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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... viscosity solutions. We approach stochastic control problems by the method of dynamic programming. The fundamental equation of dynamic programming is a nonlinear evolution equation for the value function. For controlled Markov diffusion ...
... viscosity solutions. We approach stochastic control problems by the method of dynamic programming. The fundamental equation of dynamic programming is a nonlinear evolution equation for the value function. For controlled Markov diffusion ...
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... 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 ...
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... viscosity solutions (See Corollary II.8.1.). By the dynamic programming principle (4.3), we have (see (5.1)) for small h > 0 infu(·)∈U0(t) { 1 h ∫ t+h t L(s,x(s),u(s))ds + 1 h [V(t + h, x(t + h)) − V(t, x)] } = 0. Since U is compact ...
... viscosity solutions (See Corollary II.8.1.). By the dynamic programming principle (4.3), we have (see (5.1)) for small h > 0 infu(·)∈U0(t) { 1 h ∫ t+h t L(s,x(s),u(s))ds + 1 h [V(t + h, x(t + h)) − V(t, x)] } = 0. Since U is compact ...
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... solutions. See Example II.2.2 below. This difficulty is circumvented by choosing the unique generalized solution which is also a viscosity solution, according to the definition to be given in Chapter II. Pontryagin's Principle. During ...
... solutions. See Example II.2.2 below. This difficulty is circumvented by choosing the unique generalized solution which is also a viscosity solution, according to the definition to be given in Chapter II. Pontryagin's Principle. During ...
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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