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 92
Page
... Dynamic programming principle 9 I.5 Dynamic programming equation 11 I.6 Dynamic programming and Pontryagin's principle . 18 I.7 Discounted cost with infinite horizon 25 1.8 Calculus of variations I .. 33 I.9 Calculus of variations II 37 ...
... Dynamic programming principle 9 I.5 Dynamic programming equation 11 I.6 Dynamic programming and Pontryagin's principle . 18 I.7 Discounted cost with infinite horizon 25 1.8 Calculus of variations I .. 33 I.9 Calculus of variations II 37 ...
Page
... dynamic programming. The fundamental equation of dynamic programming is a nonlinear evolution equation for the value function. For controlled Markov diffusion processes on n - dimensional euclidean space, the dynamic programming equation ...
... dynamic programming. The fundamental equation of dynamic programming is a nonlinear evolution equation for the value function. For controlled Markov diffusion processes on n - dimensional euclidean space, the dynamic programming equation ...
Page 2
... equation. See (5.3) or (7.10) below. In fact, the value function V often does not have the smoothness prop- erties needed to interpret it as a solution to the dynamic programming partial differential equation in the usual (“classical ...
... equation. See (5.3) or (7.10) below. In fact, the value function V often does not have the smoothness prop- erties needed to interpret it as a solution to the dynamic programming partial differential equation in the usual (“classical ...
Page 11
... dynamic programming principle . It is the basis of the solution technique developed by Bellman in the 1950's [ Be ] . An interesting observation is that an optimal control u * ( · ) € U ( t , x ) minimizes ... Dynamic programming equation.
... dynamic programming principle . It is the basis of the solution technique developed by Bellman in the 1950's [ Be ] . An interesting observation is that an optimal control u * ( · ) € U ( t , x ) minimizes ... Dynamic programming equation.
Page 12
... equation of first order , which we refer to as the dynamic programming equation or simply DPE . In ( 5.3 ) , D & V denotes the gradient of V ( t ,. ) . It is notationally convenient to rewrite ( 5.3 ) as ( 5.3 ' ) მ Ət · V ( t , x ) + ...
... equation of first order , which we refer to as the dynamic programming equation or simply DPE . In ( 5.3 ) , D & V denotes the gradient of V ( t ,. ) . It is notationally convenient to rewrite ( 5.3 ) as ( 5.3 ' ) მ Ət · V ( t , x ) + ...
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 Cą(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