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 72
Page
... . . . . . . . . . . . . . 280 VII.10 Large deviations for exit probabilities . . . . . . . . . . . . . . . . . 282 VII.11 Weak comparison principle in Q0 . . . . . . . . . . . . . . . . . . . . . 290 VII.12 Historical remarks ...
... . . . . . . . . . . . . . 280 VII.10 Large deviations for exit probabilities . . . . . . . . . . . . . . . . . 282 VII.11 Weak comparison principle in Q0 . . . . . . . . . . . . . . . . . . . . . 290 VII.12 Historical remarks ...
Page 1
... exit from a closed cylindrical region Q = [t0 ,t1] × O. In the other version, only controls which keep x(s) ∈ O for t ≤ s ≤ t1 are allowed (this is called a state constrained control problem.) The method of dynamic programming is the ...
... exit from a closed cylindrical region Q = [t0 ,t1] × O. In the other version, only controls which keep x(s) ∈ O for t ≤ s ≤ t1 are allowed (this is called a state constrained control problem.) The method of dynamic programming is the ...
Page 5
... exit time of x(s) from a given closed region ̄O ⊂ IRn. This is a particular case of the class of control problems to be formulated in Section 3. I.3. Finite. time. horizon. problems. In this section we formulate some classes of ...
... exit time of x(s) from a given closed region ̄O ⊂ IRn. This is a particular case of the class of control problems to be formulated in Section 3. I.3. Finite. time. horizon. problems. In this section we formulate some classes of ...
Page 6
... exit from a closed cylindrical region Q. Consider the following payoff functional J, which depends on states x(s) and controls u(s) for times s ∈ [t, τ), where τ is the smaller of t1 and the exit time of x(s) from the closure O of an ...
... exit from a closed cylindrical region Q. Consider the following payoff functional J, which depends on states x(s) and controls u(s) for times s ∈ [t, τ), where τ is the smaller of t1 and the exit time of x(s) from the closure O of an ...
Page 7
... exit from Let (t,ac) G Q, and let T' be the first time s such that 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 replace T by T'. We will give conditions under which B and ...
... exit from Let (t,ac) G Q, and let T' be the first time s such that 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 replace T by T'. We will give conditions under which B and ...
Contents
1 | |
Viscosity Solutions | 57 |
Differential Games | 375 |
A Duality Relationships 397 | 396 |
References | 409 |
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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