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

Format:

Book

Author/Creator:

Touzi, Nizar

Contributor:

Tourin, Agnès

Series:

Fields Institute monographs v. 29

Fields Institute Monographs 1069-5273 v. 29

Language:

English

Subjects (All):

Stochastic partial differential equations.

Stochastic analysis.

Stochastic control theory.

Physical Description:

1 online resource

Place of Publication:

[Toronto, Ont.] Fields Institute for Research in the Mathematical Sciences New York, NY Springer ©2013

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

Contents:

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 Backward SDEs and stochastic control Quadratic backward SDEs Probabilistic numerical methods for nonlinear PDEs Introduction to finite differences methods

Notes:

Includes bibliographical references

Print version record

Other Format:

Print version Touzi, Nizar. Optimal stochastic control, stochastic target problems, and backward SDE

ISBN:

9781461442868

1461442869

OCLC:

812174232

Access Restriction:

Restricted for use by site license