Controlled Markov Processes and Viscosity Solutions / by Wendell H. Fleming, H.M. Soner
(Stochastic Modelling and Applied Probability ; 25)
| データ種別 | 電子ブック |
|---|---|
| 版 | Second Edition |
| 出版者 | New York, NY : Springer New York |
| 出版年 | 2006 |
| 本文言語 | 英語 |
| 大きさ | XVII, 429 p : online resource |
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| 内容注記 | Deterministic 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 |
|---|---|
| 一般注記 | 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 |
| 著者標目 | *Fleming, Wendell H. author Soner, H.M. author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Operations research LCSH:Decision making LCSH:Economics, Mathematical LCSH:System theory LCSH:Probabilities LCSH:Control engineering LCSH:Robotics LCSH:Mechatronics FREE:Mathematics FREE:Probability Theory and Stochastic Processes FREE:Systems Theory, Control FREE:Control, Robotics, Mechatronics FREE:Operation Research/Decision Theory FREE:Quantitative Finance |
| 分 類 | DC23:519.2 |
| 巻冊次 | ISBN:9780387310718 
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| ISBN | 9780387310718 |
| URL | http://dx.doi.org/10.1007/0-387-31071-1 |
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