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 38
Page
... boundary conditions. In addition, the viscosity solution framework is well suited to proving continuous dependence of solutions on problem data. The book begins with an introduction to dynamic programming for deterministic optimal ...
... boundary conditions. In addition, the viscosity solution framework is well suited to proving continuous dependence of solutions on problem data. The book begins with an introduction to dynamic programming for deterministic optimal ...
Page 2
... boundary data. Another approach to optimal deterministic control is via Pontryagin's principle, which provides a general set of necessary conditions for an extremum. In Section 6 we develop, rather briefly, the connection between ...
... boundary data. Another approach to optimal deterministic control is via Pontryagin's principle, which provides a general set of necessary conditions for an extremum. In Section 6 we develop, rather briefly, the connection between ...
Page 6
... boundary and terminal boundary, respectively, of Q. Given initial data (t, x) ∈ Q, let τ denote the exit time of (s,x(s)) from Q. Thus, τ = ⎧ ⎨⎩inf{s ∈ [t,t1) : x(s) ∈/O} or t1if x(s) ∈ O for all s ∈ [t,t1) Note that (τ,x(τ) ...
... boundary and terminal boundary, respectively, of Q. Given initial data (t, x) ∈ Q, let τ denote the exit time of (s,x(s)) from Q. Thus, τ = ⎧ ⎨⎩inf{s ∈ [t,t1) : x(s) ∈/O} or t1if x(s) ∈ O for all s ∈ [t,t1) Note that (τ,x(τ) ...
Page 12
... boundary conditions. Let us describe such conditions for problems of the ... data are (5.5) V(t1,:1;) : 1b(:1;), cc G IR". We now state a theorem which ... data (t, ac) and W(t,a3) : V(t, In Theorem 5.1, denotes the solution to (3.2) with ...
... boundary conditions. Let us describe such conditions for problems of the ... data are (5.5) V(t1,:1;) : 1b(:1;), cc G IR". We now state a theorem which ... data (t, ac) and W(t,a3) : V(t, In Theorem 5.1, denotes the solution to (3.2) with ...
Page 15
... data (5.16), without reference to the initial conditions for x(s). This is ... boundary conditions for the dynamic programming equation (5.3). Then we ... boundary [t0,t1) × ∂O. This implies that, for (t, x) ∈ [t0 ,t1) × ∂O, one choice ...
... data (5.16), without reference to the initial conditions for x(s). This is ... boundary conditions for the dynamic programming equation (5.3). Then we ... boundary [t0,t1) × ∂O. This implies that, for (t, x) ∈ [t0 ,t1) × ∂O, one choice ...
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