Description: Traditional mean-variance method does not take skewness of the random rate of return into consideration. It only considers minimum variance for a given acceptable rate of return, which limited the probability of obtaining higher rate of return. If the skewness of return for the portfolio is incorporated into model of traditional approach, then the resulting non-linear programing model is not computational efficient, which certainly is complicated. On the other hand, possibilistic programming provides more efficient techniques to solve the imprecision nature of rate of return and also preserves the original linear model.

Description: The yield rate is that effective rate of interest at which the present value of his expenditures is equal to the present value of his returns. This paper encourages students of Theory of Interest class to try to approach yield rate problems by starting with the definition of yield found in Steve Kellison's text.

Description: While we agree with the conclusions expressed by Silver and Hedges The Classical Definition of Compound Interest is Adequate by Murray Silver and Bob Hedges, ARCH 1981.2, we do not believe the theorem follows from the stated Axiom. We present an alternative proof which uses only the accumulation function and not the force of interest.

Description: The conventional way to analyze grouped observations on a single variable is to construct histograms or, sometimes, fit a normal distribution. We extend this latter approach by allowing for transformations to near normality.

Description: An insurance company starts with an initial surplus, collects premium, pays claims to policyholders and pays dividends to stockholders. What remains is the following year’s surplus. The process continues. This paper describes how to calculate the distribution of surplus for any given year. With these distributions, one can make the calculations of premiums and dividends.

Description: This is the abstract of the article 'A Proposed Unified Valuation System'. This article will briefly describe some analytical examples of a stochastic modeling of risk use to illustrate the S-curve approach to valuation, but more importantly describe key additional area of research and theory, which need to be developed. The focus of this presentation is an invitation for additional research to support a new approach to statutory valuation of life and health risk that can result in better management and regulatory information.

Description: This is a letter from Jan M. Hoem to Arnold F. Shapiro about Exposed-to-risk considerations based on the Balducci assumption and other assumptions in the analysis of mortality.

Description: The paper gives two criteria for fit and uses two different criteria to transform an initial graduation into one with better fit. It is shown that the two sets of criteria give the same transformation. The mathematical relationships between the two sets of criteria are then derived. It is clear from those relationships that when one set of criteria is small, the other set is small [but reasonably the same]. Some general comments on various measures of fit are made.

Description: In a series papers by Willmot and Lin, both exponential and non-exponential bounds for the tail probability of various compound distributions have been derived. In Wilmot, it was suggested that non-exponential bounds for the ruin probability were difficult to obtain using martingale arguments. In this note, we show how to use martingale inequalities to obtain some upper bounds for the ruin probability.

Description: We propose asymptotically correct two-sided bounds for random sums where the number of summands has an arbitrary distribution which can be viewed as ruin probabilities or accumulated claim sizes in various risk processes. The bounds are fairly new and they reveal the real accuracy of some well-known and widely used asymptotic formulas. It turns out that this accuracy can be poor and the range where these formulas give appropriate approximations depends on the shape of the tail distribution of the summands. This dependence is examined in the research.