Published online by Cambridge University Press: 18 August 2016
The general subject of extra risks, and the special method of meeting such risks by making temporary deductions from the sum assured in lieu of charging an extra premium, have been more than once under discussion at this Institute. The latter problem in particular was somewhat exhaustively considered upon the occasion of a paper by the late Mr. Sunderland, “On a Method frequently adopted of treating Under-Average Lives for Assurance purposes, &c.” (J.I.A., xxix, 419).
page 155 note * Strictly, the use of μ x+t in lieu of qx+t involves the substitution of t V x + ½Pxfor t+1 V x and of (m — t — ½ )X for (m — t) X in the formulas (i) and (ii). It was considered sufficiently accurate for the purpose in view, however, to use the values of t V x and (m — t )X, leading to equations (iii) and (iv).