Angus S Macdonald and Stephen J Richards: Newton, Leibniz and Actuarial Science & The Actuarial origins of survival models

Abstract: The seminar presents two talks:

Newton, Leibniz and Actuarial Science
Angus S Macdonald

In this bicentenary year of Gompertz (1825) we advance a conjecture; that the split between Newtonian and Leibnizian forms of calculus occurring in the 18th century had a long-term influence on actuarial science in the 19th and 20th centuries. When the growing life insurance industry in Britain needed mathematical expertise, a profession with Newtonian roots was created to supply it, while elsewhere in Europe it was found in universities with Leibnizian roots. We consider the consequences up to the present day, when analysis in the Leibnizian branch has led via Kolmogorov (1933) to modern financial mathematics.

The Actuarial Origins of Survival Models
Stephen J Richards

Survival models based on individual lifetimes are a cornerstone of modern medical statistics. The foundations of survival analysis were laid by actuaries, driven by practical as well as theoretical benefits. However, technological limitations led the actuarial profession to leave the development of survival modelling to statisticians many decades later. This paper seeks to remind actuaries of their early leading role in this field, and perhaps to rekindle interest in what their forebears started, especially since computing resource has long ceased to be a limiting factor. This paper may also be of interest to non-actuaries in understanding the unique characteristics of actuarial data sets and of actuarial modelling requirements.