This book presents the main applied aspects of stochas­ tic optimization in economic models. Stochastic processes and control theory are used under optimization to illustrate the various economic implications of optimal decision rules. Unlike econometrics which deals with estimation, this book emphasizes the decision-theoretic basis of uncertainty specified by the stochastic point of view. Methods of ap­ plied stochastic control using stochastic processes have now reached an exciti~g phase, where several disciplines like systems engineering, operations research and natural reso- ces interact along with the conventional fields such as mathematical economics, finance and control systems. Our objective is to present a critical overview of this broad terrain from a multidisciplinary viewpoint. In this attempt we have at times stressed viewpoints other than the purely economic one. We believe that the economist would find it most profitable to learn from the other disciplines where stochastic optimization has been successfully applied. It is in this spirit that we have discussed in some detail the following major areas: A. Portfolio models in ·:finance, B. Differential games under uncertainty, c. Self-tuning regulators, D. Models of renewable resources under uncertainty, and ix x PREFACE E. Nonparametric methods of efficiency measurement. Stochastic processes are now increasingly used in economic models to understand the various adaptive behavior implicit in the formulation of expectation and its application in decision rules which are optimum in some sense.