Financial Networks Statics and Dynamics [Paperback]

Financial analysis is concerned with the study of capital flows over time and space. This book presents a new theory of multi-sector, multi-instrument financial systems based on the visualization of such systems as networks. The framework is both qualitative and computational and depends crucially on the methodologies of finite-dimensional variational inequality theory for the study of statics and equilibrium states and on projected dynamical systems for the study of dynamics and disequilibrium behavior. Moreover, it adds a graphical dimension to the fundamental economic structure of financial systems and their evolution through time.Financial analysis is concerned with the study of capital flows over time and space. This book presents a new theory of multi-sector, multi-instrument financial systems based on the visualization of such systems as networks. The framework is both qualitative and computational and depends crucially on the methodologies of finite-dimensional variational inequality theory for the study of statics and equilibrium states and on projected dynamical systems for the study of dynamics and disequilibrium behavior. Moreover, it adds a graphical dimension to the fundamental economic structure of financial systems and their evolution through time.I Background.- 1 Introduction and Overview.- 1.1 Sources and Notes.- 2 Foundations of Financial Economics.- 2.1 Historic Overview.- 2.2 Utility Theory and Risk Aversion.- 2.3 Market Equilibrium.- 2.4 International Financial Economics.- 2.5 Sources and Notes.- II Methodological Foundations.- 3 Variational Inequalities.- 3.1 The Variational Inequality Problem.- 3.2 Qualitative Properties.- 3.3 Algorithms.- 3.3.1 Projection Methods.- 3.3.2 Basic Decomposition Algorithms.- 3.4 Sources and Notes.- 4 Projected Dynamical Systems.- 4.1 A Projected Dynamical System.- 4.2 Stability Analysis.- 4.3 Algorithms.- 4.4 Sources and Notes.- 5 Nonlinear Networks.- 5.1 Network Optimization Problems.- 5.1.1 Special Objective FulCs