Controlled Markov Processes and Viscosity Solutions

✍ Scribed by Wendell H. Fleming, Halil Mete Soner

• Publisher: Springer
• Year: 2005
• Tongue: English
• Leaves: 436
• Series: Stochastic Modelling and Applied Probability
• Edition: 2nd ed.
• Category: Library

✦ Synopsis

This 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.

✦ Table of Contents

Cover......Page 1
Table of Contents......Page 6
Preface to Second Edition......Page 10
Preface......Page 11
Notation......Page 13
I Deterministic Optimal Control......Page 16
II Viscosity Solutions......Page 71
III Optimal Control of Markov Processes: Classical Solutions......Page 132
IV Controlled Markov Diffusions in IRn......Page 163
V Viscosity Solutions: Second-Order Case......Page 211
VI Logarithmic Transformations and Risk Sensitivity......Page 239
VII Singular Perturbations......Page 272
VIII Singular Stochastic Control......Page 304
IX Finite Difference Numerical Approximations......Page 332
X Applications to Finance......Page 358
XI Differential Games......Page 385
A Duality Relationships......Page 406
B Dynkin’s Formula for Random Evolutions with Markov Chain Parameters......Page 407
C Extension of Lipschitz Continuous Functions; Smoothing......Page 409
D Stochastic Differential Equations: Random Coefficients......Page 411
References......Page 417
Index......Page 432