The Use of Select Tables for the Calculation of Survivorship Benefits

Extract

It is generally admitted that select tables should be used for the calculation of office premiums, the tendency of aggregate tables being to underestimate the risk for the younger and to overestimate it for the older ages, so that, in the case of survivorship benefits, where the risk is that of a young life predeceasing an old one, a double error is introduced. In one of the earliest papers read before the Faculty (T. F. A., i, 49), Mr. A. E. Sprague considered the applicability of select tables to the calculation of continuous benefits; but it seems that the ordinary method of approximation, if applied without modification, may lead to an error of some importance. Most of the well-known quadrature formulas can be obtained by direct integration from Everett's Interpolation Theorem, which assumes that the law is continuous throughout; but it is well known that the rate of mortality changes very quickly during the few years following selection, and that it in fact follows a different law from that which prevails later on. The H^[M] table is not a very good one by which to test this method of approximation, for the graduation of the H^M(5) portion is not very smooth; and, as the method depends on selected values of the function, any irregularities of the table will be reflected in the final result, and it is not possible to say to what extent an error is due to this cause.