Téléchargez le livre : Optimal Stochastic Control, Stochastic Target Problems, and Backward SDE

Optimal Stochastic Control, Stochastic Target Problems, and Backward SDE

de

Éditeur :

Springer


Collection :

Fields Institute Monographs

Paru le : 2012-09-25

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Description
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 secondorder 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.?
Pages
214 pages
Collection
Fields Institute Monographs
Parution
2012-09-25
Marque
Springer
EAN papier
9781461442851
EAN EPUB
9781461442868
Informations sur l'ebook
Nombre pages copiables
2
Nombre pages imprimables
21
Taille du fichier
3031 Ko
Prix
116,04 €

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