On the construction of Models of Policy-values, and on a new method of comparing the Reserves for Policies, according to different Tables of Mortality and Rates of Interest

Abstract

There is no subject of greater importance in the conduct of the business of Life Assurance than that of the valuation of policies. It is a matter which comes before the actuary from day to day and from year to year, whether in the form of fixing the amount to be returned to an individual policyholder on the cancelment of his contract, or in that of estimating what reserve should be made in the aggregate for a mass of policies existing at the close of a valuation period. Both of these questions have been discussed before the Institute on many previous occasions, and it is not necessary to enter into them now. The task I have set before myself is the humbler one of dealing with results already arrived at. I do not propose to enquire what are the reasons for preferring one mortality table or rate of interest to another, or on what principle of calculation the surrender-value of a policy should be based. I accept the results brought out by the use of any mortality table or rate of interest agreed on, and I propose to consider how these results may be represented by means of diagrams and models, and whether by this means we can arrive at any clearer understanding of the relation to one another of the reserves brought out by different standards of valuation.