Optimal Stochastic Control, Stochastic Target Problems, and Backward SDE (Hardcover, 2013 ed.)

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. "

General

Imprint:	Springer-Verlag New York
Country of origin:	United States
Series:	Fields Institute Monographs, 29
Release date:	September 2012
First published:	2013
Authors:	Nizar Touzi
Dimensions:	235 x 155 x 19mm (L x W x T)
Format:	Hardcover
Pages:	214
Edition:	2013 ed.
ISBN-13:	978-1-4614-4285-1
Categories:	Books > Science & Mathematics > Mathematics > Probability & statistics Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Calculus of variations Books > Professional & Technical > Electronics & communications engineering > Electronics engineering > Automatic control engineering > General
LSN:	1-4614-4285-0
Barcode:	9781461442851

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