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 6-10 of 76
Page 2
... Chapter II. Closely related to dynamic programming is the idea of feedback controls, which will also be called in this book Markov control policies. According to a Markov control policy, the control u(s) is chosen based on knowing not ...
... Chapter II. Closely related to dynamic programming is the idea of feedback controls, which will also be called in this book Markov control policies. According to a Markov control policy, the control u(s) is chosen based on knowing not ...
Page 5
... chapter and in Chapter II . At the end of the section , each of these classes of problems appears as a particular case of a general formulation . A terminal time t1 will be fixed throughout . Let to < t1 and consider initial times t in ...
... chapter and in Chapter II . At the end of the section , each of these classes of problems appears as a particular case of a general formulation . A terminal time t1 will be fixed throughout . Let to < t1 and consider initial times t in ...
Page 11
... chapters , this approach requires a knowledge of the value function . Another corollary of the above computations is ... Chapter 2. After formally deriving the dynamic programming partial differential equation ( 5.3 ) , we prove two Veri ...
... chapters , this approach requires a knowledge of the value function . Another corollary of the above computations is ... Chapter 2. After formally deriving the dynamic programming partial differential equation ( 5.3 ) , we prove two Veri ...
Page 17
... chapters a Markov control policy . Consider the differential equation ( 5.23 ) d ds -x ( s ) = f ( s , x ( s ) , u ( s , x ( s ) ) ) , s Є [ t , t1 ] . 1.6 Dynamic programming and Pontryagin's principle In this section we. If ( 5.23 ) ...
... chapters a Markov control policy . Consider the differential equation ( 5.23 ) d ds -x ( s ) = f ( s , x ( s ) , u ( s , x ( s ) ) ) , s Є [ t , t1 ] . 1.6 Dynamic programming and Pontryagin's principle In this section we. If ( 5.23 ) ...
Page 20
... Chapter II . Pontryagin's Principle . During the 1950's Pontryagin formulated a " maximum principle " which provides a general set of necessary conditions for an extremum in an optimal control problem . A statement and proof of ...
... Chapter II . Pontryagin's Principle . During the 1950's Pontryagin formulated a " maximum principle " which provides a general set of necessary conditions for an extremum in an optimal control problem . A statement and proof of ...
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