The book conclusively solves problems associated with the control and estimation of nonlinear and chaotic dynamics in ?nancial systems when these are described in the form of nonlinear ordinary di?erential equations. It then addresses problems associated with the control and estimation of ?nancial systems governed by partial di?erential 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 ?nancial engineers in decision making.
The application of state-space models in ?nancial engineering means that the heuristics and empirical methods currently in use in decision-making procedures for ?nance 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 ?nancial systems to be established.
Covering the following key areas of ?nancial engineering: (i) control and stabilization of ?nancial 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 ?nancial 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 ?ltering for nonlinear dynamics in ?nancial systems.- Nonlinear optimal control and ?ltering for ?nancial systems.- Kalman Filtering Approach for detection of option mispricing inthe Black-Scholes PDE.- Kalman Filtering approach to the detection of option mispricing inelaborated PDE ?nance models.- Corporations' default probability forecasting using theDerivative-free nonlinear Kalman Filter.- Validation of ?nancial options models using neural networks with invariance to Fourier transform.- Statistical validation of ?nancial forecasting tools with generalized likelihood ratio approaches.- Distributed validation of option price forecasting tools using a statistical fault diagnosis approach.- Stabilization of ?nancial systems dynamics through feedbackcontrol of the Black-Scholes PDE.- Stabilization of the multi-asset Black-Scholes PDE using differential?atness theory.- Stabilization of commodities pricing PDE using differential ?atnesstheory.- Stabilization of mortgage price dynamics using differential ?atness theory.v>