Controlled Markov Processes and Viscosity SolutionsThis 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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Results 1-5 of 80
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... Bounded region Q VI.6 Small noise limits VI.7 H - infinity norm of a nonlinear system VI.8 Risk sensitive control . . . . VI.9 Logarithmic transformations for Markov processes VI.10 Historical remarks Singular Perturbations VII.1 ...
... Bounded region Q VI.6 Small noise limits VI.7 H - infinity norm of a nonlinear system VI.8 Risk sensitive control . . . . VI.9 Logarithmic transformations for Markov processes VI.10 Historical remarks Singular Perturbations VII.1 ...
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... bounded below } — C ( ) = { all real – valued continuous functions on } — C1 ( ) = bounded functions in C ' ( Σ ) } . If Σ is a Banach space Cp ( ) = { polynomial growing functions in C ( ) } . A function is called polynomially growing ...
... bounded below } — C ( ) = { all real – valued continuous functions on } — C1 ( ) = bounded functions in C ' ( Σ ) } . If Σ is a Banach space Cp ( ) = { polynomial growing functions in C ( ) } . A function is called polynomially growing ...
Page 6
... bounded , Lebesgue measurable , U - valued functions on [ t , to ] . In order to complete the formulation of an optimal control problem , we must specify for each initial data ( t , x ) a set U ( t , x ) CU ° ( t ) of admissible ...
... bounded , Lebesgue measurable , U - valued functions on [ t , to ] . In order to complete the formulation of an optimal control problem , we must specify for each initial data ( t , x ) a set U ( t , x ) CU ° ( t ) of admissible ...
Page 9
... bounded below ( L ≥ −M , ≥ −M for some constant M ≥ 0. ) The method of dynamic programming uses the value function as a tool in the analysis of the optimal control problem . In this section and the following one we study some basic ...
... bounded below ( L ≥ −M , ≥ −M for some constant M ≥ 0. ) The method of dynamic programming uses the value function as a tool in the analysis of the optimal control problem . In this section and the following one we study some basic ...
Page 25
... bounded , then the value function V is always finite . Unfortunately , these assumptions do not cover many examples of interest . In such cases further assumptions of a technical nature are needed to insure finiteness of V. To simplify ...
... bounded , then the value function V is always finite . Unfortunately , these assumptions do not cover many examples of interest . In such cases further assumptions of a technical nature are needed to insure finiteness of V. To simplify ...
Contents
1 | |
Viscosity Solutions | 57 |
Classical Solutions119 | 118 |
Controlled Markov Diffusions in R | 151 |
SecondOrder Case | 199 |
Logarithmic Transformations and Risk Sensitivity | 227 |
Singular Perturbations 261 | 260 |
Singular Stochastic Control | 293 |
Finite Difference Numerical Approximations | 321 |
Differential Games | 375 |
A Duality Relationships 397 | 396 |
References | 409 |
Index 425 | 424 |
Other editions - View all
Controlled Markov Processes and Viscosity Solutions Wendell H. Fleming,Halil Mete Soner No preview available - 2006 |
Common terms and phrases
admissible control assume assumptions boundary condition boundary data bounded brownian motion C₁ C¹(Q calculus of variations Chapter classical solution consider constant constraint controlled Markov diffusion convergence convex Corollary defined definition denote differential games dynamic programming equation dynamic programming principle Dynkin formula Example exists exit finite formulation given Hence HJB equation holds implies inequality initial data Ishii Lemma linear Lipschitz continuous Markov chain Markov control policy Markov processes minimizing Moreover nonlinear obtain optimal control optimal control problem partial derivatives partial differential equation progressively measurable proof of Theorem prove reference probability system Remark result risk sensitive satisfies Section semigroup Soner stochastic control stochastic control problem stochastic differential equations subset Suppose t₁ Theorem 9.1 uniformly continuous unique value function Verification Theorem viscosity solution viscosity subsolution viscosity supersolution