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 28
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... principle (continued) . . . . . . . . . . . 115 II.16 Historical remarks ... Verification Theorem; finite time horizon . . . . . . . . . . . . 134 III.9 Infinite Time Horizon ...
... principle (continued) . . . . . . . . . . . 115 II.16 Historical remarks ... Verification Theorem; finite time horizon . . . . . . . . . . . . 134 III.9 Infinite Time Horizon ...
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... Verification theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299 VIII.5 Viscosity solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311 VIII.6 Finite fuel problem ...
... Verification theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299 VIII.5 Viscosity solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311 VIII.6 Finite fuel problem ...
Page 13
... Theorem 5.1 is called a Verification Theorem. Note that, by the definition (5.4) of H, (5.7) is equivalent to (5-7') u*($) Q aYg€11,}iH{f($.w*($).v) - D@W($.w*($)) + L($»w*($)»v)}Proof of Theorem 5.1. Consider any G Z/l0(t). Using ...
... Theorem 5.1 is called a Verification Theorem. Note that, by the definition (5.4) of H, (5.7) is equivalent to (5-7') u*($) Q aYg€11,}iH{f($.w*($).v) - D@W($.w*($)) + L($»w*($)»v)}Proof of Theorem 5.1. Consider any G Z/l0(t). Using ...
Page 14
... Verification Theorem 5.1, first we have to solve (5.11) with the terminal condition (5.14) V(t1,$) : m - Dav, at G R”. We guess that the solution of (5.11) and (5.14) is a quadratic function in at. So, let I/V(t,a3) : at - P(t):L' for ...
... Verification Theorem 5.1, first we have to solve (5.11) with the terminal condition (5.14) V(t1,$) : m - Dav, at G R”. We guess that the solution of (5.11) and (5.14) is a quadratic function in at. So, let I/V(t,a3) : at - P(t):L' for ...
Page 15
... Theorem 5.1 to show that V(t,x) = W(t,x) for tmin < t ≤ t1, and to find an explicit formula for the optimal u∗(s) ... Verification Theorem (Theorem 5.2) similar to Theorem 5.1. When t = t1, we have as in (5.5): (5.18) V(t1,x) = ψ(x), x ...
... Theorem 5.1 to show that V(t,x) = W(t,x) for tmin < t ≤ t1, and to find an explicit formula for the optimal u∗(s) ... Verification Theorem (Theorem 5.2) similar to Theorem 5.1. When t = t1, we have as in (5.5): (5.18) V(t1,x) = ψ(x), x ...
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