State-space approaches for modelling and control in financial engineering : systems theory and machine learning methods

• Main Author: Rigatos, Gerasimos G., 1971- (Author)
• Format: Electronic eBook
• Language: English
• Published: Cham, Switzerland : Springer, 2017.
• Series: Intelligent systems reference library ; v. 125.
• Subjects: Financial engineering > Mathematics.; Finance > Decision making.; Kalman filtering.; elektronické knihy; electronic books
• ISBN: 9783319528663; 9783319528656
• Physical Description: 1 online resource (xxviii, 310 pages) : illustrations (some color)

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 s...

Table of Contents:

• Foreword; Preface; Acknowledgements; Contents; 1 Systems Theory and Stability Concepts; 1.1 Outline; 1.2 Characteristics of the Dynamics of Nonlinear Systems; 1.3 Computation of Isoclines; 1.4 Stability Features of Dynamical Systems; 1.4.1 The Phase Diagram; 1.4.2 Stability Analysis of Nonlinear Systems; 1.4.3 Local Stability Properties of a Nonlinear Model; 1.5 Phase Diagrams and Equilibria; 1.5.1 Phase Diagrams for Linear Dynamical Systems; 1.5.2 Multiple Equilibria for Nonlinear Dynamical Systems; 1.5.3 Limit Cycles; 1.6 Bifurcations; 1.6.1 Bifurcations of Fixed Points.
• 1.6.2 Saddle-Node Bifurcations of Fixed Points in a One-Dimensional System1.6.3 Pitchfork Bifurcation of Fixed Points; 1.6.4 The Hopf Bifurcation; 1.7 Chaos in Dynamical Systems; 1.7.1 Chaotic Dynamics; 1.7.2 Examples of Chaotic Dynamical Systems; 2 Main Approaches to Nonlinear Control; 2.1 Outline; 2.2 Overview of Main Approaches to Nonlinear Control; 2.3 Control Based on Global Linearization Methods; 2.3.1 Overview of Differential Flatness Theory; 2.3.2 Differential Flatness for Finite Dimensional Systems; 2.4 Control Based on Approximate Linearization Methods.
• 2.4.1 Approximate Linearization Round Temporary Equilibria2.4.2 The Nonlinear H-Infinity Control; 2.4.3 Approximate Linearization with Local Fuzzy Models; 2.5 Control Based on Lyapunov Stability Analysis; 2.5.1 Transformation of Nonlinear Systems into a Canonical Form; 2.5.2 Adaptive Control Law for Nonlinear Systems; 2.5.3 Approximators of System Unknown Dynamics; 2.5.4 Lyapunov Stability Analysis for Dynamical Systems; 3 Main Approaches to Nonlinear Estimation; 3.1 Outline; 3.2 Linear State Observers; 3.3 The Continuous-Time Kalman Filter for Linear Models.
• 3.4 The Discrete-Time Kalman Filter for Linear Systems3.5 The Extended Kalman Filter for Nonlinear Systems; 3.6 Sigma-Point Kalman Filters; 3.7 Particle Filters; 3.7.1 The Particle Approximation of Probability Distributions; 3.7.2 The Prediction Stage; 3.7.3 The Correction Stage; 3.7.4 The Resampling Stage; 3.7.5 Approaches to the Implementation of Resampling; 3.8 The Derivative-Free Nonlinear Kalman Filter; 3.8.1 Conditions for solving the estimation problem in single-input nonlinear systems; 3.8.2 State Estimation with the Derivative-Free Nonlinear Kalman Filter.
• 3.8.3 Derivative-Free Kalman Filtering for multivariable Nonlinear Systems3.9 Distributed Extended Kalman Filtering; 3.9.1 Calculation of Local Extended Kalman Filter Estimations; 3.9.2 Extended Information Filtering for State Estimates Fusion; 3.10 Distributed Sigma-Point Kalman Filtering; 3.10.1 Calculation of Local Unscented Kalman Filter Estimations; 3.10.2 Unscented Information Filtering for State Estimates Fusion; 3.11 Distributed Particle Filter; 3.11.1 Distributed Particle Filtering for State Estimation Fusion; 3.11.2 Fusion of the Local Probability Density Functions.