Stochastic control and mathematical modeling : applications in economics / Hiroaki Morimoto.

Format:

Book

Author/Creator:

Morimoto, Hiroaki, 1945- author.

Series:

Encyclopedia of mathematics and its applications ; v. 131.

Encyclopedia of mathematics and its applications ; volume 131

Language:

English

Subjects (All):

Stochastic control theory.

Optimal stopping (Mathematical statistics).

Stochastic differential equations.

Physical Description:

1 online resource (xiii, 325 pages) : digital, PDF file(s).

Other Title:

Stochastic Control & Mathematical Modeling

Place of Publication:

Cambridge : Cambridge University Press, 2010.

Language Note:

English

Summary:

This is a concise and elementary introduction to stochastic control and mathematical modelling. 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 Hamilton-Jacobi-Bellman (HJB) equation with boundary conditions. Major mathematical prerequisites are contained in the preliminary chapters or in the appendix so that readers can proceed without referring to other materials.

Contents:

Stochastic calculus and optimal control theory

Foundations of stochastic calculus

Stochastic differential equations: weak formulation

Dynamic programming

Viscosity solutions of Hamilton-Jacobi-Bellman equations

Classical solutions of Hamilton-Jacobi-Bellman equations

Applications to mathematical models in economics

Production planning and inventory

Optimal consumption/investment models

Optimal exploitation of renewable resources

Optimal consumption models in economic growth

Optimal pollution control with long-run average criteria

Optimal stopping problems

Investment and exit decisions

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-Arzelà theorem.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references and index.

ISBN:

1-139-88581-2

1-107-10187-5

1-107-09937-4

1-107-08697-3

1-107-09319-8

1-139-08735-5

1-107-09003-2

OCLC:

776973799