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Stochastic Modelling and Applied Probability #25: Controlled Markov Processes and Viscosity Solutions

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Stochastic Modelling and Applied Probability #25: Controlled Markov Processes and Viscosity Solutions Cover

 

Synopses & Reviews

Publisher Comments:

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

Synopsis:

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.

Table of Contents

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.

Product Details

ISBN:
9781441920782
Author:
Fleming, Wendell H.
Publisher:
Springer
Author:
Soner, Halil Mete
Location:
New York, NY
Subject:
Statistics
Subject:
Probability Theory and Stochastic Processes
Subject:
Systems Theory, Control
Subject:
Control, Robotics, Mechatronics
Subject:
Operations Research/Decision Theory
Subject:
Quantitative Finance <P>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
Subject:
Business-Accounting and Finance
Subject:
Quantitative Finance
Subject:
Operation Research/Decision Theory
Subject:
Mathematics
Subject:
B
Subject:
mathematics and statistics
Subject:
Distribution (Probability theory)
Subject:
Systems theory.
Subject:
Operations Research
Subject:
Finance
Copyright:
Edition Description:
Softcover reprint of hardcover 2nd ed. 2006
Series:
Stochastic Modelling and Applied Probability
Series Volume:
25
Publication Date:
20101119
Binding:
TRADE PAPER
Language:
English
Pages:
446
Dimensions:
235 x 155 mm 674 gr

Related Subjects

Business » Accounting and Finance
Reference » Science Reference » Technology
Science and Mathematics » Electricity » General Electricity
Science and Mathematics » Mathematics » Applied
Science and Mathematics » Physics » General

Stochastic Modelling and Applied Probability #25: Controlled Markov Processes and Viscosity Solutions New Trade Paper
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Product details 446 pages Springer - English 9781441920782 Reviews:
"Synopsis" by , 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.
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