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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... . . . . . 230 VI.4 Auxiliary stochastic control problem . . . . . . . . . . . . . . . . . . 235 VI.5 Bounded region Q . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 VI.6 Small noise limits ...
... . . . . . 230 VI.4 Auxiliary stochastic control problem . . . . . . . . . . . . . . . . . . 235 VI.5 Bounded region Q . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 VI.6 Small noise limits ...
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... stochastic calculus and control methods to analyze financial market models has expanded at a remarkable rate. A new Chapter X gives an introduction to the role of stochastic optimal control in portfolio optimization and in pricing ...
... stochastic calculus and control methods to analyze financial market models has expanded at a remarkable rate. A new Chapter X gives an introduction to the role of stochastic optimal control in portfolio optimization and in pricing ...
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... stochastic control for continuous time Markov processes and to the theory of viscosity solutions. We approach stochastic control problems by the method of dynamic programming. The fundamental equation of dynamic programming is a ...
... stochastic control for continuous time Markov processes and to the theory of viscosity solutions. We approach stochastic control problems by the method of dynamic programming. The fundamental equation of dynamic programming is a ...
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... stochastic control problems. 1n the deterministic case, one simply considers control functions instead of admissible control systems (Section 111.9) or progressively measurable control processes (Section 1V.5). The following is one ...
... stochastic control problems. 1n the deterministic case, one simply considers control functions instead of admissible control systems (Section 111.9) or progressively measurable control processes (Section 1V.5). The following is one ...
Page 57
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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