State-Space Approaches for Modelling and Control in Financial Engineering Systems theory and machine learning methods - Rigatos, Gerasimos G.; SpringerLink (Online service) (Cham : Springer International Publishing : Imprint: Springer, 2017)
The book conclusively solves problems associated with the control and estimation of nonlinear and chaotic dynamics in ﬁnancial systems when these are described in the form of nonlinear ordinary diﬀerential equations. It then addresses problems associated with the control and estimation of ﬁnancial systems governed by partial diﬀerential equations (e.g. the Black-Scholes partial differential equation (PDE) and its variants). Lastly it an offers optimal solution to the problem of statistical validation of computational models and tools used to support ﬁnancial engineers in decision making. The application of state-space models in ﬁnancial engineering means that the heuristics and empirical methods currently in use in decision-making procedures for ﬁnance can be eliminated. It also allows methods of fault-free performance and optimality in the management of assets and capitals and methods assuring stability in the functioning of ﬁnancial systems to be established. Covering the following key areas of ﬁnancial engineering: (i) control and stabilization of ﬁnancial systems dynamics, (ii) state estimation and forecasting, and (iii) statistical validation of decision-making tools, the book can be used for teaching undergraduate or postgraduate courses in ﬁnancial engineering. It is also a useful resource for the engineering and computer science community.
Systems theory and stability concepts -- Main approaches to nonlinear control -- Main approaches to nonlinear estimation -- Linearizing control and ﬁltering for nonlinear dynamics in ﬁnancial systems -- Nonlinear optimal control and ﬁltering for ﬁnancial systems -- Kalman Filtering Approach for detection of option mispricing in the Black-Scholes PDE -- Kalman Filtering approach to the detection of option mispricing in elaborated PDE ﬁnance models -- Corporations' default probability forecasting using the Derivative-free nonlinear Kalman Filter -- Validation of ﬁnancial options models using neural networks with invariance to Fourier transform -- Statistical validation of ﬁnancial forecasting tools with generalized likelihood ratio approaches -- Distributed validation of option price forecasting tools using a statistical fault diagnosis approach -- Stabilization of ﬁnancial systems dynamics through feedback control of the Black-Scholes PDE -- Stabilization of the multi-asset Black-Scholes PDE using differential ﬂatness theory -- Stabilization of commodities pricing PDE using differential ﬂatness theory -- Stabilization of mortgage price dynamics using differential ﬂatness theory.v> .
Keywords: Computational intelligence; Financial risk management; Nonlinear Optics; Control engineering; Dynamics; Nonlinear theories; Electronics; Computational Intelligence; Risk Management; Nonlinear Optics; Control and Systems Theory; Applied Dynamical Systems; Electronics and Microelectronics, Instrumentation