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: 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 analyzes the U. S. Treasury monthly interest rates from 1953 to 1992, and the daily rates from 1981 to 1992 for various forms of chaotic behavior. The primary analysis was in determining the Burst Exponent by the use of Rescaled Range Analysis. This paper also discusses other possible uses of Fractional Brownian Motion in Finance Theory, Macroeconomics, and Actuarial Science. From Actuarial Research Clearing House 1994 VOL. 1.

Description: Design and future maintenance of an asset portfolio backing a new line of business is critical for proper asset and liability management for that business. Most portfolio optimization methods utilize linear or quadratic programming and require the user to specify the asset and liability attributes and cash flows into the program. The programmer must also supply an objective function to allow the program to find the optimal asset mix for the associated liabilities. Two problems with this approach are that the liability cash flows are fairly static and that one must frequently rebalance the portfolio. An alternative approach would be to develop a corporate model of both the assets and liabilities and incorporate various economic scenarios as input into the model. Asset strategies would be measured against a specific objective function that is calculated by the corporate model. Unfortunately, the majority of maximization algorithms available are very time consuming, and obtaining a reasonable portfolio mix becomes impractical. This paper overcomes this difficulty by using a very rapid optimization method from the chemical engineering profession called the Floppy Triangle. The paper includes an example of the use of this process to determine an optimal portfolio. It also discusses modifications of the algorithm that is required when the shorting of assets is not permitted.

Description: This paper examines a differential equation model, whose solutions have yield curve shapes. The paper also examines the relevance of the model with historical monthly U. S. Treasury nominal rates. From the Actuarial Research Clearing House 1992 Vol. 1 .

Description: This paper addresses various modifications of the Kimeldorf-Jones Bayesian graduation method. These enhancements entail the use of time series and eigenvalue decomposition. By augmenting the existing method one can empirically smooth the Kimeldorf-Jones technique. From Actuarial Research Clearing House 1991, VOL. 1.