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: 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: A European call option pricing model similar to the Black-Scholes equation [1] is derived. Like the Black-Scholes equation, the model is based upon an assumption of a lognormal distribution of the price of a risky, non-dividend-paying security at a given point in the future. However, unlike Black-Scholes, the market's risk preference is recognized through a parameter that permits refinement of the model to agree either with experience or with future advances in the underlying theory.

Description: This is a letter to readers of The Actuary from Arnold Dicke and Walter Lowrie to solicit opinions on the problem which seems to crop up each time an examination is to be set.

Description: Demography is a very exciting subject. With a simple mathematical model, students can project a country's population forward 25, 59, 75 even 100 years. This paper will focus on six ideas from demography. They all can be useful to an actuary, yet none of them would be considered at any length if the actuary didn’t study demography.

Description: In this note, we rearrange the statement and the proof of a theorem in Greville. The presentation appears to be more compact the materials, however, are not new.].

Description: The theory underlying the Moving Weighted Average graduation method is restated in the language of linear algebra which provides for an enrichment of the family of formulas. A comparison of the results of applying six members of the family to 100 simulated data sets is provided.

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: 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: In the present paper, we propose and investigate a numerical method of computing the probability distribution of S. Inversion of the Laplace transform moment generating function is shown to be a better approach than the existing recursive method for find the distribution of sum of several independent random variables. In the continuous case, in many situations, numerical inversion needs to be used to compute the probability distribution function of the sum.