AN INTRODUCTION TO DYNAMIC PROGRAMMING

DYNAMI C programming, a mathematical field that has grown up in the past few years, is recognized in the U.S.A. as an important new research tool. However, in other countries, little interest has as yet been taken in the subject, nor has much research been performed. The objective of this paper is to give an expository introduction to the field, and give an indication of the variety of actual and possible areas of application, including actuarial theory. In the last decade a large amount of research has been performed by a small body of mathematicians, most of them members of the staff of the RAND Corporation, in the field of multi-stage decision processes, and during this time the theory and practice of the art have experienced great advances. The leading force in these advances has been Richard Bellman, whose contributions to the subject, which he has entitled Dynamic Programming(I), have had effects not only in immediate fields of application but also in general mathematical theory; for example, the calculus of variations (see chapter IX of (I)), and linear programming (chapter VI). The work done so far has paved the way for innumerable further research and applications, and hence the field, besides being a very stimulating one, is one which new blood will find potentially highly fruitful. As will be seen when the concept of dynamic programming is defined and illustrated more fully below, a further development in the last decade that has made research in the subject more feasible and useful has been the evolution of the digital computer, which has made it possible to simulate complicated processes and hence deduce their properties by Monte Carlo methods; sometimes,