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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Results 1-5 of 81
Page 1
... Section 2. It often happens that a system is being controlled only for x(s) ∈ O, where O is the closure of some given open set O ⊂IRn. Two versions of that situation are formulated in Section 3. In one version, control occurs only ...
... Section 2. It often happens that a system is being controlled only for x(s) ∈ O, where O is the closure of some given open set O ⊂IRn. Two versions of that situation are formulated in Section 3. In one version, control occurs only ...
Page 2
... Section 4, and also Section 7 for infinite time horizon problems. The value function V for a deterministic optimal control problem satisfies, at least for- mally, a first order nonlinear partial differential equation. See (5.3) or (7.10) ...
... Section 4, and also Section 7 for infinite time horizon problems. The value function V for a deterministic optimal control problem satisfies, at least for- mally, a first order nonlinear partial differential equation. See (5.3) or (7.10) ...
Page 5
... Section 3 . 1.3 Finite time horizon problems In this section we formulate some classes of deterministic optimal control problems , which will be studied in the rest of this chapter and in Chapter II . At the end of the section , each of ...
... Section 3 . 1.3 Finite time horizon problems In this section we formulate some classes of deterministic optimal control problems , which will be studied in the rest of this chapter and in Chapter II . At the end of the section , each of ...
Page 12
... Section 3. Boundary conditions for state constrained prob- lems ( class D , Section 3 ) will be described later in Section II.12 . For class A , we have QQo . By ( 3.4 ) the terminal ( Cauchy ) data are ( 5.5 ) V ( t1 , x ) = ( x ) , x ...
... Section 3. Boundary conditions for state constrained prob- lems ( class D , Section 3 ) will be described later in Section II.12 . For class A , we have QQo . By ( 3.4 ) the terminal ( Cauchy ) data are ( 5.5 ) V ( t1 , x ) = ( x ) , x ...
Page 15
... Section VI.8 we will encounter a class of problems in which M ( s ) is negative definite . Such problems are called LQRP problems with indefinite sign . In this case , P ( t ) may not be nonnegative definite and tmin may be finite . The ...
... Section VI.8 we will encounter a class of problems in which M ( s ) is negative definite . Such problems are called LQRP problems with indefinite sign . In this case , P ( t ) may not be nonnegative definite and tmin may be finite . The ...
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