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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... G C'k( if there exist E open with E C E and Q5 G Ck(E) such that ac) for all an G E. Spaces C£'(E),C1I;(E) are ... Q0 I {t[),t1) X IR”, X <©| O H T O H>—l \/ Given O C R" open Q:1t0vt1)X O: Q:1t01t11X6 8*Q : xvi Notation.
... G C'k( if there exist E open with E C E and Q5 G Ck(E) such that ac) for all an G E. Spaces C£'(E),C1I;(E) are ... Q0 I {t[),t1) X IR”, X <©| O H T O H>—l \/ Given O C R" open Q:1t0vt1)X O: Q:1t01t11X6 8*Q : xvi Notation.
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... (Q0 ×U). We call L the running cost function and ψ the terminal cost function. B. Control until exit from a closed cylindrical region Q ... g(Ta a3(T))XT<t1 + ¢(x(t1))XTIt1 Here X denotes an indicator function. 6 I. Deterministic Optimal ...
... (Q0 ×U). We call L the running cost function and ψ the terminal cost function. B. Control until exit from a closed cylindrical region Q ... g(Ta a3(T))XT<t1 + ¢(x(t1))XTIt1 Here X denotes an indicator function. 6 I. Deterministic Optimal ...
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... G 3*Q. Thus, T' is the exit time of (s,a:(s)) from Q, rather that from Q as for class B above. In (3.5) we now ... Q0. Let Q be a where T is the exit time of (s, from This. function, such that g(t,£l3) (15, I13) G {(50,251) X 1R" (3.6) !P ...
... G 3*Q. Thus, T' is the exit time of (s,a:(s)) from Q, rather that from Q as for class B above. In (3.5) we now ... Q0. Let Q be a where T is the exit time of (s, from This. function, such that g(t,£l3) (15, I13) G {(50,251) X 1R" (3.6) !P ...
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... G Q0 >< IR" H(tv'/Bap) : S125 {_p ' .f(t:$vv) _ L(tv $1 14)} ' 1n analogy with a quantity occurring in classical mechanics, we call this function the Hamiltonian. The dynamic programming equation (5.3') is sometimes also called a ...
... G Q0 >< IR" H(tv'/Bap) : S125 {_p ' .f(t:$vv) _ L(tv $1 14)} ' 1n analogy with a quantity occurring in classical mechanics, we call this function the Hamiltonian. The dynamic programming equation (5.3') is sometimes also called a ...
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... g(t, See Example 11.2.3. At such points, strict inequality holds in (5.19) ... Q0.) For (t, ac) G Q define a set-valued map F* (t, m) by F*<r.r> - {f<r.r.r> ... G 'u*(s,a3* Substituting this into the state dynamics yields (5.22) G F*(s, 5 G ...
... g(t, See Example 11.2.3. At such points, strict inequality holds in (5.19) ... Q0.) For (t, ac) G Q define a set-valued map F* (t, m) by F*<r.r> - {f<r.r.r> ... G 'u*(s,a3* Substituting this into the state dynamics yields (5.22) G F*(s, 5 G ...
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