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 89
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... Optimal Control of Markov Processes : Classical Solutions119 III.1 Introduction . 119 III.2 Markov processes and ... problem . 152 IV.3 Hamilton - Jacobi - Bellman PDE 155 IV.4 Uniformly parabolic case . 161 IV.5 Infinite time horizon . 164 ...
... Optimal Control of Markov Processes : Classical Solutions119 III.1 Introduction . 119 III.2 Markov processes and ... problem . 152 IV.3 Hamilton - Jacobi - Bellman PDE 155 IV.4 Uniformly parabolic case . 161 IV.5 Infinite time horizon . 164 ...
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... optimal stochastic control for con- tinuous time Markov processes and to the theory of viscosity solutions. We ap ... problem data. The book begins with an introduction to dynamic programming for de- terministic optimal control problems ...
... optimal stochastic control for con- tinuous time Markov processes and to the theory of viscosity solutions. We ap ... problem data. The book begins with an introduction to dynamic programming for de- terministic optimal control problems ...
Page 1
... problem is one of optimal control. In this introductory chapter we are concerned with deterministic optimal control models in which the dynamics of the system being controlled are gov- erned by a set of ... Optimal Control Introduction.
... problem is one of optimal control. In this introductory chapter we are concerned with deterministic optimal control models in which the dynamics of the system being controlled are gov- erned by a set of ... Optimal Control Introduction.
Page 2
... optimal control prob- lems. In dynamic programming, a value function V is introduced which is the optimum value of the payoff considered as a function of initial data. See Section 4, and also Section 7 for infinite time horizon problems ...
... optimal control prob- lems. In dynamic programming, a value function V is introduced which is the optimum value of the payoff considered as a function of initial data. See Section 4, and also Section 7 for infinite time horizon problems ...
Page 3
... problem on a given finite time interval t≤s ≤ t1 . Given an initial inventory x ( t ) = x , the problem is to choose the production rate u ( s ) to minimize ( 2.2 ) t1 h ( x ( s ) ) ds + 4 ( x ( t1 ) ) . We call t1 ... Optimal Control 3.
... problem on a given finite time interval t≤s ≤ t1 . Given an initial inventory x ( t ) = x , the problem is to choose the production rate u ( s ) to minimize ( 2.2 ) t1 h ( x ( s ) ) ds + 4 ( x ( t1 ) ) . We call t1 ... Optimal Control 3.
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 C¹(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