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 92
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... Optimal Control .......................... 1 I.1 Introduction ... control and viscosity solutions . . . . 78 II.8 Viscosity solutions: first order case . . . . . . . . . . . . . . . . . . . . 83 II.9 Uniqueness: first order case ...
... Optimal Control .......................... 1 I.1 Introduction ... control and viscosity solutions . . . . 78 II.8 Viscosity solutions: first order case . . . . . . . . . . . . . . . . . . . . 83 II.9 Uniqueness: first order case ...
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... control methods to analyze financial market models has expanded at a remarkable rate. A new Chapter X gives an introduction to the role of stochastic optimal control in portfolio optimization and in pricing derivatives in incomplete ...
... control methods to analyze financial market models has expanded at a remarkable rate. A new Chapter X gives an introduction to the role of stochastic optimal control in portfolio optimization and in pricing derivatives in incomplete ...
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... optimal stochastic control for continuous time Markov processes and to the theory of viscosity solutions. We approach stochastic control problems by the method of dynamic programming. The fundamental equation of dynamic programming is a ...
... optimal stochastic control for continuous time Markov processes and to the theory of viscosity solutions. We approach stochastic control problems by the method of dynamic programming. The fundamental equation of dynamic programming is a ...
Page 1
... the other version, only controls which keep x(s) ∈ O for t ≤ s ≤ t1 are allowed (this is called a state constrained control problem.) The method of dynamic programming is the one which will Deterministic Optimal Control Introduction.
... the other version, only controls which keep x(s) ∈ O for t ≤ s ≤ t1 are allowed (this is called a state constrained control problem.) The method of dynamic programming is the one which will Deterministic Optimal Control Introduction.
Page 2
... optimal control problems. 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 problems. 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 ...
Contents
1 | |
Viscosity Solutions | 57 |
Differential Games | 375 |
A Duality Relationships 397 | 396 |
References | 409 |
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 calculus of variations Chapter classical solution consider constant controlled Markov diffusion convergence convex Corollary cost function define definition denote differential games dynamic programming equation dynamic programming principle Dynkin formula Example exists exit finite first formulation G Q0 Hamilton-Jacobi equation Hence HJB equation holds implies inequality initial data Ishii Lemma linear Lipschitz continuous Markov chain Markov control policy Markov processes maximum principle 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 satisfying Section semigroup Soner stochastic control stochastic control problem stochastic differential equations subset Suppose Theorem 9.1 uniformly continuous unique value function Verification Theorem viscosity solution viscosity subsolution viscosity supersolution