Description: The authors offer a method for estimating parameters for well-known three-parameter models of force of mortality. The method involves fitting a series of linear regressions, and finding the least-squares estimates of all the parameters by using the Golden Section Search method. From Actuarial Research Clearing House 1993, VOL. 1.

Description: This paper discusses the numerical stability of Panjer's recursion in computing aggregate claims distributions. From Actuarial Research Clearing House 1993, 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 presents an approach in which a defective renewal equation is solved in terms of a related compound geometric distribution. The advantage of this approach is discussed. The authors then apply this approach to a defective renewal equation which involves the time of ruin, the surplus before ruin and the total deficit at the time of ruin. They show how to compute the moments of the time of ruin as well as the joint distribution of the surplus before ruin and the deficit at the time of ruin. Two important cases in terms of claim size distributions are considered in detail. First, the authors consider exponential claim size distributions. They then consider a combination of two exponentials. The moments of the time of ruin are given in both cases.

Description: The results obtained during the last one-third of the research project and the project at whole are presented. The report only contains brief descriptions of the results which are placed in addendums and which are in reality copies of papers and a chapter of a book submitted for publication. Some theoretical and applied problems induced by the research are discussed.

Description: In this paper, we propose measures of the risk that the value of the liabilities becomes larger than the value of the assets, and this especially for insurance companies. We study probabilities of mismatching and a degree of mismatching in unsegmented and multidimensional models of the balance, in which we stress the influence of interest rates on the active and passive side of the balance.

Description: This paper shows that Balucci hypothesis imposed on a survivorship function over a closed interval is dual to the uniform distribution of deaths hypothesis imposed on the survivorship function over the same interval.

Description: The objective of this paper is to present and to apply a numerical method in the calculation of the minimal and maximal ultimate ruin probabilities in two risk models given some moment constraints on the individual claimsize distribution. An application of this optimization problem is to find the extremal lower and upper bounds of the ultimate ruin probabilities given those constraints. The paper considers the classical risk models with constant and variable premiums.

Description: This paper compares percentile estimates of a large number of cash flow testing scenarios, where only a very small number fall in the ruin tail, by parametric and non-parametric methods.

Description: Two-dimensional data can be smoothed by minimizing a combination of the sum of weighted absolute deviations from initial estimates and the sums of absolute values of differences in the two directions. This paper discusses the techniques of parametric programming which make it feasible to explore the different results obtained by varying the emphasis given to fit versus smoothness. From Actuarial Research Clearing House 1994, VOL. 1.