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Controlled Markov Processes and Viscosity Solutions [electronic resource] / by Wendell H. Fleming, H.M. Soner.

By: Fleming, Wendell H [author.]Contributor(s): Soner, H.M [author.] | SpringerLink (Online service)Material type: TextTextSeries: Stochastic Modelling and Applied Probability ; 25Publisher: New York, NY : Springer New York, 2006Edition: Second EditionDescription: XVII, 429 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9780387310718Subject(s): Mathematics | Operations research | Decision making | Economics, Mathematical | System theory | Probabilities | Control engineering | Robotics | Mechatronics | Mathematics | Probability Theory and Stochastic Processes | Systems Theory, Control | Control, Robotics, Mechatronics | Operation Research/Decision Theory | Quantitative FinanceAdditional physical formats: Printed edition:: No titleDDC classification: 519.2 LOC classification: QA273.A1-274.9QA274-274.9Online resources: Click here to access online
Contents:
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.
In: Springer eBooksSummary: 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.
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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.

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.

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