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Modelling excess mortality using GLIM

Attempts to incorporate regression-like models into life-table analysis would appear to have gone largely untried by the British actuarial profession. Essentially this is because in life insurance, data bases are large and the establishment view is that such models are inappropriate when sampling variation is small. Also mortality is of less significance as a factor than economic variables like inflation and investment earnings. All the actuary needs to do is not understate the level of mortality rather than get it exactly right. The purpose of this paper is two-fold.

The cocktail problem: the relationship between composite yield and component yields

When two or more independent or component loans are consolidated to form a single composite loan the result is often referred to as a cocktail loan. In this paper we analyse properties of a composite loan induced by properties of the component loans. Of particular interest are the properties of the composite yield in terms of the yields and other characteristics of the component loans. Some upper and lower bounds are also established for the composite yield in terms of the component yields.

An actuarial model for AIDS

In this note I describe the mathematical formulation of a model for representing the spread of AIDS in a population, which is designed for actuarial use in dealing with life insurance companies and pension funds. A major requirement of actuaries is that the model should be age-specific, and should take into account normal age-specific mortality as well as the extra sickness and mortality from AIDS.

Years of life lost and other mortality indices

In 1953 together with a colleague (Benjamin and Logan) the author called attention to a paper by Haenzel (1950) describing a new index of mortality years of life lost. The argument was that many people were living for more than the three score and ten years and that every earlier death represented a loss of potential further years of life; that adding up the total years of life lost might be a significant measure of the toll of largely preventable disease; that changes in this total year by year would maximize the improvement gained by curative and especially preventative medicine.

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