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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... partial differential equations used in these chapters concern classical solutions ( not viscosity solutions . ) These chapters can be read independently of Chapters II and V. On the other hand , readers wishing an introduction to ...
... partial differential equations used in these chapters concern classical solutions ( not viscosity solutions . ) These chapters can be read independently of Chapters II and V. On the other hand , readers wishing an introduction to ...
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... partial derivatives of or orders ≤ k are bounded } Ck ( 0 ) = { € Ck ( O ) : all partial derivatives of of orders ≤ k are 4 Given O CIR " open Q = [ to ,. polynomially growing } . For a measurable set E CIR " , we say that Є Ck ( E ) ...
... partial derivatives of or orders ≤ k are bounded } Ck ( 0 ) = { € Ck ( O ) : all partial derivatives of of orders ≤ k are 4 Given O CIR " open Q = [ to ,. polynomially growing } . For a measurable set E CIR " , we say that Є Ck ( E ) ...
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... partial derivatives of or orders < in t and of orders ≤ k in x are continuous on Ĝ . For example , we often 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 ...
... partial derivatives of or orders < in t and of orders ≤ k in x are continuous on Ĝ . For example , we often 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 ...
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... partial differential equation. See (5.3) or (7.10) below. In fact, the value ... derivative of the state (u(s)= ̇x(s)) and there are no control constraints ... differential equations can be interpreted as Hamilton-Jacobi equations, by ...
... partial differential equation. See (5.3) or (7.10) below. In fact, the value ... derivative of the state (u(s)= ̇x(s)) and there are no control constraints ... differential equations can be interpreted as Hamilton-Jacobi equations, by ...
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... partial derivatives fx , La . , 9x , Va , exist and are continuous for i = 1 , ... · · , n . As above , let u ... differential equations ( 6.2 ) d ds Pj ( s ) == n მ - fi ( s , x * ( s ) , u * ( s ) ) Pi ( s ) dxj i = 1 მ · L ( s , x ...
... partial derivatives fx , La . , 9x , Va , exist and are continuous for i = 1 , ... · · , n . As above , let u ... differential equations ( 6.2 ) d ds Pj ( s ) == n მ - fi ( s , x * ( s ) , u * ( s ) ) Pi ( s ) dxj i = 1 მ · L ( s , 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 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