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 74
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... Finite time horizon problems 5 I.4 Dynamic programming principle 9 I.5 Dynamic programming equation 11 I.6 Dynamic programming and Pontryagin's principle . 18 I.7 Discounted cost with infinite horizon 25 1.8 Calculus of variations I ...
... Finite time horizon problems 5 I.4 Dynamic programming principle 9 I.5 Dynamic programming equation 11 I.6 Dynamic programming and Pontryagin's principle . 18 I.7 Discounted cost with infinite horizon 25 1.8 Calculus of variations I ...
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... finite time horizon Infinite Time Horizon 134 139 III.10 Viscosity solutions 145 III.11 Historical remarks 148 IV Controlled Markov Diffusions in R TM 151 IV.1 Introduction 151 IV.2 Finite time horizon problem . 152 IV.3 Hamilton ...
... finite time horizon Infinite Time Horizon 134 139 III.10 Viscosity solutions 145 III.11 Historical remarks 148 IV Controlled Markov Diffusions in R TM 151 IV.1 Introduction 151 IV.2 Finite time horizon problem . 152 IV.3 Hamilton ...
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... Finite fuel problem . 317 IX IX.1 VIII.7 Historical remarks Finite Difference Numerical Approximations Introduction .319 321 321 IX.2 Controlled discrete time Markov chains 322 IX.3 IX.4 IX.5 Finite difference approximations to HJB ...
... Finite fuel problem . 317 IX IX.1 VIII.7 Historical remarks Finite Difference Numerical Approximations Introduction .319 321 321 IX.2 Controlled discrete time Markov chains 322 IX.3 IX.4 IX.5 Finite difference approximations to HJB ...
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... finite interval, namely, I = [t, t1 ] = {s : t ≤ s ≤ t1 }, then the differential equations describing the time evolution of x(s) are (3.2) below. The cost functional to be optimized takes the form (3.4). During the 1950's and 1960's ...
... finite interval, namely, I = [t, t1 ] = {s : t ≤ s ≤ t1 }, then the differential equations describing the time evolution of x(s) are (3.2) below. The cost functional to be optimized takes the form (3.4). During the 1950's and 1960's ...
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... finite-time horizon deterministic optimal control problems. For infinite-time horizon problems, these are summarized in Section 7. I.2. Examples. We start our discussion by giving some examples. In choosing examples, in this section and ...
... finite-time horizon deterministic optimal control problems. For infinite-time horizon problems, these are summarized in Section 7. I.2. Examples. We start our discussion by giving some examples. In choosing examples, in this section and ...
Contents
1 | |
Viscosity Solutions | 57 |
Classical Solutions119 | 118 |
Controlled Markov Diffusions in R | 151 |
SecondOrder Case | 199 |
Logarithmic Transformations and Risk Sensitivity | 227 |
Singular Perturbations 261 | 260 |
Singular Stochastic Control | 293 |
Finite Difference Numerical Approximations | 321 |
Differential Games | 375 |
A Duality Relationships 397 | 396 |
References | 409 |
Index 425 | 424 |
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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 C₁ C¹(Q calculus of variations Chapter classical solution consider constant constraint controlled Markov diffusion convergence convex Corollary defined definition denote differential games dynamic programming equation dynamic programming principle Dynkin formula Example exists exit finite formulation given Hence HJB equation holds implies inequality initial data Ishii Lemma linear Lipschitz continuous Markov chain Markov control policy Markov processes 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 Section semigroup Soner stochastic control stochastic control problem stochastic differential equations subset Suppose t₁ Theorem 9.1 uniformly continuous unique value function Verification Theorem viscosity solution viscosity subsolution viscosity supersolution