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 84
Page 2
... satisfies, at least formally, a first order nonlinear partial differential 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 ...
... satisfies, at least formally, a first order nonlinear partial differential 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 ...
Page 8
... satisfies the following “switching” condition (3.9). Roughly speaking, condition (3.9) states that if we replace an admissible control by another admissible one after a certain time, then the resulting control is still admissible. More ...
... satisfies the following “switching” condition (3.9). Roughly speaking, condition (3.9) states that if we replace an admissible control by another admissible one after a certain time, then the resulting control is still admissible. More ...
Page 17
... satisfies the optimality condition (5.7) if x∗(·) is a solution to the differential inclusion (5.22). Feedback controls (Markov control policies). Corollary 5.1 is closely related to the idea of optimal feedback control, according to ...
... satisfies the optimality condition (5.7) if x∗(·) is a solution to the differential inclusion (5.22). Feedback controls (Markov control policies). Corollary 5.1 is closely related to the idea of optimal feedback control, according to ...
Page 18
... satisfies the dynamic programming equation (5.3) at a point (t, Then we show how dynamic programming is related to Pontryagin's principle, which gives necessary conditions for to minimize .](t, cc; We call a function V differentiable at ...
... satisfies the dynamic programming equation (5.3) at a point (t, Then we show how dynamic programming is related to Pontryagin's principle, which gives necessary conditions for to minimize .](t, cc; We call a function V differentiable at ...
Page 20
... satisfies (5.3) for almost all (t,x)∈Q. Corollary 6.1. Let U be compact and U(t,x) = U0(t). If V is locally Lipschitz on Q, then V is a generalized solution of the dynamic programming equation (5.3). Later we will prove two theorems ...
... satisfies (5.3) for almost all (t,x)∈Q. Corollary 6.1. Let U be compact and U(t,x) = U0(t). If V is locally Lipschitz on Q, then V is a generalized solution of the dynamic programming equation (5.3). Later we will prove two theorems ...
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