Courses in Actuarial Mathematics
In this country university courses in the theory of probability, up to the beginning of this century, were largely confined to the solution of questions of a priori probability, that is, throwing of dice, drawing of cards, tossing of coins, and employment of combinations, permutations, substitutions, and the like, to find the numerator and denominator of the fraction expressing the required chance. This approach to the subject was the natural outcome of adherence to English texts and acceptance of the practices of the British school of mathematicians.
The first volume of Biometrika appeared in 1901-2, but it was a long time before the English and Scotch actuaries knew much about the new methods of approach used by Karl Pearson and his followers. The application of the methods of empirical probability to important practical problems, largely social in character — one of which was life insurance — was hardly known to our college and university mathematicians, and little study had been given by any of them to this unlimited field of useful and interesting material awaiting refined mathematical treatment.
It might fairly be said that students of the natural sciences recognized this situation before the mathematicians did. With mathematical equipment unequal to the task, they were trying as best they could to solve problems which they knew could be solved but with which they were unprepared to deal except by methods of elementary mathematical approach. It was this situation which first decided the writer to introduce in the University of Michigan courses in mathematics involving primarily the study of empirical probability.
One of the most important applications of this theory was actuarial mathematics. Early in the present century a number of foreign universities had developed actuarial courses in their departments of mathematics. This was, of course, to a considerable extent, due to national insurance and pension plans already under way. Although the total insurance in force in the United States was more than that of all the rest of the companies in the world put together, no training of technical actuarial content was available in this country. It was, therefore, under most favorable conditions that such courses were started at the University of Michigan.
Personal conversations and conferences made it apparent that the life insurance companies were favorably disposed toward this new plan. Accordingly, in the fall of 1902, the first course in this field was offered in the University of Michigan. It appeared in the University Calendar for 1902-3 as Mathematics 45, "Theory of Annuities and Insurance (II), two hours, Dr. Glover." It was elected by eleven men and one woman, and was given on Tuesday and Thursday in Room 17, University Hall, North Wing (now known as Mason Hall). Oliver Winfred Perrin ('01, A.M. '04), Associate Actuary of the Penn Mutual Life Insurance Company, was a member of this class and the first graduate of the University to enter and remain in the actuarial profession.
These courses were first announced both in the Department of Mathematics and in the Department of Political Economy (see Part III: Department of Economics). The faculty of the latter department was cordially disposed and was most helpful in the organization of the courses; it co-operated by encouraging election of these courses by students of political economy who had sufficient preparation in mathematics to undertake them with profit. The plan was to supplement the technical courses in actuarial mathematics by courses in Page 655political economy which would develop more fully the social aspects of insurance.
It should be acknowledged here that from the beginning to the present time busy executives and officers of insurance companies throughout the country have given valuable and cordial support to this work and have frequently taken the trouble to come to Ann Arbor and lecture to our classes on various phases of their business. This interest from outside the University has stimulated the students and has undoubtedly contributed much to the success of the venture. The companies also have recognized the training received here by sending their officers year after year to select University of Michigan actuarial graduates for technical positions in various departments of the home offices. Many students from this department have advanced from modest actuarial positions to become secretaries, vice-presidents, presidents, and directors in the important life and casualty insurance companies of this country. University of Michigan students from China, Japan, Mexico, the Philippine Islands, and other countries are now holding responsible positions in such companies organized in their native lands. In a number of cases University of Michigan graduates in actuarial mathematics have organized successful companies which they now head.
Up to the present time about four hundred students have taken all the actuarial courses and most of them are now actively engaged in executive positions of high rank. Not a few of them hold official positions in government insurance offices in this and other countries. Among them are about fifty women graduates, of whom one-third have married and have retired from active business life.
Although the number of professional actuarial graduates is relatively small — about four hundred — the elementary courses necessary to prepare students for advanced actuarial theory led to a new development for students not planning to become actuaries. They wanted an elementary course in financial mathematics, in which the mathematical content included simple and compound interest, annuities, sinking funds, valuation of securities, and depreciation. When such a course was offered, it attracted many students who were interested in the above subjects as a matter of general information and as a preparation for one of the many lines of modern business. This course injected into the classroom work a certain practical interest not ordinarily found in elementary mathematics courses. The result was a steadily increasing demand for Mathematics 51, (now Mathematics 47), for which in some years as many as three hundred students each semester were enrolled. And, since the elementary course in financial mathematics was begun at the University of Michigan in 1902, a similar course has been introduced into the mathematics department of almost every college and university in this country.
These courses at the University were organized and given at first by the writer, but additions to the teaching force were soon required because of the increasing number of students. Most of the work of instruction in actuarial science has been carried on of late by H. C. Carver, C. C. Craig, W. O. Menge, J. A. Nyswander, T. E. Raiford, and R. B. Robbins.
The curriculum in actuarial science has, in effect, developed a small professional field within the Department of Mathematics and a new group of elementary courses in finance, insurance, and statistics which have a strong appeal for many students who do not plan to enter the actuarial profession.