Fields Institute Monographs

Optimal Stochastic Control, Stochastic Target Problems, and Backward SDE

Authors: Touzi, Nizar

  • ​Provides a self-contained presentation of the recent developments in Stochastic target problems which cannot be found in any other monograph
  • Approaches quadratic backward stochastic differential equations following the point of view of Tevzadze and presented in a way to maximize the ease of understanding
  • Contains relevant examples from finance, including the Nash equilibrium example​
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Hardcover $139.99
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  • ISBN 978-1-4939-0042-8
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About this book

This book collects some recent developments in stochastic control theory with applications to financial mathematics. We first address standard stochastic control problems from the viewpoint of the recently developed weak dynamic programming principle. A special emphasis is put on the regularity issues and, in particular, on the behavior of the value function near the boundary. We then provide a quick review of the main tools from viscosity solutions which allow to overcome all regularity problems. We next address the class of stochastic target problems which extends in a nontrivial way the standard stochastic control problems. Here the theory of viscosity solutions plays a crucial role in the derivation of the dynamic programming equation as the infinitesimal counterpart of the corresponding geometric dynamic programming equation. The various developments of this theory have been stimulated by applications in finance and by relevant connections with geometric flows. Namely, the second order extension was motivated by illiquidity modeling, and the controlled loss version was introduced following the problem of quantile hedging. The third part specializes to an overview of Backward stochastic differential equations, and their extensions to the quadratic case.​

Reviews

“This is an excellent book on the topic of Stochastic Control Problems (SCP). The author transformed his notes for a graduate course at the Field Institute into a volume that will serve also as a good reference in the area. … The author has chosen the framework of diffusions, which makes the exposition more friendly and accessible to a larger audience, in particular for those who want to learn this topic.” (Jaime San Martín, Bulletin of the American Mathematical Society, Vol. 54 (2), April, 2017)

Table of contents (13 chapters)

Buy this book

eBook $109.00
price for USA in USD (gross)
  • ISBN 978-1-4614-4286-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.99
price for USA in USD
  • ISBN 978-1-4614-4285-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $139.99
price for USA in USD
  • ISBN 978-1-4939-0042-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Optimal Stochastic Control, Stochastic Target Problems, and Backward SDE
Authors
Series Title
Fields Institute Monographs
Series Volume
29
Copyright
2013
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4614-4286-8
DOI
10.1007/978-1-4614-4286-8
Hardcover ISBN
978-1-4614-4285-1
Softcover ISBN
978-1-4939-0042-8
Series ISSN
1069-5273
Edition Number
1
Number of Pages
X, 214
Topics