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></div></div>.

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.

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