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 paper investigates nonparametric estimators of the distribution function that are based on mixtures of gamma distributions when we have a random sample from a continuous distribution function. From Actuarial Research Clearing House 1993, VOL. 3.

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: 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.

Description: This paper investigates the use of models of dependent mortality for determining annuity values. We discuss a broad class of parametric models using a bivariate survivorship function called a copula. Using data from a large insurance company to illustrate our methods, we calculate maximum likelihood estimates to calibrate the rnodel.

Description: The purpose of this paper is to present a parsimonious parametric model that explains the pattern of mortality for select and ultimate mortality tables. Specifically, the author modeled the combined rates found in the 1965-70 ALB Basic Tables. From Actuarial Research Clearing House 1994, VOL. 1.

Description: This paper presents well-known results in the theory of dependent competing risks that are fundamental in extending multiple-decrement theory towards a dependent-decrement theory. From the Transactions of Society of Actuaries 1994, Vol. 46.

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: 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 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.