First published in 2004, 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 emphasises 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.
• Rigorous but user-friendly book filling gaps in mathematical economics and finance literatures • Thorough and concise resource for learning stochastic control theory with applications to economics and finance • Discussion and comparison of the various methods of finding a closed-form representation of the value function of a stochastic control problem
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.
Review of the hardback: '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