Description: By the use of resampling and extreme value statistics we will develop a method to reduce the time and costs of testing insurance company insolvency. Most ruin models require assumptions about the surplus distribution and/or assumptions about the claims count and severity distributions. The actuary may not be comfortable in making these ruin assumptions. Instead, he or she may generate such distributions by running extensive computer simulations of corporate models, I introduce a method to reduce the number of simulations necessary' to estimate the 1 and 0.1 percentiles of the surplus distribution. This approach 'cuts off' the tail at approximately the tenth percentile of the sample distribution and generates new tails for the distribution by resampling. Averages of the new order statistics approximate the I and 0.1 percentiles.

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 main aim of this paper is to apply some of the techniques of modern time series and econometric analysis to analyse investment data in order to better understand the nature of long run relationships in investment series typically used in stochastic investment models. The paper attempts to identify and address fundamental issues that need to be considered before developing a particular stochastic investment model.

Description: This 1997 presentation from the 32nd Actuarial Research Conference develops a stochastic generator for the generation of scenarios of the S&P 500 index, dividend yield, consumer price index, and U.S. Treasury yields. The authors first create a set of 'stylized facts' for these series. They estimate statistical models for these series. These in-sample statistical models are themselves not suitable for generation of scenarios for decision making, but instead are additional 'stylized facts' that assist in model development. The 'best' statistical model according to standard statistical model selection criteria can easily lead to a model that is highly unsuitable for generation of scenarios for decision making. The authors develop a stochastic generator that is suitable for decision making under uncertainty.

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: The financing for Social Security is a pay-as-you-go system, rather than the full-reserve system utilized in private insurance, and the financing conditions of the trust funds have more uncertainty than does the reserve in private insurance. Traditionally, the financing conditions have been decided by a deterministic approach using economic and demographic assumptions that rely upon negotiation among experts at various government agencies. This paper proposes an econometric approach, called the 'co-integrated multivariate time series model,' for forecasting the financing conditions of the trust funds. This stochastic approach not only establishes the interrelationships but also clarifies the co-movements among the economic assumptions. Furthermore, it helps analyze the original assumptions rather than the differences of the nonstationary assumption variables adopted by researchers in the past that are more difficult to interpret. Use of this approach permits the assessment of the probability distribution of the future balance of trust funds instead of assessing estimates from the three alternative deterministic assumptions. This distribution will provide policy-makers with a better assessment of stability of the trust funds.

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 presents a method involving re-sampling 'with replacement but without random numbers', numerical convolutions for sums and quotients, and estimation of confidence intervals for trend in average size claim. In this paper, this method is applied to major medical claims.

Description: This panel discussion session focused on the practical applications of risk theory.