Controlled Markov Processes and Viscosity Solutions

Lieferzeit: Lieferbar innerhalb 14 Tagen

181,89 €

inkl. 7 % MwSt. zzgl. Versandkosten

Stochastic Modelling and Applied Probability 25

ISBN: 0387260455
ISBN 13: 9780387260457
Autor: Fleming, Wendell H/Soner, Halil Mete
Verlag: Springer Verlag GmbH
Umfang: xvii, 429 S.
Erscheinungsdatum: 17.11.2005
Auflage: 2/2006
Format: 2.4 x 24.1 x 15.8
Gewicht: 723 g
Produktform: Gebunden/Hardback
Einband: GEB

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

Artikelnummer: 1445938 Kategorie:

Beschreibung

InhaltsangabePreface.- Preface to Second Edition.- Notation.- Deterministic Optimal Control.- Viscosity Solutions.- Optimal Control of Markov Processes:Classical Solutions.- Controlled Markov Diffusions in IRn.- Viscosity Solutions: Scond-Order Case.- Logarithmic Transformations and Risk Sensitivity.- Singular Perturbations.- Singular Stochastic Control.- Finite Difference Numerical Approximations.- Applications to Finance.- Differential Games.- Duality Relationships.- Dynkin 's Formula for Random Evolutions with Markov Chain Parameters.- Extension of Lipschitz Continuous Functions; Smoothing.

Inhaltsverzeichnis

Preface.- Preface to Second Edition.- Notation.- Deterministic Optimal Control.- Viscosity Solutions.- Optimal Control of Markov Processes:Classical Solutions.- Controlled Markov Diffusions in IRn.- Viscosity Solutions: Scond-Order Case.- Logarithmic Transformations and Risk Sensitivity.- Singular Perturbations.- Singular Stochastic Control.- Finite Difference Numerical Approximations.- Applications to Finance.- Differential Games.- Duality Relationships.- Dynkin ¿s Formula for Random Evolutions with Markov Chain Parameters.- Extension of Lipschitz Continuous Functions; Smoothing.

Autorenporträt

InhaltsangabeDeterministic Optimal Control.- Viscosity Solutions.- Optimal Control of Markov Processes: Classical Solutions.- Controlled Markov Diffusions in ?n.- Viscosity Solutions: Second-Order Case.- Logarithmic Transformations and Risk Sensitivity.- Singular Perturbations.- Singular Stochastic Control.- Finite Difference Numerical Approximations.- Applications to Finance.- Differential Games.

Das könnte Ihnen auch gefallen …