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. |
From inside the book
Results 1-5 of 73
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... Chapter X gives an introduction to the role of stochastic optimal control in portfolio optimization and in pricing derivatives in incomplete markets. Risk-sensitive stochastic control has been another active research area since the ...
... Chapter X gives an introduction to the role of stochastic optimal control in portfolio optimization and in pricing derivatives in incomplete markets. Risk-sensitive stochastic control has been another active research area since the ...
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... Chapter I, and to the corresponding theory of viscosity solutions in Chapter II. A rather elementary introduction to dynamic programming for controlled Markov processes is provided in Chapter III. This is followed by the more technical ...
... Chapter I, and to the corresponding theory of viscosity solutions in Chapter II. A rather elementary introduction to dynamic programming for controlled Markov processes is provided in Chapter III. This is followed by the more technical ...
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... Chapter IX. Chapters III, IV and VI rely on probabilistic methods. The only results about partial differential equations used in these chapters concern classical solutions (not viscosity solutions.) These chapters can be read ...
... Chapter IX. Chapters III, IV and VI rely on probabilistic methods. The only results about partial differential equations used in these chapters concern classical solutions (not viscosity solutions.) These chapters can be read ...
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... chapters. For example, Theorem II.5.1 refers to Theorem 5.1 in Chapter II. Similarly, IV(3.7) refers to formula (3.7) of Chapter IV; and within Chapter IV we write simply (3.7) for such a reference. IRn denotes n-dimensional euclidean ...
... chapters. For example, Theorem II.5.1 refers to Theorem 5.1 in Chapter II. Similarly, IV(3.7) refers to formula (3.7) of Chapter IV; and within Chapter IV we write simply (3.7) for such a reference. IRn denotes n-dimensional euclidean ...
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... chapter we are concerned with deterministic optimal control models in which the dynamics of the system being controlled are governed by a set of ordinary differential equations. In these models the system operates for times s in some ...
... chapter we are concerned with deterministic optimal control models in which the dynamics of the system being controlled are governed by a set of ordinary differential equations. In these models the system operates for times s in some ...
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