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Stochastic Control and Mathematical Modeling
Applications in Economics

£105.00

Part of Encyclopedia of Mathematics and its Applications

  • Date Published: April 2010
  • availability: Available
  • format: Hardback
  • isbn: 9780521195034

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  • 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.

    • Ideal for students and researchers who do not major in control theory
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    Product details

    • Date Published: April 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.

  • Author

    Hiroaki Morimoto, Ehime University, Japan
    Hiroaki Morimoto is a Professor in Mathematics at the Graduate School of Science and Engineering at Ehime University. His research interests include stochastic control, mathematical economics and finance and insurance applications, and the viscosity solution theory.

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