Description: In this paper we study the pricing of financial options and contingent claims. We show that two time-honored concepts in actuarial science - the Esscher transform and the adjustment coefficient - are efficient tools for pricing many options and derivative securities if the logarithms of the prices of the primitive securities are certain stochastic processes with stationary and independent increments. We also study the pricing of American options on two stocks without expiration date and with payoff functions which are homogeneous with respect to the two stock prices.

Description: This is the fourth paper on n-year roll forward reserve financing of public benefit systems, especially Old-Age, Survivors and disability Insurance OASDI, prepared by University of Michigan faculty and students. As the papers have developed, some ideas have been simplified, while others have become more complex. It is concluded that the theoretical model requires further attention. This research can be extended to expand our knowledge of OASDI financing and the applicability of n-year roll forward reserve financing.

Description: In this paper,we present a method which first converges a two dimensional data to a univariate one and then uses the interval censoring technique to estimate the probability of failure of a Joint-life status from a heavily censored data. Our study shows that the life annuities of joint-life status calculated assuming independence overestimates the ones evaluated from an actual sample of population.

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 paper is a sequel to Shapiro et. al. in that it discusses a similar role for CAI in topics specific to the text Actuarial Mathematics, by Bowers et. al 1986. The topics covered are the previous topics of actuarial notation, basic concepts, and what-if analysis, along with some new ideas for the presentation of stochastic models.

Description: These are the abstract, outline, graphs and tables of the paper “Conclusions from Michigan Studies of Social Security Financing”. By such studies we mean the papers prepared during the past five years by actuarial students and Cecil Nesbitt, and which have appeared in ARCH. The paper is in three parts: A lengthy Abstract, followed by 17 pages of text, graphs, tables and references. The third part is a 10 page Appendix which gives the proofs of text statements.

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: This is the program for the 30th Annual Actuarial Research Conference held at The Penn State Scanticon Conference Center in University Park, PA on August 17-19, 1995. From Actuarial Research Clearing House 1996, Vol. 1.

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.