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

Author: Gerasimos G Rigatos
Publisher: Cham, Switzerland : Springer, 2017.
Series: Intelligent systems reference library, v. 125.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: (OCoLC)967364620
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Gerasimos G Rigatos
ISBN: 9783319528663 3319528661
OCLC Number: 981912173
Description: 1 online resource (xxviii, 310 pages) : illustrations (some color).
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
Series Title: Intelligent systems reference library, v. 125.
Responsibility: Gerasimos G. Rigatos.

Abstract:

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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