Knowledge that Transforms

Abstract : The theory of dynamic programming treats problems involving multi- stage processes by means of a transformation of the problem from the space of decisions to the space of functions. This is accomplished by deriving a functional equation whose solution is equivalent to the solution of the original problem. To illustrate this approach most clearly, free of extraneous analytic details, a simple but nontrivial multi-stage investment problem is considered. How exact solutions may be obtained in some cases, approximate solutions in others, and how these approximate solutions may be used to obtain more accurate solutions in the general case is shown. Of particular importance is the decrease in the number of independent variables made possible by this approach. This is not only important from the theoretical standpoint, but is also of great value in reducing the cost in time and effort of numerical computation.

Stimulating, provocative, often infuriating, but well worth reading.—Peter Newman, Economica His critical blast blows like a north wind against the more pretentious erections of modern economics. It is however a healthy and invigorating blast, without malice and with a sincere regard for scientific objectivity.—K.E. Boulding, Political Science Quarterly Certainly one of the most engrossing volumes that has appeared recently in economic theory.—William J. Baumol, Review of Economics and Statistics

EVER SINCE mathematicians first began to study the measurement of risk there has been general agreement on the following proposition: Expected values are computed by multiplying each possible gain by the number of ways in which it can occur, and then dividing the sum of these products by the total number of possible cases where, in this theory, the consideration of cases which are all of the same probability is insisted upon. If this rule be accepted, what remains to be done within the framework of this theory amounts to the enumeration of all alternatives, their breakdown into equi-probable cases and, finally, their insertion into corresponding classifications…