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 73
Page
... exit probabilities VII.11 Weak comparison principle in Qo VII.12 Historical remarks VIII Singular Stochastic Control VIII.1 Introduction VIII.2 Formal discussion VIII.3 Singular stochastic control VIII.4 Verification theorem .. VIII.5 ...
... exit probabilities VII.11 Weak comparison principle in Qo VII.12 Historical remarks VIII Singular Stochastic Control VIII.1 Introduction VIII.2 Formal discussion VIII.3 Singular stochastic control VIII.4 Verification theorem .. VIII.5 ...
Page 1
... exit from a closed cylindrical region Q = [t0 ,t1 ] × O. In the other version, only controls which keep x(s) ∈ O for t≤s ≤ t1 are allowed (this is called a state constrained control problem.) The method of dynamic programming is the ...
... exit from a closed cylindrical region Q = [t0 ,t1 ] × O. In the other version, only controls which keep x(s) ∈ O for t≤s ≤ t1 are allowed (this is called a state constrained control problem.) The method of dynamic programming is the ...
Page 5
... exit time of x ( s ) from a given closed region Ō CIR " . This is a particular case of the class of control problems to be formulated in Section 3 . 1.3 Finite time horizon problems In this section we formulate some classes of ...
... exit time of x ( s ) from a given closed region Ō CIR " . This is a particular case of the class of control problems to be formulated in Section 3 . 1.3 Finite time horizon problems In this section we formulate some classes of ...
Page 6
... exit from a closed cylindrical region Q. Consider the following payoff functional J , which depends on states x ( s ) and controls u ( s ) for times s Є [ t , 7 ) , where 7 is the smaller of t1 and the exit time of x ( s ) from the ...
... exit from a closed cylindrical region Q. Consider the following payoff functional J , which depends on states x ( s ) and controls u ( s ) for times s Є [ t , 7 ) , where 7 is the smaller of t1 and the exit time of x ( s ) from the ...
Page 7
... exit from Q. Let ( t , x ) E Q , and let 7 ' be the first time s such that ( s , x ( s ) ) = * Q . Thus , 7 ' is the exit time of ( s , x ( s ) ) from Q , rather that from Q as for class B above . In ( 3.5 ) we now replace 7 by 7 ' . We ...
... exit from Q. Let ( t , x ) E Q , and let 7 ' be the first time s such that ( s , x ( s ) ) = * Q . Thus , 7 ' is the exit time of ( s , x ( s ) ) from Q , rather that from Q as for class B above . In ( 3.5 ) we now replace 7 by 7 ' . We ...
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 |
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 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