Description: This article investigates the properties of the Gompertz distribution function. Explicit formulas for continuous life insurances and annuities are given in terms of the left-truncated gamma function. Moreover, approximations for the mean, variance, skewness and kurtosis of the Gompertz distribution are also given. Finally, the article shows that using a Gompertz assumption at fractional ages produces better a approximation than the usual UDD assumption.

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 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: 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 argues that the self-financing axiom with mild assumptions on the conditional expected returns yields a market with an eventual arbitrage. This is accomplished by minimizing the conditional variance of a trade when the conditional expectation is a fixed constant. Examples with common processes shows that most models yield an eventual arbitrage. As a final application, a cost model is applied to prices of stripped coupon and principal payments on U.S. government bonds, where rates of return are estimated and lower bounds on market costs given.

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 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: 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 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 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 .