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 54
Page
... equation for the value function. For controlled Markov diffusion processes on n - dimensional euclidean space, the dynamic programming equation becomes a nonlinear partial differential equation of second order, called a Hamilton ...
... equation for the value function. For controlled Markov diffusion processes on n - dimensional euclidean space, the dynamic programming equation becomes a nonlinear partial differential equation of second order, called a Hamilton ...
Page
... equation only in a few cases, including the linear–quadratic regulator problem, and some special problems in finance ... partial differential equations used in these chapters concern classical solutions (not viscosity solutions.) These ...
... equation only in a few cases, including the linear–quadratic regulator problem, and some special problems in finance ... partial differential equations used in these chapters concern classical solutions (not viscosity solutions.) These ...
Page 2
... partial differential equation. See (5.3) or (7.10) below. In fact, the value function V often does not have the smoothness properties needed to interpret it as a solution to the dynamic programming partial differential equation in the ...
... partial differential equation. See (5.3) or (7.10) below. In fact, the value function V often does not have the smoothness properties needed to interpret it as a solution to the dynamic programming partial differential equation in the ...
Page 11
... partial differential equation satisfied by the value function. In general however, the value function is not differentiable. In that case a notion of “weak” solutions to this equation is needed. This will be the subject of Chapter 2 ...
... partial differential equation satisfied by the value function. In general however, the value function is not differentiable. In that case a notion of “weak” solutions to this equation is needed. This will be the subject of Chapter 2 ...
Page 12
... partial differential equation of first order, which we refer to as the dynamic programming equation or simply DPE. 1n (5.3), D@V denotes the gradient of V(t, 1t is notationally convenient to rewrite (5.3) as 3 aw —5V@®+H@@DJWwD:& where ...
... partial differential equation of first order, which we refer to as the dynamic programming equation or simply DPE. 1n (5.3), D@V denotes the gradient of V(t, 1t is notationally convenient to rewrite (5.3) as 3 aw —5V@®+H@@DJWwD:& where ...
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