“The Current State of Genetic Testing: An Insurance Industry Perspective on the Rush to Legislate”, Charles S. Jones,Jr., January, 1999

Abstract

We propose a new type of retirement plan, aimed at achieving a compromise between stability in cost for the plan sponsor and guaranteed accumulation for the participants. The behavior of the plan is compared with that of a money purchase plan for both deterministic and stochastic investment scenarios. The proposed plan is shown to provide more stable and predictable benefits than a money purchase plan. Obstacles to the establishment of such a plan, from the perspective of U.S. pensions legislation, are considered.     

“Modeling the Impact of Genetics on Insurance”, Angus S. Macdonald,January, 1999

Abstract

Current formulas in credibility theory often estimate expected claims as a function of the sample mean of the experience claims of a policyholder. An actuary may wish to estimate future claims as a function of some statistic other than the sample arithmetic mean of claims, such as the sample geometric mean. This can be suggested to the actuary through the exercise of regressing claims on the geometric mean of prior claims. It can also be suggested through a particular probabilistic model of claims, such as a model that assumes a lognormal conditional distribution. In the first case, the actuary may lean towards using a linear function of the geometric mean, depending on the results of the data analysis. On the other hand, through a probabilistic model, the actuary may want to use the most accurate estimator of future claims, as measured by squared-error loss. However, this estimator might not be linear.

In this paper, I provide a method for balancing the conflicting goals of linearity and accuracy. The credibility estimator proposed minimizes the expectation of a linear combination of a squared-error term and a second-derivative term. The squared-error term measures the accuracy of the estimator, while the second-derivative term constrains the estimator to be close to linear. I consider only those families of distributions with a one-dimensional sufficient statistic and estimators that are functions of that sufficient statistic or of the sample mean. Claim estimators are evaluated by comparing their conditional mean squared errors. In general, functions of the sufficient statistics prove to be better credibility estimators than functions of the sample mean.     

“Actuarial Issues in the Novels of Jane Austen”, Daniel D. Skwire,January 1997

Social security systems for old age have been explicitly studied in a public choice framework for more than 30 years. They illustrate extremely well the problems of allocating economic resources through a system of voting. Despite actuarial interest in state pension systems and despite the actuarial calculations that are needed to understand long-term public choice trends, there is almost no reference to public choice economics in the actuarial pensions literature. It can be argued that pension systems currently provide some of the most significant threats to the long-term budget positions of developed countries, a point that was made in the Nobel Laureate lecture of Professor James Buchanan over 24 years ago. In this article, we look at the costs and benefits that will be faced by different groups of voters as a result of state pension reform in the United Kingdom. The results of this analysis suggest that a majority of the electorate will have a strong financial interest in opposing state pension reform except where reform involves raising retirement ages. These results are in accordance not just with theoretical work but with other empirical work and practical observations.     

“Statistical Independence and Fractional Age Assumptions”, Gordon E. Willmot,January 1997

Abstract

The People’s Republic of China has experienced substantial growth in insurance demand over the last decade. However, development of the related laws and regulations has not kept pace with the development of the insurance industry there. This paper reports on a pioneering study comparing different statutory reserve, solvency, and early warning systems in a sample of countries and regions in three of the world’s important economic regions–Asia, North America, and Europe. It begins with the construction of a model office applicable to the People’s Republic of China’s regulatory framework and unique market environment. Reserve standards and solvency measurement systems in different supervisory frameworks then are applied to the model office. The results are analyzed as a comparative study of the People’s Republic of China’s total assets required for the reserves and solvency margins under the practices of other jurisdictions. Early warning systems also are discussed.     

“Life Expectancy in the Future: A Summary of a Discussion among Experts”, Robert B. Friedland,October 1998

Abstract

In this paper we present an econometric model of implied volatilities of S&;P500 index options. First, we model the dynamics the CBOE VIX index as a proxy for the general level of implied volatilities. We then describe a parametric model of the implied volatility surface for options with a term of up to two years. We show that almost all of the variation in the implied volatility surface can be explained by the VIX index and one or two other uncorrelated factors. Finally, we present a model of the dynamics of these factors.     

“Relative Importance of Risk Sources in Insurance Systems”, Edward W. Frees,April 1998

Abstract

This paper considers a Sparre Andersen collective risk model in which the distribution of the interclaim time is that of a sum of n independent exponential random variables; thus, the Erlang(n) model is a special case. The analysis is focused on the function φ(u), the expected discounted penalty at ruin, with u being the initial surplus. The penalty may depend on the deficit at ruin and possibly also on the surplus immediately before ruin. It is shown that the function φ(u) satisfies a certain integro-differential equation and that this equation can be solved in terms of Laplace transforms, extending a result found in Lin (2003). As a consequence, a closed-form expression is obtained for the discounted joint probability density of the deficit at ruin and the surplus just before ruin, if the initial surplus is zero. For this formula and other results, the roots of Lundberg’s fundamental equation in the right half of the complex plane play a central role. Also, it is shown that φ(u) satisfies Li’s (2003) renewal equation. Under the assumption that the penalty depends only on the deficit at ruin and that the individual claim amount density is a combination of exponential densities, a closed-form expression for φ(u) is derived. In this context, known results of the Cauchy matrix are useful. Surprisingly, certain results are best expressed in terms of divided differences, a topic deleted from the actuarial examinations at the end of last century.