Theoretically, financial risks models are models of a real and a financial "uncertainty", based on both common and private information and economic theories defining the rules that financial markets comply to.
Focusing on stochastic control of partially observable systems, this book highlights its significance in real-world applications where deterministic and fully observed stochastic control are merely approximations. It begins with algebraic methods for linear theory problems, progressing to nonlinear filtering theory that addresses infinite-dimensional statistics. The text emphasizes the development of approximations and perturbation methods, aiming to provide a comprehensive framework for numerical implementation in complex control scenarios.
Focusing on both classical and advanced topics, this book delves into the estimation and control of dynamical systems, highlighting stochastic control. It uniquely integrates concepts from control theory with mathematical finance and explores differential games, offering insights that are often scattered across multiple sources. This comprehensive approach makes it a valuable resource for those seeking a deeper understanding of these interconnected fields.
This unified, revised second edition of a two-volume set is a self-contained account of quadratic cost optimal control for a large class of infinite-dimensional systems. The original editions received outstanding reviews, yet this new edition is more concise and self-contained. New material has been added to reflect the growth in the field over the past decade. There is a unique chapter on semigroup theory of linear operators that brings together advanced concepts and techniques which are usually treated independently. The material on delay systems and structural operators has not yet appeared anywhere in book form.
The book collects many techniques that are helpul in obtaining regularity results for solutions of nonlinear systems of partial differential equations. They are then applied in various cases to provide useful examples and relevant results, particularly in fields like fluid mechanics, solid mechanics, semiconductor theory, or game theory. In general, these techniques are scattered in the journal literature and developed in the strict context of a given model. In the book, they are presented independently of specific models, so that the main ideas are explained, while remaining applicable to various situations. Such a presentation will facilitate application and implementation by researchers, as well as teaching to students.