Stochastic Optimization in Continuous Time

This is a rigorous but user-friendly book on the application of stochastic control theory to economics. A distinctive feature of the book is that mathematical concepts are introduced in a language and terminology familiar to graduate students of economics. The standard topics of many mathematics, economics, and finance books are illustrated with real examples documented in the economic literature. Moreover, the book emphasizes the dos and don'ts of stochastic calculus, cautioning the reader that certain results and intuitions cherished by many economists do not extend to stochastic models. A special chapter (Chapter 5) is devoted to exploring various methods of finding a closed-form representation of the value function of a stochastic control problem, which is essential for ascertaining the optimal policy functions. The book also includes many practice exercises for the reader. Notes and suggested readings are provided at the end of each chapter for more references and possible extensions.

Table of Contents:
List of figures; Preface; 1. Probability theory; 2. Wiener processes; 3. Stochastic calculus; 4. Stochastic dynamic programming; 5. How to solve it; 6. Boundaries and absorbing barriers; Appendix. Miscellaneous applications and exercises; Bibliography; Index.

About the Author :
Professor Chang received his BS from National Taiwan University, holds a PhD in Economics from the University of Chicago and a PhD in Mathematics from State University of New York at Stony Brook. His graduate-level courses include price theory sequence and mathematical economics (stochastic control theory and applications, economics of uncertainty). He has been an invited visiting scholar to the Center for Economic Studies (CES) of the University of Munich, Germany, and the Economic Research Center (ERC) of Nagoya Univeristy, Japan. He is also a recipient of the 1986 Outstanding Junior Faculty Awards of Indiana University, a recipient of the 2004 IU Trustees Teaching Awards, and a research fellow of the CESifo Research Network. Professor Chang has published papers in prestigious journals in economics and mathematics, including Econometrica, the Review of Economic Studies, the Journal of Economic Theory, the Proceedings of American Mathematical Society, and the Journal of Optimization Theory and Applications. In 2004 he published Stochastic Optimization in Continuous Time with Cambridge University Press.

Review :
'Written by an expert on stochastic calculus and optimization and a gifted writer and economist, this graduate-level textbook provides a rigorous yet highly readable and intuitive introduction to stochastic calculus and optimization with major applications in economics. I most highly recommend Stochastic Optimization in Continuous Time to the serious student and practitioner of economics and finance.' George M. Constantinides, University of Chicago 'This immediately becomes the definitive rigorous monograph for economists that is devoted to optimization in dynamic settings under uncertainty. By beginning with a careful introduction to the mathematical foundations, and then turning to a tasteful modern blend of applications from across economics, including finance monetary theory, and production, Chang has done a great service by lowering the costs of entry for doctoral students and researchers. The accessible treatments of stochastic integration and stochastic control will be especially well appreciated.' Darrell Duffie, Stanford University 'Mathematically rigorous, yet full of economic intuitions. A 'must read' for students and researchers interested in dynamic economic models.' Chi-Fu Huang, Oak Hill Platinum Partners, L.L.C. 'Economists have missed the opportunity to use stochastic calculus as much as financial theorists and therefore have left most of the harvesting from this methodology to finance. In this book, Professor Chang demonstrates clearly that economics has much to gain by using the methods of stochastic calculus. Although the author uses a formal presentation with rigorous mathematics, he supplements it with elegant examples from monetary economics, labor economics, investments and growth. The discussion on stochastic growth is quite unique and currently not available in any other text. Professor Chang has performed a valuable service to economists by writing this useful and elegant book.' A.G. Malliaris, Loyola University, Chicago 'The book is well written and should prove useful in graduate courses for economists and also in courses for other professionals who are willing to go into the mathematics of economic models.' Zentralblatt MATH