Description: This paper critiques and supplements Professor Schuette's 'Linear Programming Approach to Graduation.' The main points are: 1. The graduation is a problem of estimating the mean vector of a multivariate variable under certain assumptions. Schuette and other discussants emphasized the robustness property of their proposed estimation. This paper points out their mistake and suggests some correcting directions based on Bayesian theory. 2. This paper provides a more complete theoretical rationale for the parameter choosing in the graduation problem. 3. This paper points out the incompleteness of a theorem's proof in Schuette's paper and supplements some interpretations and mathematical details for the proof of some other theorems from a different viewpoint.

Description: Option bounds are obtained in a discrete-time framework with transaction costs. The model represents an extension of the Cox-Ross-Rubinstein binomial option pricing model to cover the case of proportional transaction costs. The method proceeds by constructing the appropriate replicating portfolio at each trading interval. From Actuarial Research Clearing House 1991, VOL. 1.

Description: This paper presents a solution to the problem of discounting cash flows when the cash flows and discount factors are random variables with given distributions.

Description: This research paper presents a method for smoothing mortality rates using multi-dimensional Whittaker-Henderson Graduation. The paper answers the question: For a given level of fit, how are the smoothness parameters to be chosen so that the graduated rates form, in some natural sense, the smoothest discrete surface?

Description: A short note on derivatives of decreasing life annuities that was motivated by Exercise 5.35 on page 156 of 'Actuarial Mathematics'. Actuarial Research Clearing House 1993 VOL. 2

Description: This paper investigates nonparametric estimators of the distribution function that are based on mixtures of gamma distributions when we have a random sample from a continuous distribution function. From Actuarial Research Clearing House 1993, VOL. 3.

Description: This paper provides an outline of the pricing methodology used by Blue Cross and Blue Shield of Virginia which incorporates trend analysis by trend component. From Actuarial Research Clearing House 1993, VOL. 3.

Description: The standard deviation of the present value of benefits of portfolios of identical insurance contracts are examined when both the mortality and the force of interest are stochastic. Several models for the force of interest are presented. The impact of the different stochastic models for the force of interest and of different parameters on the mortality risk and the interest risk is investigated. From Actuarial Research Clearing House 1994, VOL. 1.

Description: This paper proposes to put the environment into financial markets. It explains how to do it, and why the financial approach is practically the only one able to stop and invert environmental degradation. The author concentrates on deforestation which is the largest environmental problem in the third world, and explains how to start the project and what kind of optimization problems should be solved for applications of the project.

Description: The author previously wrote about extending the general nonparallel shlft approach to duration analysis. This paper explores the immunization properties of that model. In addition, applications to asset-liability management are explored. From Actuarial Research Clearing House 1990 VOL. 2.