Description: The two-parameter Pareto distribution is a commonly used model in reliability and risk modeling. Minimum variance unbiased estimates of the parameters of Pareto distribution are not known. In this paper, we propose and investigate a method of estimation of the parameters of the Pareto distribution. This method is based on minimization of the Kolmogorov-Smirnov distance between the empirical cumulative distribution function [cdf] and the cdf of the Pareto distribution.

Description: The classical approach to life contingencies has treated actuarial functions as fixed quantities. In point of fact, these functions really represent the mean or expected values of random variables which are functions at the length of time to death of a life aged x. In this paper, we will present some examples of this approach. Talk given at the thirteenth annual Actuarial Research Conference held at Ball State University, Muncie, Indiana, September 1, 1978.

Description: The investment risk generated by a stochastic interest rate is recognized as often the greatest risk associated with a whole life or retirement policy. Recent research has investigated the mathematics of this risk when the interest rate follows a stochastic process and the time to death is considered to be random. In this paper we focus on the use of the zero coupon bond as an investment instrument to fund a whole life policy. It is unlikely that a company will entirely fund a particular single policy with a zero coupon bond.

Description: In this expository paper several comments are made with respect to the statistical independence of the curtate future lifetime and the fractional part of the future lifetime, both of a general status. In particular, the conditions for independence need to be stated carefully. The last-survivor status is cited as an example. More general assumptions than the uniform distribution of deaths assumption are then considered, together with applications to insurances, annuities, and reserves. Similar results to those under the uniform distribution of deaths assumption are obtained. Brief comments are made with respect to contingent probabilities in multiple lives and multiple decrement theory.

Description: This is a proof on Lidstone's theorem. It contains formulas for calculating policy dividends.

Description: This is a simplified approach to calculating the variance of the whole life random variable in certain, very common circumstances.

Description: This is a summary of the presentation given during the ARC Conference. Its purpose was to give a brief introduction to subexponential behavior and to show that the family of subexponential distributions provides ideal characteristics to model insurance risks. Although the literature related to this topic accumulated quickly during the last years, a textbook explaining the applications of extreme value theory with intuition as well as insight was still to be written. Embrechts et al, {I 997} satisfies this need and most of the results presented here can be found in this new classic in the actuarial literature.

Description: This paper shows how discrete multivariate analysis or multidimensional contingency table methods may be applied to data arising in actuarial work. A brief introduction to the theory is followed by two detailed examples of its application. Finally, the concluding remarks indicate how the procedure could be incorporated into a complete rate-making procedure. This work was performed for the U.S. Department of Housing and Urban Development.

Description: This paper discusses a model that is used for the loss process, ratemaking problem and risk classification.

Description: This is a sequel to author's earlier paper on Installment Premiums. This paper explores the parallel case of apportionable premiums, another situation in which a special adjustment payment at death causes an otherwise somewhat complex policy to be identical with a more simple and familiar one. As with installment premiums, this will result in terminal reserves for the complex policy being exactly equal to those for its corresponding familiar policy.