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. |
From inside the book
Results 1-5 of 43
Page
... Lipschitz Continuous Functions; Smoothing 401 D Stochastic Differential Equations: Random Coefficients . .403 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409 Index ...
... Lipschitz Continuous Functions; Smoothing 401 D Stochastic Differential Equations: Random Coefficients . .403 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409 Index ...
Page 19
... continuous optimal control u∗(·) exists. In Section 9 we will show that there is a continuous optimal control, for ... Lipschitz on Q if: for every compact set K ⊂ Q there exists a constant M K such that |W(t,x) − W(t,x)| ≤ MK(|t− t| + | ...
... continuous optimal control u∗(·) exists. In Section 9 we will show that there is a continuous optimal control, for ... Lipschitz on Q if: for every compact set K ⊂ Q there exists a constant M K such that |W(t,x) − W(t,x)| ≤ MK(|t− t| + | ...
Page 20
Wendell H. Fleming, Halil Mete Soner. or [Zi]) every locally Lipschitz function ... Lipschitz on Q, then V is a generalized solution of the dynamic programming ... continuous for i = 1,···,n. As above, let u∗(·) denote an optimal control ...
Wendell H. Fleming, Halil Mete Soner. or [Zi]) every locally Lipschitz function ... Lipschitz on Q, then V is a generalized solution of the dynamic programming ... continuous for i = 1,···,n. As above, let u∗(·) denote an optimal control ...
Page 33
... Lipschitz continuous on [t, t1] if and only if u(·) is bounded and Lebesgue measurable on [t, t1]. If we write · = d/ds, then the problem is to minimize (8.2) J = ∫ t1t L(s,x(s), ̇x(s))ds + ψ(x(t1)) among all Lipschitz continuous, IRn ...
... Lipschitz continuous on [t, t1] if and only if u(·) is bounded and Lebesgue measurable on [t, t1]. If we write · = d/ds, then the problem is to minimize (8.2) J = ∫ t1t L(s,x(s), ̇x(s))ds + ψ(x(t1)) among all Lipschitz continuous, IRn ...
Page 35
You have reached your viewing limit for this book.
You have reached your viewing limit for this book.
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