Preface

The present monograph contains new results and findings on control and estimation problems for financial systems and for statistical validation of computational tools used for financial decision-making. The use of state-space models in financial engineering will allow to eliminate heuristics and empirical methods currently in use in decision-making procedures for finance. On the other side, it will permit to establish methods of fault-free performance and optimality in the management of assets and capitals and methods assuring stability in the functioning of financial systems (e.g. of several financial institutions and of the banking sector). As it can be confirmed from an overview of the relevant bibliography, the systems theory-based and machine learning methods developed by the monograph stand for a genuine and significant contribution to the field of financial engineering. First, the monograph solves in a conclusive manner problems associated with the control and stabilization of nonlinear and chaotic dynamics in financial systems, when these are described in the form of nonlinear ordinary differential equations. Next, it solves in a conclusive manner problems associated with the control and stabilization of financial systems governed by spatiotemporal dynamics, that is systems described by partial differential equations (e.g. the Black–Scholes PDE and its variants). Moreover, the monograph solves the problem of filtering for the aforementioned types of financial models, that is of estimation of the entire dynamics of the financial systems when using limited information (partial observations) obtained from them. Finally, the monograph solves in a conclusive and optimal manner the problem of statistical validation of computational models and tools used to support financial engineers in decision taking. Through the methods it develops, the monograph enables to identify inconsistent and inappropriately parameterized financial models and to take necessary actions for their update. The monograph comes to address the need about decision-making in finance that will be no longer based on heuristics and intuition but will make use of computational methods and tools characterized by fault-free performance and optimality. Through the synergism of systems theory and machine learning methods, the monograph offers solutions, in a conclusive manner, to the following key problems met in financial engineering: (i) control and stabilization of financial systems