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. |
From inside the book
Results 1-5 of 63
Page
... nonlinear system VI.8 Risk sensitive control . . . . VI.9 Logarithmic transformations for Markov processes VI.10 Historical remarks Singular Perturbations VII.1 Introduction VII.2 Examples ... VII.3 Barles and Perthame procedure . VII.4 ...
... nonlinear system VI.8 Risk sensitive control . . . . VI.9 Logarithmic transformations for Markov processes VI.10 Historical remarks Singular Perturbations VII.1 Introduction VII.2 Examples ... VII.3 Barles and Perthame procedure . VII.4 ...
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... nonlinear H-infinity control and as totally risk-averse limits in risk-sensitive stochastic control. Other changes from the First Edition include an updated treatment in Chapter V of viscosity solutions for second-order PDEs. Mate- rial ...
... nonlinear H-infinity control and as totally risk-averse limits in risk-sensitive stochastic control. Other changes from the First Edition include an updated treatment in Chapter V of viscosity solutions for second-order PDEs. Mate- rial ...
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... nonlinear evolution equation for the value function. For controlled Markov diffusion processes on n - dimensional euclidean space, the dynamic programming equation becomes a nonlinear partial differential equation of second order ...
... nonlinear evolution equation for the value function. For controlled Markov diffusion processes on n - dimensional euclidean space, the dynamic programming equation becomes a nonlinear partial differential equation of second order ...
Page 2
... nonlinear partial differential 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 ...
... nonlinear partial differential 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 ...
Page 11
... nonlinear partial differential equation satisfied by the value function . In general however , the value function is not differentiable . In that case a notion of “ weak " solutions to this equation is needed . This will be the subject ...
... nonlinear partial differential equation satisfied by the value function . In general however , the value function is not differentiable . In that case a notion of “ weak " solutions to this equation is needed . This will be the subject ...
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