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 88
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... 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 . Rn denotes n - dimensional euclidean ...
... 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 . Rn denotes n - dimensional euclidean ...
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... example , we often consider Є C1 , 2 ( G ) , where either GQ or G = Q. The spaces cl , k ( G ) , Cl , k ( G ) are defined similarly as above . Þ € The gradient vector and matrix of second - order partial derivatives of Þ ( t , · ) are ...
... example , we often consider Є C1 , 2 ( G ) , where either GQ or G = Q. The spaces cl , k ( G ) , Cl , k ( G ) are defined similarly as above . Þ € The gradient vector and matrix of second - order partial derivatives of Þ ( t , · ) are ...
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... Examples. We start our discussion by giving some examples. In choosing examples, in this section and later in the book, we have included several highly simplified models chosen from such diverse applications as inventory theory , 2 I ...
... Examples. We start our discussion by giving some examples. In choosing examples, in this section and later in the book, we have included several highly simplified models chosen from such diverse applications as inventory theory , 2 I ...
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... Example 2.1 . Consider the production planning of a factory producing n commodities . Let xi ( s ) , u ( s ) denote respectively the inventory level and production rate for commodity i = 1 , ... , n at time s . In this simple model we ...
... Example 2.1 . Consider the production planning of a factory producing n commodities . Let xi ( s ) , u ( s ) denote respectively the inventory level and production rate for commodity i = 1 , ... , n at time s . In this simple model we ...
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... Example 2.3. If U = [−a, a] with a < ∞, it is an example of a linear regulator problem with a saturation constraint. One can also consider the problem of controlling the solution x(s)=(x 1 (s), x2 (s)) to (2.4) on an infinite time ...
... Example 2.3. If U = [−a, a] with a < ∞, it is an example of a linear regulator problem with a saturation constraint. One can also consider the problem of controlling the solution x(s)=(x 1 (s), x2 (s)) to (2.4) on an infinite time ...
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