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 viscosity ...
... 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 viscosity ...
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... partial derivatives of Q5 or orders § k are bounded} C17,“ (O) I G Ck (O) : all partial derivatives of Q5 of orders § k are polynomially growing}. For a measurable set E C R”, we say that Q5 G C'k( if there exist E open with E C E and ...
... partial derivatives of Q5 or orders § k are bounded} C17,“ (O) I G Ck (O) : all partial derivatives of Q5 of orders § k are polynomially growing}. For a measurable set E C R”, we say that Q5 G C'k( if there exist E open with E C E and ...
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... partial derivatives of Q5 or orders § E in t and of orders § k in an are continuous on G. For example, we often consider Q3 G G1'2(G), where either G : Q or G : The spaces Cg'k(G), GŁ'k(G) are defined similarly as above. The gradient ...
... partial derivatives of Q5 or orders § E in t and of orders § k in an are continuous on G. For example, we often consider Q3 G G1'2(G), where either G : Q or G : The spaces Cg'k(G), GŁ'k(G) are defined similarly as above. The gradient ...
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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 fxi,Lxi,gxi,ψxi exist and are continuous for i = 1,···,n. As above, let u∗(·) denote an optimal ... differential equations (6.2) d dsPj(s) = − n∑ i=1 ∂ ∂xjfi(s, x∗(s),u∗(s))P i(s) − ∂ ∂xjL(s, x∗(s),u∗(s)) ...
... partial derivatives fxi,Lxi,gxi,ψxi exist and are continuous for i = 1,···,n. As above, let u∗(·) denote an optimal ... differential equations (6.2) d dsPj(s) = − n∑ i=1 ∂ ∂xjfi(s, x∗(s),u∗(s))P i(s) − ∂ ∂xjL(s, x∗(s),u∗(s)) ...
Contents
1 | |
Viscosity Solutions | 57 |
Differential Games | 375 |
A Duality Relationships 397 | 396 |
References | 409 |
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 calculus of variations Chapter classical solution consider constant controlled Markov diffusion convergence convex Corollary cost function define definition denote differential games dynamic programming equation dynamic programming principle Dynkin formula Example exists exit finite first formulation G Q0 Hamilton-Jacobi equation Hence HJB equation holds implies inequality initial data Ishii Lemma linear Lipschitz continuous Markov chain Markov control policy Markov processes maximum principle 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 satisfying Section semigroup Soner stochastic control stochastic control problem stochastic differential equations subset Suppose Theorem 9.1 uniformly continuous unique value function Verification Theorem viscosity solution viscosity subsolution viscosity supersolution