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 53
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... . . . . . . . . . . . . . . 205 V.4 An equivalent formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 V.5 Semiconvex, concave approximations . . . . . . . . . . . . . . . . . . 214 V.6 Crandall-Ishii Lemma ...
... . . . . . . . . . . . . . . 205 V.4 An equivalent formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 V.5 Semiconvex, concave approximations . . . . . . . . . . . . . . . . . . 214 V.6 Crandall-Ishii Lemma ...
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... formulation . . . . . . . . . . . . . . . . . . . . . . . . . 377 XI.4 Upper and lower value functions . . . . . . . . . . . . . . . . . . . . . . 381 XI.5 Dynamic programming principle . . . . . . . . . . . . . . . . . . . . . . 382 XI ...
... formulation . . . . . . . . . . . . . . . . . . . . . . . . . 377 XI.4 Upper and lower value functions . . . . . . . . . . . . . . . . . . . . . . 381 XI.5 Dynamic programming principle . . . . . . . . . . . . . . . . . . . . . . 382 XI ...
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... formulated in Section 3. In one version, control occurs only until the time of exit from a closed cylindrical region Q = [t0 ,t1] × O. In the other version, only controls which keep x(s) ∈ O for t ≤ s ≤ t1 are allowed (this is called ...
... formulated in Section 3. In one version, control occurs only until the time of exit from a closed cylindrical region Q = [t0 ,t1] × O. In the other version, only controls which keep x(s) ∈ O for t ≤ s ≤ t1 are allowed (this is called ...
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... formulations in classical mechanics. These matters are treated in Section 10. Another part of optimal control theory concerns the existence of optimal controls. In Section 11 we prove two special existence theorems which are used ...
... formulations in classical mechanics. These matters are treated in Section 10. Another part of optimal control theory concerns the existence of optimal controls. In Section 11 we prove two special existence theorems which are used ...
Page 5
... formulation. A terminal time t1 will be fixed throughout. Let t0 < t1 and consider initial times t in the finite interval [t0 ,t1). (One could equally well take −∞ <t<t 1, but then certain assumptions in the problem formulation become ...
... formulation. A terminal time t1 will be fixed throughout. Let t0 < t1 and consider initial times t in the finite interval [t0 ,t1). (One could equally well take −∞ <t<t 1, but then certain assumptions in the problem formulation become ...
Contents
1 | |
Viscosity Solutions | 57 |
Differential Games | 375 |
A Duality Relationships 397 | 396 |
References | 409 |
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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