SPRINGER OPTIMAL STOCHASTIC CONTROL STOCHASTIC TARGET PROBLEMS AND BACKWARD SDE 2013 RETAIL

TITLE: OPTIMAL STOCHASTIC CONTROL, STOCHASTIC TARGET
PROBLEMS, AND BACKWARD SDE
PUBLISHER: SPRINGER LANGUAGE: ENGLISH
LINK: http://is.gd/C0ujzF RELEASE TYPE: RETAIL
FORMAT: PDF RELEASE DATE: 2014.06.22
ISBN: 9781461442868 STORE DATE: 2013
SAVED.MONEY: 45 EURO DISKCOUNT: 01 x 05MB
AUTHOR: TOUZI, NIZAR

BOOK

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

The book concludes with a review of the numerical approximation
techniques for nonlinear partial differential equations based on
monotonic schemes methods in the theory of viscosity solutions