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 41
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... cost with infinite horizon . . . . . . . . . . . . . . . . . . 25 I.8 Calculus of variations I ... function . . . . . . . . . . . . . . . . . . . . . . 99 viii III IV V II.11 Discounted cost with infinite horizon.
... cost with infinite horizon . . . . . . . . . . . . . . . . . . 25 I.8 Calculus of variations I ... function . . . . . . . . . . . . . . . . . . . . . . 99 viii III IV V II.11 Discounted cost with infinite horizon.
Page 1
... cost function) which depends on the control inputs to the system, then the problem is one of optimal control. In ... cost functional to be optimized takes the form (3.4). During the 1950's and 1960's aerospace engineering applications ...
... cost function) which depends on the control inputs to the system, then the problem is one of optimal control. In ... cost functional to be optimized takes the form (3.4). During the 1950's and 1960's aerospace engineering applications ...
Page 2
... function V is introduced which is the optimum value of the payoff considered as a function of initial data. See ... cost function in the control problem. The reader should refer to Section 3 for notations and assumptions used in this ...
... function V is introduced which is the optimum value of the payoff considered as a function of initial data. See ... cost function in the control problem. The reader should refer to Section 3 for notations and assumptions used in this ...
Page 6
... cost function and ψ the terminal cost function. B. Control until 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 ...
... cost function and ψ the terminal cost function. B. Control until 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 ...
Page 7
... function g is called a boundary cost function, and is assumed continuous. B'. Control until 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 ...
... function g is called a boundary cost function, and is assumed continuous. B'. Control until 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 ...
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