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 63
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... Control of Markov Processes : Classical Solutions119 III.1 Introduction . 119 III.2 ... stochastic differential equations 127 III.6 Controlled Markov processes 130 ... problem . 152 IV.3 Hamilton - Jacobi - Bellman PDE 155 IV.4 Uniformly ...
... Control of Markov Processes : Classical Solutions119 III.1 Introduction . 119 III.2 ... stochastic differential equations 127 III.6 Controlled Markov processes 130 ... problem . 152 IV.3 Hamilton - Jacobi - Bellman PDE 155 IV.4 Uniformly ...
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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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... problem X.4 General utility and duality X.5 X.6 X.7 X.8 Portfolio selection ... control limit game . .387 XI.8 Time discretizations ... .390 XI.9 Strictly ... Stochastic Differential Equations : Random Coefficients . . 403 References ...
... problem X.4 General utility and duality X.5 X.6 X.7 X.8 Portfolio selection ... control limit game . .387 XI.8 Time discretizations ... .390 XI.9 Strictly ... Stochastic Differential Equations : Random Coefficients . . 403 References ...
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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 ...
Page 2
... stochastic optimal control prob- lems. In dynamic programming, a value function V is introduced which is the optimum ... control problem satisfies, at least for- mally, a first order nonlinear partial differential equation. See (5.3) or ...
... stochastic optimal control prob- lems. In dynamic programming, a value function V is introduced which is the optimum ... control problem satisfies, at least for- mally, a first order nonlinear partial differential equation. See (5.3) or ...
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 |
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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