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 46
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... Dynamic programming principle . . . . . . . . . . . . . . . . . . . . . . 9 I.5 Dynamic programming equation . . . . . . . . . . . . . . . . . . . . . . 11 I.6 Dynamic programming and Pontryagin's principle. . . . . . . 18 I.7 ...
... Dynamic programming principle . . . . . . . . . . . . . . . . . . . . . . 9 I.5 Dynamic programming equation . . . . . . . . . . . . . . . . . . . . . . 11 I.6 Dynamic programming and Pontryagin's principle. . . . . . . 18 I.7 ...
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... principle (continued) . . . . . . . . . . . 115 II.16 Historical remarks ... Dynamic programming: formal description . . . . . . . . . . . . . 131 III.8 ... Dynamic programming principle . . . . . . . . . . . . . . . . . . . . . . 176 IV ...
... principle (continued) . . . . . . . . . . . 115 II.16 Historical remarks ... Dynamic programming: formal description . . . . . . . . . . . . . 131 III.8 ... Dynamic programming principle . . . . . . . . . . . . . . . . . . . . . . 176 IV ...
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... Dynamic programming principle . . . . . . . . . . . . . . . . . . . . . . 382 XI.6 Value functions as viscosity solutions . . . . . . . . . . . . . . . . . . 384 XI.7 Risk sensitive control limit game ...
... Dynamic programming principle . . . . . . . . . . . . . . . . . . . . . . 382 XI.6 Value functions as viscosity solutions . . . . . . . . . . . . . . . . . . 384 XI.7 Risk sensitive control limit game ...
Page 2
... dynamic programming, a value function V is introduced which is the optimum value of the payoff considered as a ... principle, which provides a general set of necessary conditions for an extremum. In Section 6 we develop, rather briefly, the ...
... dynamic programming, a value function V is introduced which is the optimum value of the payoff considered as a ... principle, which provides a general set of necessary conditions for an extremum. In Section 6 we develop, rather briefly, the ...
Page 9
... Dynamic programming principle It is convenient to consider a family of optimization problems with different initial conditions (t, Consider the minimum value of the payoff function as a function of this ... Dynamic programming principle.
... Dynamic programming principle It is convenient to consider a family of optimization problems with different initial conditions (t, Consider the minimum value of the payoff function as a function of this ... Dynamic programming principle.
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