Controlled Markov Processes and Viscosity Solutions

Halil Mete Soner

ISBN 10: 1441920781 / ISBN 13: 9781441920782

Edité par Springer New York, Springer US, 2010

A propos de cet article

Druck auf Anfrage Neuware - Printed after ordering - This book is intended as an introduction to optimal stochastic control for continuous time Markov processes and to the theory of viscosity solutions. Stochastic control problems are treated using the dynamic programming approach. The authors approach stochastic control problems by the method of dynamic programming. The fundamental equation of dynamic programming is a nonlinear evolution equation for the value function. For controlled Markov diffusion processes, this becomes a nonlinear partial differential equation of second order, called a Hamilton-Jacobi-Bellman (HJB) equation. Typically, the value function is not smooth enough to satisfy the HJB equation in a classical sense. Viscosity solutions provide framework in which to study HJB equations, and to prove continuous dependence of solutions on problem data. The theory is illustrated by applications from engineering, management science, and financial economics.In this second edition, new material on applications to mathematical finance has been added. Concise introductions to risk-sensitive control theory, nonlinear H-infinity control and differential games are also included.Review of the earlier edition:'This book is highly recommended to anyone who wishes to learn the dinamic principle applied to optimal stochastic control for diffusion processes. Without any doubt, this is a fine book and most likely it is going to become a classic on the area. .'SIAM Review, 1994.

N° de réf. du vendeur 9781441920782

Détails bibliographiques

• Titre: Controlled Markov Processes and Viscosity Solutions
• Éditeur: Springer New York, Springer US
• Date de parution: 2010
• Langue: anglais
• ISBN à 10 chiffres: 1441920781
• ISBN à 13 chiffres: 9781441920782
• Reliure: Taschenbuch
• Édition: 2ème Édition
• État de l'article: Neu
• Dimensions: 235 L x 155 H x 25 P (en millimètres) 235 millimètres de largeur par 155 millimètres de hauteur par 25 millimètres de profondeur
• Poids: 674 grammes

A propos de ce titre

Synopsis

This book is an introduction to optimal stochastic control for continuous time Markov processes and the theory of viscosity solutions. The authors approach stochastic control problems by the method of dynamic programming. The text covers dynamic programming for deterministic optimal control problems, as well as to the corresponding theory of viscosity solutions. New chapters introduce the role of stochastic optimal control in portfolio optimization and in pricing derivatives in incomplete markets and two-controller, zero-sum differential games. Also covered are controlled Markov diffusions and viscosity solutions of Hamilton-Jacobi-Bellman equations. The authors use illustrative examples and selective material to connect stochastic control theory with other mathematical areas (e.g. large deviations theory) and with applications to engineering, physics, management, and finance.

Présentation de l'éditeur

This book is an introduction to optimal stochastic control for continuous time Markov processes and the theory of viscosity solutions. It covers dynamic programming for deterministic optimal control problems, as well as to the corresponding theory of viscosity solutions. New chapters in this second edition introduce the role of stochastic optimal control in portfolio optimization and in pricing derivatives in incomplete markets and two-controller, zero-sum differential games.