Actuarial Science—A Survey of Theoretical Developments

Abstract

A CTUARIAL SCIENCE, at least as term is used in English speaking countries, differs radically from some other sciences in that great amounts of practical material are included. For this reason, a survey of field, such as we customarily attempt at turn of centuries and half centuries, is most effectively made in two articles, one on theory, one on practice. Conceive, if you please, that botany, horticulture, and greenhouse operation were all lumped together under heading Plant Science, and you would have something of same situation. Here we are concerned with theoretical developments and it is just here that we come up against first problem. While it is true that no sharp line of demarcation exists between theory and practice, it is not too difficult to make a rough separation of material on empirical grounds. This, however, does not provide a categorical answer to question of just what, fundamentally, constitutes a theoretical development of Actuarial Science. Before attempting to answer this question, a brief review of subject matter is useful in order to provide a point of departure. There is probably no better method of summarizing content of actuarial theory than to list and comment on subjects studied by beginners in profession in order that they are taken up in their course of study. After passing tests to assure himself of adequacy of his formal mathematical equipment, which includes some training in finite differences and theory of probability and mathematical statistics, student at once plunges into basic insurance mathematics generally known by term contingencies. This subject presupposes existence of a mortality table, which might be thought of as sprung fully computed from head of Jove; it has been defined by famous English actuary, George King, as the instrument by means of which are measured probabilities of life and probabilities of death. From this table are derived net premiums and reserves for various forms of life insurance policies as well as expectation of life and solution to population problems. The student is then led into intricacies of working with multiple decrement tables, which enable him to handle effect of sickness, withdrawal,