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
Page
... Dynamic programming principle . . . . . . . . . . . . . . . . . . . . . . 9 I.5 Dynamic programming equation . . . . . . . . . . . . . . . . . . . . . . 11 I.6 Dynamic programming and Pontryagin's principle. . . . . . . 18 I.7 ...
... Dynamic programming principle . . . . . . . . . . . . . . . . . . . . . . 9 I.5 Dynamic programming equation . . . . . . . . . . . . . . . . . . . . . . 11 I.6 Dynamic programming and Pontryagin's principle. . . . . . . 18 I.7 ...
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... dynamic programming. The fundamental equation of dynamic programming is a nonlinear evolution equation for the value function. For controlled Markov diffusion processes on n - dimensional euclidean space, the dynamic programming equation ...
... dynamic programming. The fundamental equation of dynamic programming is a nonlinear evolution equation for the value function. For controlled Markov diffusion processes on n - dimensional euclidean space, the dynamic programming equation ...
Page 2
... equation. See (5.3) or (7.10) below. In fact, the value function V often does not have the smoothness properties needed to interpret it as a solution to the dynamic programming partial differential equation in the usual (“classical ...
... equation. See (5.3) or (7.10) below. In fact, the value function V often does not have the smoothness properties needed to interpret it as a solution to the dynamic programming partial differential equation in the usual (“classical ...
Page 11
... dynamic programming principle. It is the basis of the solution technique developed by Bellman in the 1950's [Be]. An interesting observation is that an optimal control u∗(·) ∈ U(t,x) minimizes (4.3) at ... Dynamic programming equation.
... dynamic programming principle. It is the basis of the solution technique developed by Bellman in the 1950's [Be]. An interesting observation is that an optimal control u∗(·) ∈ U(t,x) minimizes (4.3) at ... Dynamic programming equation.
Page 12
... dynamic programming equation (5.3') is sometimes also called a HamiltonGJacobiGBellman PDE. Equation (5.3) is to be considered in Q, with appropriate terminal or boundary conditions. Let us describe such conditions for problems of the ...
... dynamic programming equation (5.3') is sometimes also called a HamiltonGJacobiGBellman PDE. Equation (5.3) is to be considered in Q, with appropriate terminal or boundary conditions. Let us describe such conditions for problems of the ...
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