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 84
Page 3
... assume that the demand rates di are fixed constants, known to the planner. Let x(s)=(x 1(s),···,x n(s)), u(s)=(u 1(s),···,u n(s)), d = (d1,···,dn). They are, respectively, the inventory and control vectors at time s, and the demand ...
... assume that the demand rates di are fixed constants, known to the planner. Let x(s)=(x 1(s),···,x n(s)), u(s)=(u 1(s),···,u n(s)), d = (d1,···,dn). They are, respectively, the inventory and control vectors at time s, and the demand ...
Page 8
... assume that (3-9) 11s(-) E 7/{(8, H2 /3 in §/ ?/ PlI/\ CI: I/\ :11 where denotes the restriction to [5, t1] of and T is the exit time from Q of (5, Note that (3.9) implies, in particular, that an admissible control always stays ...
... assume that (3-9) 11s(-) E 7/{(8, H2 /3 in §/ ?/ PlI/\ CI: I/\ :11 where denotes the restriction to [5, t1] of and T is the exit time from Q of (5, Note that (3.9) implies, in particular, that an admissible control always stays ...
Page 11
... assume that the value function is continuously differentiable and proceed formally to obtain a nonlinear partial differential equation satisfied by the value function. In general however, the value function is not differentiable. In ...
... assume that the value function is continuously differentiable and proceed formally to obtain a nonlinear partial differential equation satisfied by the value function. In general however, the value function is not differentiable. In ...
Page 15
... assume that (3.11) holds on the lateral boundary [t0,t1) × ∂O. This implies that, for (t, x) ∈ [t0 ,t1) × ∂O, one choice is to exit immediately from Q (thus, τ = t). Therefore, 1/(tam) g g(t>$)1 (t1$)€ 1t0;t1) X 1f it is optimal I ...
... assume that (3.11) holds on the lateral boundary [t0,t1) × ∂O. This implies that, for (t, x) ∈ [t0 ,t1) × ∂O, one choice is to exit immediately from Q (thus, τ = t). Therefore, 1/(tam) g g(t>$)1 (t1$)€ 1t0;t1) X 1f it is optimal I ...
Page 16
... assumed, in addition to (3.11), then 1/(t,5c) Z 0. Since g E 0 when (3.10) holds, (5.19) implies that the lateral ... assume W G C1(Q) Fl rather than W G G1 A situation where such a weaker assumption on W is convenient will arise in ...
... assumed, in addition to (3.11), then 1/(t,5c) Z 0. Since g E 0 when (3.10) holds, (5.19) implies that the lateral ... assume W G C1(Q) Fl rather than W G G1 A situation where such a weaker assumption on W is convenient will arise in ...
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