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The Resource Optimal stochastic control, stochastic target problems, and backward SDE, Nizar Touzi ; with chapter 13 by Agnès Tourin

Optimal stochastic control, stochastic target problems, and backward SDE, Nizar Touzi ; with chapter 13 by Agnès Tourin

Label
Optimal stochastic control, stochastic target problems, and backward SDE
Title
Optimal stochastic control, stochastic target problems, and backward SDE
Statement of responsibility
Nizar Touzi ; with chapter 13 by Agnès Tourin
Creator
Contributor
Subject
Language
eng
Summary
  • "This book collects some recent developments in stochastic control theory with applications to financial mathematics. In the first part of the volume, standard stochastic control problems are addressed from the viewpoint of the recently developed weak dynamic programming principle. A special emphasis is put on regularity issues and, in particular, on the behavior of the value function near the boundary. Then a quick review of the main tools from viscosity solutions allowing one to overcome all regularity problems is provided
  • The second part is devoted to 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 presents an overview of backward stochastic differential equations and their extensions to the quadratic case. Backward stochastic differential equations are intimately related to the stochastic version of Pontryagin's maximum principle and can be viewed as a strong version of stochastic target problems in the non-Markov context. The main applications to the hedging problem under market imperfections, the optimal investment problem in the exponential or power expected utility framework, and some recent developments in the context of a Nash equilibrium model for interacting investors, are presented."--Pub. desc
Member of
Cataloging source
GW5XE
http://library.link/vocab/creatorName
Touzi, Nizar
Dewey number
519.2/2
Index
no index present
LC call number
QA274.25
LC item number
.T68 2013
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
Tourin, Agnès
Series statement
Fields Institute Monographs,
Series volume
v. 29
http://library.link/vocab/subjectName
  • Stochastic partial differential equations
  • Stochastic analysis
  • Stochastic control theory
  • MATHEMATICS
  • Stochastic control theory
  • Stochastic analysis
  • Stochastic partial differential equations
Label
Optimal stochastic control, stochastic target problems, and backward SDE, Nizar Touzi ; with chapter 13 by Agnès Tourin
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Backward SDEs and stochastic control
  • Quadratic backward SDEs
  • Probabilistic numerical methods for nonlinear PDEs
  • Introduction to finite differences methods
  • Conditional expectation and linear parabolic PDEs
  • Stochastic control and dynamic programming
  • Optimal stopping and dynamic programming
  • Solving control problems by verification
  • Introduction to viscosity solutions
  • Dynamic programming equation in the viscosity sense
  • Stochastic target problems
  • Second order stochastic target problems
Control code
812174232
Dimensions
unknown
Extent
1 online resource (x, 214 pages).
File format
unknown
Form of item
online
Isbn
9781461442868
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)812174232
Label
Optimal stochastic control, stochastic target problems, and backward SDE, Nizar Touzi ; with chapter 13 by Agnès Tourin
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Backward SDEs and stochastic control
  • Quadratic backward SDEs
  • Probabilistic numerical methods for nonlinear PDEs
  • Introduction to finite differences methods
  • Conditional expectation and linear parabolic PDEs
  • Stochastic control and dynamic programming
  • Optimal stopping and dynamic programming
  • Solving control problems by verification
  • Introduction to viscosity solutions
  • Dynamic programming equation in the viscosity sense
  • Stochastic target problems
  • Second order stochastic target problems
Control code
812174232
Dimensions
unknown
Extent
1 online resource (x, 214 pages).
File format
unknown
Form of item
online
Isbn
9781461442868
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)812174232

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