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This is a concise and elementary introduction to stochastic control and mathematical modeling. This book is designed for researchers in stochastic control theory studying its application in mathematical economics and those in economics who are interested in mathematical theory in control. It is also a good guide for graduate students studying applied mathematics, mathematical economics, and non-linear PDE theory. Contents include the basics of analysis and probability, the theory of stochastic differential equations, variational problems, problems in optimal consumption and in optimal stopping, optimal pollution control, and solving the HJB equation with boundary conditions. Major mathematical requisitions are contained in the preliminary chapters or in the appendix so that readers can proceed without referring to other materials.Read more
- Ideal for students and researchers who do not major in control theory
Reviews & endorsements
"This book provides an excellent introduction to controlled diffusions and their economic applications and it is self-contained..."
Vivek S. Borkar, Mathematical ReviewsSee more reviews
"As the title indicates, the author’s presentation is clearly focussed on economics and provides neither exercises nor questions for further investigation. However, the chapters should allow the reader to identify future research areas. As such the text has much to commend it and the time taken to understand the material presented will reap benefits. For those interested in theoretical expositions, this is a text that I can recommend."
Carl M. O’Brien, International Statistical Review
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- Date Published: January 2010
- format: Hardback
- isbn: 9780521195034
- length: 340 pages
- dimensions: 241 x 163 x 28 mm
- weight: 0.61kg
- availability: Available
Table of Contents
Part I. Stochastic Calculus and Optimal Control Theory:
1. Foundations of stochastic calculus
2. Stochastic differential equations: weak formulation
3. Dynamic programming
4. Viscosity solutions of Hamilton-Jacobi-Bellman equations
5. Classical solutions of Hamilton-Jacobi-Bellman equations
Part II. Applications to Mathematical Models in Economics:
6. Production planning and inventory
7. Optimal consumption/investment models
8. Optimal exploitation of renewable resources
9. Optimal consumption models in economic growth
10. Optimal pollution control with long-run average criteria
11. Optimal stopping problems
12. Investment and exit decisions
Part III. Appendices: A. Dini's theorem
B. The Stone-Weierstrass theorem
C. The Riesz representation theorem
D. Rademacher's theorem
E. Vitali's covering theorem
F. The area formula
G. The Brouwer fixed point theorem
H. The Ascoli-Arzela theorem.
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