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: This article investigates the simplicity of the Balducci hypothesis, and compares the fractional-age death probability given by three widely used assumptions: uniform distribution of deaths, the Balducci hypothesis, and constant force of mortality [1, 2].

Description: Statistical properties of interest, annuity and insurance functions are examined when mortality and interest are treated as having a random component. Several special models of interest rate fluctuation are examined in detail. It is hoped that such theory will be useful in developing fluctuation reserves and premium margins. Presented at the 13th Annual Actuarial Research Conference, Ball State University, August 31st. September lst, 2nd. 1978.

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: Because mortality tables are generally tabulated at yearly intervals actuaries frequently must make assumptions about intermediate values in developing formulas for insurance and annuity functions. This paper examines the effect on insurance and annuity formulas of assuming Mx+t to be linear within each interval.

Description: The objectives of this paper are to determine the extent to which Makeham's or Gompertz's laws describe recent insurance and population mortality analyze how the constants in the two laws vary with respect to some factors and propose a simple extension to Makeham's law to account for recent departures from the laws, related to difference in sex. Presented at Actuarial Research Conference at Ball State University, September 1, 1978

Description: In this paper, we study a survival regression model known as Cox's proportional Hazards model. We assume that the data available are already grouped and develop a minimum distance estimation procedure that is also applicable when the data are also left or right censored. Asymptotic properties of the estimators are established and the numerical implementation of the method based on an iterated reweighted least squares algorithm is discussed.

Description: What are the possible future implications to insurance companies of significant improvements in mortality? How can futurism techniques be used in research? The formation of the mortality improvement study group at the Principal Financial Group was the first step toward examining the issue of mortality improvement. In an interactive format, we will present what we learned about mortality and futurism techniques by participating in this group.

Description: This paper discusses a general model for calculating life contingencies including formulation of the model and net reserves and contingency reserves.

Description: Actuarial literature in the twenty-five years includes discussions of a well known inequality. Among the recent papers on various aspects of this classic result are those by Berin 1970, Olson 1975 and Sarason 1960. A standard method for achieving this inequality uses Jensen's inequality. This is the method used by Bowers, et al 1983. We will also employ this method in an attempt to learn about it.