Optimal Stochastic Control, Stochastic Target Problems, and Backward SDE

Nizar Touzi

ISBN 10: 1493900420 / ISBN 13: 9781493900428

Edité par Springer New York, Springer US Okt 2014, 2014

A propos de cet article

Neuware -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.¿Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 224 pp. Englisch.

N° de réf. du vendeur 9781493900428

Détails bibliographiques

• Titre: Optimal Stochastic Control, Stochastic Target Problems, and Backward SDE
• Éditeur: Springer New York, Springer US Okt 2014
• Date de parution: 2014
• Langue: anglais
• ISBN à 10 chiffres: 1493900420
• ISBN à 13 chiffres: 9781493900428
• Reliure: Taschenbuch
• État de l'article: Neu
• Dimensions: 235 L x 155 H x 13 P (en millimètres) 235 millimètres de largeur par 155 millimètres de hauteur par 13 millimètres de profondeur
• Poids: 347 grammes

A propos de ce titre

Synopsis

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.​

Présentation de l'éditeur

This book collects recent developments in stochastic control theory with applications to financial mathematics. It approaches quadratic backward stochastic differential equations following the point of view of Tevzadze.