Stochastic Modelling and Applied Probability

Controlled Markov Processes and Viscosity Solutions

Authors: Fleming, Wendell H., Soner, Halil Mete

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About this book

This book is intended as an introduction to optimal stochastic control for continuous time Markov processes and to the theory of viscosity solutions. Stochastic control problems are treated using the dynamic programming approach. The authors approach stochastic control problems by the method of dynamic programming. The fundamental equation of dynamic programming is a nonlinear evolution equation for the value function. For controlled Markov diffusion processes, this becomes a nonlinear partial differential equation of second order, called a Hamilton-Jacobi-Bellman (HJB) equation. Typically, the value function is not smooth enough to satisfy the HJB equation in a classical sense. Viscosity solutions provide framework in which to study HJB equations, and to prove continuous dependence of solutions on problem data. The theory is illustrated by applications from engineering, management science, and financial economics.

In this second edition, new material on applications to mathematical finance has been added. Concise introductions to risk-sensitive control theory, nonlinear H-infinity control and differential games are also included.

Review of the earlier edition:

"This book is highly recommended to anyone who wishes to learn the dinamic principle applied to optimal stochastic control for diffusion processes. Without any doubt, this is a fine book and most likely it is going to become a classic on the area... ."

SIAM Review, 1994

Table of contents (4 chapters)

Buy this book

eBook $129.00
price for USA (gross)
  • ISBN 978-0-387-31071-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $169.00
price for USA
  • ISBN 978-0-387-26045-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $169.00
price for USA
  • ISBN 978-1-4419-2078-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Controlled Markov Processes and Viscosity Solutions
Authors
Series Title
Stochastic Modelling and Applied Probability
Series Volume
25
Copyright
2006
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York
eBook ISBN
978-0-387-31071-8
DOI
10.1007/0-387-31071-1
Hardcover ISBN
978-0-387-26045-7
Softcover ISBN
978-1-4419-2078-2
Series ISSN
0172-4568
Edition Number
2
Number of Pages
XVII, 429
Topics