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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... classical sense. However, under quite general assumptions the value function is the unique viscosity solution of the HJB equation with appropriate boundary conditions. In addition, the viscosity solution framework is well suited to ...
... classical sense. However, under quite general assumptions the value function is the unique viscosity solution of the HJB equation with appropriate boundary conditions. In addition, the viscosity solution framework is well suited to ...
Page 2
... solution to the dynamic programming partial differential equation in the usual (“classical”) sense. However, in such cases V can be interpreted as a viscosity solution, as will be explained in Chapter II. Closely related to dynamic ...
... solution to the dynamic programming partial differential equation in the usual (“classical”) sense. However, in such cases V can be interpreted as a viscosity solution, as will be explained in Chapter II. Closely related to dynamic ...
Page 3
... classical mechanics. Example 2.1. Consider the production planning of a factory producing n commodities. Let x i (s), u i (s) denote respectively the inventory level and production rate for commodity i = 1,···,n at time s. In this ...
... classical mechanics. Example 2.1. Consider the production planning of a factory producing n commodities. Let x i (s), u i (s) denote respectively the inventory level and production rate for commodity i = 1,···,n at time s. In this ...
Page 4
... solution x(s)=(x 1(s), x2 (s)) to (2.4) on an infinite time horizon, say on ... solution, it has been applied to a large number of engineering problems. Let x(s) ... classical calculus of variations is to determine a function x(·) which ...
... solution x(s)=(x 1(s), x2 (s)) to (2.4) on an infinite time horizon, say on ... solution, it has been applied to a large number of engineering problems. Let x(s) ... classical calculus of variations is to determine a function x(·) which ...
Page 12
... classical mechanics, we call this function the Hamiltonian. The dynamic programming equation (5.3') is sometimes also called a HamiltonGJacobiGBellman PDE. Equation (5.3) is to be considered in Q, with appropriate terminal or boundary ...
... classical mechanics, we call this function the Hamiltonian. The dynamic programming equation (5.3') is sometimes also called a HamiltonGJacobiGBellman PDE. Equation (5.3) is to be considered in Q, with appropriate terminal or boundary ...
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