Stochastic Optimization in Continuous Time

Erscheinungsjahr 2011
ISBN: 978-0-521-83406-3
Verlag: Cambridge University Press

Buch, Englisch, 344 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 713 g

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.

Autoren/Hrsg.

Chang, Fwu-Ranq

Fachgebiete

• Wirtschaftswissenschaften Volkswirtschaftslehre Volkswirtschaftslehre Allgemein Ökonometrie
• Mathematik | Informatik Mathematik Mathematik Allgemein
• Interdisziplinäres Wissenschaften Wissenschaften: Allgemeines Populärwissenschaftliche Werke
• Wirtschaftswissenschaften Betriebswirtschaft Unternehmensfinanzen Finanzierung, Investition, Leasing
• Wirtschaftswissenschaften Betriebswirtschaft Wirtschaftsmathematik und -statistik
• Wirtschaftswissenschaften Finanzsektor & Finanzdienstleistungen Unternehmensfinanzierung

Inhaltsverzeichnis

1. Probability theory: 1.1 Introduction; 1.2 Stochastic processes; 1.3 Conditional expectation; 1.4 Notes and further readings; 2. Wiener processes: 2.1 Introduction; 2.2 A Heuristic approach; 2.3 Markov processes; 2.4 Wiener processes; 2.5 Notes and further readings; 3. Stochastic calculus: 3.1 Introduction; 3.2 A Heuristic approach; 3.3 The Ito integral; 3.4 Ito's lemma: autonomous case; 3.5 Ito's lemma for time-dependent functions; 3.6 Notes and further readings; 4. Stochastic dynamic programming: 4.1 Introduction; 4.2 Bellman equation; 4.3 Economic applications; 4.4 Extension: recursive utility; 4.5 Notes and further readings; 5. How to solve it: 5.1 Introduction; 5.2 HARA functions; 5.3 Divine revelation; 5.4 Symmetry; 5.5 The substitution method; 5.6 Matingale representation method; 5.7 Inverse optimum method; 5.8 Notes and further readings; 6. Boundaries and absorbing barriers: 6.1 Introduction; 6.2 Nonnegativity constraint; 6.3 Other constraints; 6.4 Stopping rules - certainty case; 6.5 The expected discount factor; 6.6 Optimal stopping times; 6.7 Notes and further readings.

Über Autor(innen)

Chang, Fwu-Ranq
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.