes the probability that it will be one of three claim types, or any possible combination of them. The conditional severity component describes the claim amount structure according to the combination of types paid. The presenters provide appropriate statistical models for each component and calibrate them to the available data. These building blocks are consequently used to predict the future development of open RBNS claims.

Description: This is the abstract for the presentation on long-tail longitudinal modeling of insurance company expenses.

Description: The insurance industry is known to have high operating expenses in the financial services sector. Insurers, investors and regulators are interested in models to understand the behavior of expenses. However, the current practice ignores skewness, occasional negative values as well as their temporal dependence. Addressing these three features, this presentation develops a longitudinal model of insurance company expenses that can be used for prediction, to identify unusual behavior, and to measure firm efficiency. Specifically, it uses a three parameter asymmetric Laplace density for the marginal distribution of insurers’ expenses in each year. Copula functions are employed to accommodate their temporal dependence. As a function of explanatory variables, the location parameter allows the presenters to analyze an insurer’s expenses in light of the firm’s characteristics. Their model can be interpreted as a longitudinal quantile regression.