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 49
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... formulation 210 V.5 Semiconvex , concave approximations 214 V.6 Crandall - Ishii Lemma 216 V.7 Properties of H . 218 V.8 Comparison 219 V.9 Viscosity solutions in Qo 222 V.10 Historical remarks 225 VI VII Introduction VI.2 Risk ...
... formulation 210 V.5 Semiconvex , concave approximations 214 V.6 Crandall - Ishii Lemma 216 V.7 Properties of H . 218 V.8 Comparison 219 V.9 Viscosity solutions in Qo 222 V.10 Historical remarks 225 VI VII Introduction VI.2 Risk ...
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... formulation . . .377 XI.4 Upper and lower value functions 381 XI.5 Dynamic programming principle .382 XI.6 Value functions as viscosity solutions .384 XI.7 Risk sensitive control limit game . .387 XI.8 Time discretizations ... .390 XI.9 ...
... formulation . . .377 XI.4 Upper and lower value functions 381 XI.5 Dynamic programming principle .382 XI.6 Value functions as viscosity solutions .384 XI.7 Risk sensitive control limit game . .387 XI.8 Time discretizations ... .390 XI.9 ...
Page 1
... 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 ...
Page 2
... 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 to < t1 and consider initial times t in the finite interval [ to , t1 ) . ( One could equally well take ∞ < t < t1 , but then certain assumptions in the problem formulation ...
... formulation . A terminal time t1 will be fixed throughout . Let to < t1 and consider initial times t in the finite interval [ to , t1 ) . ( One could equally well take ∞ < t < t1 , but then certain assumptions in the problem formulation ...
Contents
1 | |
Viscosity Solutions | 57 |
Classical Solutions119 | 118 |
Controlled Markov Diffusions in R | 151 |
SecondOrder Case | 199 |
Logarithmic Transformations and Risk Sensitivity | 227 |
Singular Perturbations 261 | 260 |
Singular Stochastic Control | 293 |
Finite Difference Numerical Approximations | 321 |
Differential Games | 375 |
A Duality Relationships 397 | 396 |
References | 409 |
Index 425 | 424 |
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 C₁ C¹(Q calculus of variations Chapter classical solution consider constant constraint controlled Markov diffusion convergence convex Corollary defined definition denote differential games dynamic programming equation dynamic programming principle Dynkin formula Example exists exit finite formulation given Hence HJB equation holds implies inequality initial data Ishii Lemma linear Lipschitz continuous Markov chain Markov control policy Markov processes 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 Section semigroup Soner stochastic control stochastic control problem stochastic differential equations subset Suppose t₁ Theorem 9.1 uniformly continuous unique value function Verification Theorem viscosity solution viscosity subsolution viscosity supersolution