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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... stochastic differential equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 III.6 Controlled Markov processes . . . . . . . . . . . . . . . . . . . . . . . . . 130 III.7 Dynamic programming ...
... stochastic differential equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 III.6 Controlled Markov processes . . . . . . . . . . . . . . . . . . . . . . . . . 130 III.7 Dynamic programming ...
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... Differential Games . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375 XI.1 Introduction ... Stochastic Differential Equations: Random Coefficients . .403 References ...
... Differential Games . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375 XI.1 Introduction ... Stochastic Differential Equations: Random Coefficients . .403 References ...
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... stochastic control for continuous time Markov processes and to the theory of ... differential equation of second order, called a Hamilton – Jacobi – Bellman ... equations. Typically, the value function is not smooth enough to satisfy the ...
... stochastic control for continuous time Markov processes and to the theory of ... differential equation of second order, called a Hamilton – Jacobi – Bellman ... equations. Typically, the value function is not smooth enough to satisfy the ...
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... stochastic optimal control problems. In dynamic programming, a value ... differential equation. See (5.3) or (7.10) below. In fact, the value ... equations can be interpreted as Hamilton-Jacobi equations, by using duality for convex ...
... stochastic optimal control problems. In dynamic programming, a value ... differential equation. See (5.3) or (7.10) below. In fact, the value ... equations can be interpreted as Hamilton-Jacobi equations, by using duality for convex ...
Page 120
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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