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 30
Page
... Calculus of variations I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 I.9 Calculus of variations II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 I.10 Generalized solutions to Hamilton-Jacobi equations ...
... Calculus of variations I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 I.9 Calculus of variations II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 I.10 Generalized solutions to Hamilton-Jacobi equations ...
Page 2
... calculus of variations. For a calculus of variations problem, the dynamic programming equation is called a Hamilton-Jacobi partial differential equation. Many first-order nonlinear partial differential equations can be interpreted as ...
... calculus of variations. For a calculus of variations problem, the dynamic programming equation is called a Hamilton-Jacobi partial differential equation. Many first-order nonlinear partial differential equations can be interpreted as ...
Page 4
... calculus of variations is to determine a function x(·) which minimizes a functional (2.8) ∫ t1t L(s, x(s), ̇x(s))ds + ψ(x(t1)), subject to given conditions on x(t) and x(t1)). Here, · 4 I. Deterministic Optimal Control.
... calculus of variations is to determine a function x(·) which minimizes a functional (2.8) ∫ t1t L(s, x(s), ̇x(s))ds + ψ(x(t1)), subject to given conditions on x(t) and x(t1)). Here, · 4 I. Deterministic Optimal Control.
Page 5
... calculus of variations problems in some detail in Sections 8 – 10. In the formulation in Section 8, we allow the possibility that the fixed upper limit t1 in (2.8) is replaced by a time τ which is the smaller of t1 and the exit time of ...
... calculus of variations problems in some detail in Sections 8 – 10. In the formulation in Section 8, we allow the possibility that the fixed upper limit t1 in (2.8) is replaced by a time τ which is the smaller of t1 and the exit time of ...
Page 19
... calculus of variations type. For further results about existence and continuity properties of optimal controls see [FR, Chap III], Cesari [Ce] and Section 11. If the control space U is compact and U(t,x) = U0(t), assumption (b) is ...
... calculus of variations type. For further results about existence and continuity properties of optimal controls see [FR, Chap III], Cesari [Ce] and Section 11. If the control space U is compact and U(t,x) = U0(t), assumption (b) is ...
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