Description: Multiple decrement theory traditionally is based on the assumption that competing causes of decrement are stochastically independent even though this assumption is usually not true in reality. This paper presents some fundamental results towards a dependent decrement theory. First, the author shows how to model dependence with copula functions, then he presents a theorem that characterizes the mathematical relationship between the crude and net probabilities when the decrements are dependent, and finally he applies the results by examining the effect of removing cancer from the United States population when cancer is correlated with the other causes of death. From Actuarial Research Clearing House 1994, VOL. 1.

Description: This paper presents a parsimonious 11-parameter model that explains the pattern of mortality for the female and male mortality rates of the 1975–80 Select and Ultimate Basic Tables. This parametric model is useful because it can predict the select mortality rates beyond the 15-year select period and because it can predict the select rates for issue ages greater than 70 years old. From the Transactions of Society of Actuaries 1994, Vol. 46.

Description: This paper investigates salary functions as they are used in the valuation of pension plans. Pension actuaries may find many of the ideas in this article useful. Moreover, the paper may be interesting to researchers in actuarial science. The main conclusion of this paper is that salary functions, as derived from the parametric models, yield gains and losses that can be quite small and, in some cases, less variable than non-parametric methods. From Actuarial Research Clearing House 1998, Vol. 1.

Description: Develops a statistical procedure to fit bivariate distributions of claims in presence of covariates, which allows for a more accurate study of insureds' choice and size in the frequency and severity of the two types of claims.

Description: This paper develops the formula for estimation of multivariate copula. These results can be applied to the estimation of correlation coefficients. From the Actuarial Research Clearing House 1994 Vol. 2 .

Description: In 1993, the Chicago Board of Trade introduced a futures contract on a financial index that reflects the insurance claims emerging from catastrophes in a portfolio of policies. This article presents a valuation formula for the contract, under the assumption that catastrophes emerge as a Poisson process over time and that the claims from each catastrophe emerge as a Compound Poisson process. The formula is developed by taking conditional expectations with respect to a history of information that includes knowledge about the time of the catastrophes.

Description: This paper discusses a mixed lognormal estimator of a risk distribution. Using the observed claim frequencies of a portfolio, the author presents a continuous nonparametric estimator of the risk distribution that reproduces some of the empirical moments and converges uniformly. The estimator that is investigated is a mixture of log-normal distributions whose parameters are calculated by considering the determinants of certain moment matrices. From Actuarial Research Clearing House 1993, VOL. 1.

Description: This article discusses a continuous estimator of a mixing distribution. Specifically the estimator investigated is a mixture of gamma distributions whose parameters are calculated by considering the determinants of certain moment matrices. From Actuarial Research Clearing House 1993, VOL. 2.

Description: In this paper, the unconditional probability density functions of portfolio claim amounts based on several assumed risk distributions are found. From the Actuarial Research Clearing House 1994 Vol. 2 .

Description: Consider a portfolio of insurance policies where the mean frquency of claims for each policy may vary. A reasonable assumption is that the number of claims for a policy is a Poisson random variable. In this paper the author shows how to test this hypothesis under certain conditions. He then presents some nonparametric tests for this and other hypotheses about the risk distribution function. Actuarial Research Clearing House 1992, VOL. 1.