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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 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.

Synopsis:

This book is intended as an introduction to optimal stochastic control for continuous time Markov processes and to the theory of viscosity solutions. The authors approach stochastic control problems by the method of dynamic programming. The text provides an introduction to dynamic programming for deterministic optimal control problems, as well as to the corresponding theory of viscosity solutions. A new Chapter X gives an introduction to the role of stochastic optimal control in portfolio optimization and in pricing derivatives in incomplete markets. Chapter VI of the First Edition has been completely rewritten, to emphasize the relationships between logarithmic transformations and risk sensitivity. A new Chapter XI gives a concise introduction to two-controller, zero-sum differential games. Also covered are controlled Markov diffusions and viscosity solutions of Hamilton-Jacobi-Bellman equations. The authors have tried, through 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. 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.

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:
9780387260457
Author:
Fleming, Wendell H.
Publisher:
Springer
Author:
Soner, Halil Mete
Author:
Cram101 Textbook Reviews
Author:
Soner, H. M.
Author:
Fleming, W. H.
Location:
New York, NY
Subject:
Engineering - Electrical & Electronic
Subject:
Finance
Subject:
Applied
Subject:
Markov processes
Subject:
Stochastic control theory.
Subject:
Electricity
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:
Education-General
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
Copyright:
Edition Number:
2
Edition Description:
2nd ed. 2006
Series:
Stochastic Modelling and Applied Probability
Series Volume:
25
Publication Date:
20051117
Binding:
HARDCOVER
Language:
English
Pages:
446
Dimensions:
235 x 155 mm 1770 gr

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Related Subjects

Business » Accounting and Finance
Science and Mathematics » Electricity » General Electricity
Science and Mathematics » Mathematics » Applied
Science and Mathematics » Mathematics » Probability and Statistics » General
Science and Mathematics » Mathematics » Probability and Statistics » Statistics

Stochastic Modelling and Applied Probability #25: Controlled Markov Processes and Viscosity Solutions New Hardcover
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$180.25 In Stock
Product details 446 pages Springer - English 9780387260457 Reviews:
"Synopsis" by , This book is intended as an introduction to optimal stochastic control for continuous time Markov processes and to the theory of viscosity solutions. The authors approach stochastic control problems by the method of dynamic programming. The text provides an introduction to dynamic programming for deterministic optimal control problems, as well as to the corresponding theory of viscosity solutions. A new Chapter X gives an introduction to the role of stochastic optimal control in portfolio optimization and in pricing derivatives in incomplete markets. Chapter VI of the First Edition has been completely rewritten, to emphasize the relationships between logarithmic transformations and risk sensitivity. A new Chapter XI gives a concise introduction to two-controller, zero-sum differential games. Also covered are controlled Markov diffusions and viscosity solutions of Hamilton-Jacobi-Bellman equations. The authors have tried, through 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. 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.
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