The nomographic estimation of the influence of substandard mortality on the policy value.

Abstract

In this article we are concerned with the problem of interpreting numerically the relative variations which the policy value based on a standard mortality table undergoes when this table is replaced by one which allows for 100T% extra mortality.This question is of particular interest from two points of view. First, it is of consequence for the technique of insurance of abnormal risks to obtain some idea of the numerical effect of percentage additions to the mortality on such important lifecontingency functions as surrender values. Further, in the treatment of this question as a typical approximation problem of lifecontingency mathematics, it appears that the solution most suited to the essence of the inquiry and for practical applications is obtained by a nomographic evaluation of the quantities under consideration. As regards the importance of nomography in the practical application of insurance mathematics the author has already made a thorough exposition and given examples in a series of earlier publications; in future, in life-contingency problems, the necessary consideration will always be given to the development of the appropriate nomographic methods, particularly in connexion with the introduction of typical approximate methods.