On the determination of the critical duration in certain actuarial problems

Extract

Students of the subjects of compound interest and life contingencies are usually baffled by the type of problem in which the value of a premium, say P, can only be ascertained when one knows the number of years, say n, after which there is some definite change in the conditions of the problem. Such is, for example, the valuation of a variable annuity-certain subject to different remunerative and reproductive rates of interest when, in the beginning, the payments under the annuity are too small to meet requisite interest payments. In Chapter IV, article 16, of Todhunter, the student is advised that in such cases the value must in general be sought by trial and error. Similar exhortations perplex the student's mind when he turns to the subject of life contingencies, in which he is frequently required to evaluate the premium for a complicated assurance in which the death benefit is defined by different expressions before and after a period of time which is itself unknown.