Stochastic Control Theory: Dynamic Programming by Makiko Nisio HARDBACK

Springer Verlag, Japan

Master the principles of stochastic control theory with this comprehensive guide to the dynamic programming principle. This book offers a systematic introduction to optimal stochastic control theory, presenting the dynamic programming principle as a powerful tool for analyzing control problems. It delves into completely observable control problems with finite horizons, constructing a nonlinear semigroup related to the dynamic programming principle and characterizing the value function via this semigroup. Control-stopping problems are also treated within the same framework, with applications to American option pricing. The book further explores zero-sum two-player time-homogeneous stochastic differential games and viscosity solutions of Isaacs equations. For partially observable control problems, it discusses stochastic parabolic equations driven by colored Wiener noises and control problems for Zakai equations, presenting a nonlinear semigroup whose generator provides the HJB equation on a Banach space. Key Features: * Systematic introduction to optimal stochastic control theory via the dynamic programming principle. * Covers completely observable control problems with finite horizons and control-stopping problems. * Discusses zero-sum two-player stochastic differential games and Isaacs equations. * Explores partially observable control problems and stochastic parabolic equations. * Provides a generalized treatment of the topic compared to previous works. This edition is ideal for researchers and advanced students in control theory, mathematics, and related fields seeking a deep understanding of stochastic control and its applications.