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 84
Page
... consider Є C1 , 2 ( G ) , where either GQ or G = Q. The spaces cl , k ( G ) , Cl , k ( G ) are defined similarly as above . Þ € The gradient vector and matrix of second - order partial derivatives of Þ ( t , · ) are denoted by DÞ , D2Þ ...
... consider Є C1 , 2 ( G ) , where either GQ or G = Q. The spaces cl , k ( G ) , Cl , k ( G ) are defined similarly as above . Þ € The gradient vector and matrix of second - order partial derivatives of Þ ( t , · ) are denoted by DÞ , D2Þ ...
Page 2
... consider a special class of control problems, in which the control is the time derivative of the state (u(s)= ̇x(s)) and there are no control constraints. Such problems belong to the classical calculus of varia- tions. For a calculus of ...
... consider a special class of control problems, in which the control is the time derivative of the state (u(s)= ̇x(s)) and there are no control constraints. Such problems belong to the classical calculus of varia- tions. For a calculus of ...
Page 3
... Consider the production planning of a factory producing n commodities . Let xi ( s ) , u ( s ) denote respectively the inventory level and production rate for commodity i = 1 , ... , n at time s . In this simple model we assume that the ...
... Consider the production planning of a factory producing n commodities . Let xi ( s ) , u ( s ) denote respectively the inventory level and production rate for commodity i = 1 , ... , n at time s . In this simple model we assume that the ...
Page 4
... consider the problem of controlling the simple harmonic oscilla- tor on a finite time interval t ≤ s ≤ t1 . An initial position and velocity (x1 (t),x 2 (t)) = (x1 ,x2 ) are given. We seek to minimize a quadratic criterion of the form ...
... consider the problem of controlling the simple harmonic oscilla- tor on a finite time interval t ≤ s ≤ t1 . An initial position and velocity (x1 (t),x 2 (t)) = (x1 ,x2 ) are given. We seek to minimize a quadratic criterion of the form ...
Page 5
... 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 become slightly more complicated . ) The objective is to minimize some ...
... 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 become slightly more complicated . ) The objective is to minimize some ...
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