Dynamic programming and inverse optimal problems in mathematical economics

A number of important processes in mathematical economics may be viewed as multistage decision processes, or, equivalently, as control processes, and thus attacked profitably by means of the theory of dynamic programming [l, 21, or by means of the calculus of variations [3, 4, 51.1 As in the fields of engineering and physics, there are considerable benefits to be gained from viewing a process as if it were an optimization process. This leads to the inverse problem of constructing optimization processes for which an observed behavior is an optimal policy [6]. In [7], we indicated some of the advantages of using dynamic programming to study inverse problems of classic type. Here we wish to show that the techniques are equally advantageous in dealing with problems that are characteristically of economic type. Detailed analytic investigations of the problem we use as an example will be found in [I] and [5]. Let us also point out that the methods we employ can be used with equal effectiveness in dealing with stochastic and adaptive processes. In these areas, the calculus of variations is of little use.