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 20
Page
... Differential Games 375 XI.1 Introduction 375 XI.2 Static games 376 XI.3 Differential game formulation . . .377 XI.4 Upper and lower value functions 381 XI.5 Dynamic programming principle .382 XI.6 Value functions as viscosity solutions ...
... Differential Games 375 XI.1 Introduction 375 XI.2 Static games 376 XI.3 Differential game formulation . . .377 XI.4 Upper and lower value functions 381 XI.5 Dynamic programming principle .382 XI.6 Value functions as viscosity solutions ...
Page
... differential games. Included are differential games which arise in nonlinear H-infinity control and as totally risk-averse limits in risk-sensitive stochastic control. Other changes from the First Edition include an updated treatment in ...
... differential games. Included are differential games which arise in nonlinear H-infinity control and as totally risk-averse limits in risk-sensitive stochastic control. Other changes from the First Edition include an updated treatment in ...
Page 117
You have reached your viewing limit for this book.
You have reached your viewing limit for this book.
Page 375
You have reached your viewing limit for this book.
You have reached your viewing limit for this book.
Page 376
You have reached your viewing limit for this book.
You have reached your viewing limit for this book.
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