The Reticent Trio: Some Little-Known Early Discoveries in Life Insurance Mathematics by L.H.F. Oppermann, T.N. Thiele and J.P. Gram

Abstract

Insurance mathematics has a pattern of early discovery of important notions which failed to get the attention they deserved at the time, fell in oblivion, and were rediscovered and put to good use only later. Sometimes the rediscovery was made independently by people who must have had little knowledge of the actuarial tradition. This development was brought about by a combination of factors, ranging from the publication of the new ideas in inaccessible places and uncommon languages (like Swedish or Danish), via the inability of the international actuarial community to utilize suggestions made, to the lack of interest in actuarial matters shown by most outsiders. There are several instances of this nature in the early history of Danish life insurance mathematics. This paper recounts those that have seemed most important to the author: Oppermann's first use of least squares to fit a mortality formula, and Gram's independent deduction of general formulae (i) for optimal moving averages, and (ii) for variances corresponding to actuarial values in life insurance. We also briefly indicate some early discoveries which did make an impact, on occasion in spite of extreme inattention to the requirement of publication, such as Thiele's differential equation for the premium reserve.