Stochastic control and mathematical modeling : applications in economics /

Stochastic control and mathematical modeling : applications in economics /

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Bibliographic Details
Author / Creator:	Morimoto, Hiroaki, 1945-
Imprint:	Cambridge ; New York : Cambridge University Press, 2010.
Description:	xiii, 325 p. ; 25 cm.
Language:	English
Series:	Encyclopedia of mathematics and its applications ; [131] Encyclopedia of mathematics and its applications ; v. 131.
Subject:	Stochastic control theory. Optimal stopping (Mathematical statistics) Stochastic differential equations. Optimal stopping (Mathematical statistics) Stochastic control theory. Stochastic differential equations.
Format:	Print Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/7933554

Hidden Bibliographic Details
ISBN:	9780521195034 (hardback) 0521195039 (hardback)
Notes:	Series numbering from jacket. Includes bibliographical references and index.
Summary:	"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"--Provided by publisher.

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