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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... Stochastic Control VIII.1 Introduction VIII.2 Formal discussion VIII.3 Singular stochastic control VIII.4 Verification theorem .. VIII.5 Viscosity solutions 280 282 290 292 293 293 294 . 296 299 .311 VIII.6 Finite fuel problem . 317 IX ...
... Stochastic Control VIII.1 Introduction VIII.2 Formal discussion VIII.3 Singular stochastic control VIII.4 Verification theorem .. VIII.5 Viscosity solutions 280 282 290 292 293 293 294 . 296 299 .311 VIII.6 Finite fuel problem . 317 IX ...
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... 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 derivatives in incomplete ...
... 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 derivatives in incomplete ...
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... stochastic control for con- tinuous time Markov processes and to the theory of viscosity solutions. We ap- proach stochastic control problems by the method of dynamic programming. The fundamental equation of dynamic programming is a ...
... stochastic control for con- tinuous time Markov processes and to the theory of viscosity solutions. We ap- proach stochastic control problems by the method of dynamic programming. The fundamental equation of dynamic programming is a ...
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... stochastic control problems . In the deterministic case , one simply considers control functions u ( · ) instead of ad- missible control systems ( Section III.9 ) or progressively measurable control processes ( Section IV.5 ) . The ...
... stochastic control problems . In the deterministic case , one simply considers control functions u ( · ) instead of ad- missible control systems ( Section III.9 ) or progressively measurable control processes ( Section IV.5 ) . The ...
Page 57
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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 Cą(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