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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... Bounded region Q . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 VI.6 Small noise limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 VI.7 H-infinity norm of a nonlinear system ...
... Bounded region Q . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 VI.6 Small noise limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 VI.7 H-infinity norm of a nonlinear system ...
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... bounded below} C'(E) : {all real — valued continuous functions on E} C'b(E) : bounded functions in C(E)}. If E is a Banach space C'p(E) : {polynomial growing functions in C(E)}. A function Q5 is called polynomially growing if there ...
... bounded below} C'(E) : {all real — valued continuous functions on E} C'b(E) : bounded functions in C(E)}. If E is a Banach space C'p(E) : {polynomial growing functions in C(E)}. A function Q5 is called polynomially growing if there ...
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... bounded below (L Z —M,Q Z —M for some constant M Z O.) 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 Z —M,Q Z —M for some constant M Z O.) 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 ...
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... 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 the ...
... 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 the ...
Page 35
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Contents
1 | |
Viscosity Solutions | 57 |
Differential Games | 375 |
A Duality Relationships 397 | 396 |
References | 409 |
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 calculus of variations Chapter classical solution consider constant controlled Markov diffusion convergence convex Corollary cost function define definition denote differential games dynamic programming equation dynamic programming principle Dynkin formula Example exists exit finite first formulation G Q0 Hamilton-Jacobi equation Hence HJB equation holds implies inequality initial data Ishii Lemma linear Lipschitz continuous Markov chain Markov control policy Markov processes maximum principle 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 satisfying Section semigroup Soner stochastic control stochastic control problem stochastic differential equations subset Suppose Theorem 9.1 uniformly continuous unique value function Verification Theorem viscosity solution viscosity subsolution viscosity supersolution