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 6-10 of 92
Page 5
... control problems to be formulated in 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 ...
... control problems to be formulated in 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 ...
Page 6
... optimal control problem , we must specify for each initial data ( t , x ) a set U ( t , x ) CU ° ( t ) of admissible controls and a payoff functional J ( t , x ; u ) to be minimized . Let us first for- mulate some particular classes of ...
... optimal control problem , we must specify for each initial data ( t , x ) a set U ( t , x ) CU ° ( t ) of admissible controls and a payoff functional J ( t , x ; u ) to be minimized . Let us first for- mulate some particular classes of ...
Page 7
... optimal control problems . C. Final endpoint constraint . Suppose that in case A , the additional restriction x ( t ) EM is imposed , where M is a given closed subset of IR " . In particular , if M = { 1 } consists of a ... Optimal Control 7.
... optimal control problems . C. Final endpoint constraint . Suppose that in case A , the additional restriction x ( t ) EM is imposed , where M is a given closed subset of IR " . In particular , if M = { 1 } consists of a ... Optimal Control 7.
Page 8
... control problem is as follows : given initial data ( t , x ) Q , find u * ( · ) € U ( t , x ) such that J ( t , x ; u * ) ≤ J ( t , x ; u ) for all u ( · ) ¤ U ( t , x ) . Such a u * ( · ) is called an optimal control . Relation ...
... control problem is as follows : given initial data ( t , x ) Q , find u * ( · ) € U ( t , x ) such that J ( t , x ; u * ) ≤ J ( t , x ; u ) for all u ( · ) ¤ U ( t , x ) . Such a u * ( · ) is called an optimal control . Relation ...
Page 9
... optimal control problem . In this section and the following one we study some basic properties of the value function . Then we illustrate the use of these properties in an example for which ... Optimal Control 9 Dynamic programming principle.
... optimal control problem . In this section and the following one we study some basic properties of the value function . Then we illustrate the use of these properties in an example for which ... Optimal Control 9 Dynamic programming principle.
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 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