Financial Networks

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.

Inhalt

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 Functions.- 5.1.2 Special Network Topology.- 5.1.3 Special Objective Functions and Topologies.- 5.1.4 Separable Nonlinear Optimization Problem.- 5.2 Network Optimization Algorithms.- 5.2.1 The Primal Truncated Newton Method.- 5.2.2 The Splitting Equilibration Algorithm.- 5.2.3 An Exact Equilibration Algorithm.- 5.2.4 A Primal-Dual Decomposition Method.- 5.3 Network Equilibrium Problems.- 5.4 Network Equilibrium Algorithms.- 5.4.1 The Projection Method.- 5.4.2 A General Equilibration Algorithm for Separable Link.- Cost Functions.- 5.5 Dynamic Network Problems.- 5.5.1 Tatonnement Processes for Network Equilibrium Problems.- 5.5.2 Discrete Time Algorithms.- 5.6 Sources and Notes.- III Single Country Models.- 6 Static Single Country Models.- 6.1 A General Utility Function Model.- 6.1.1 Quadratic Utility Functions.- 6.2 Qualitative Properties.- 6.3 Network Optimization Reformulation.- 6.4 Computation of Financial Equilibria.- 6.4.1 The Modified Projection Method.- 6.4.2 The Primal-Dual Method.- 6.5 Sources and Notes.- 7 Static Single Country Hedging Models.- 7.1 Models with Futures.- 7.1.1 Quadratic Utility Functions.- 7.2 Qualitative Properties.- 7.3 Network Optimization Reformulation.- 7.4 Computation of Equilibria with Futures.- 7.4.1 Numerical Examples.- 7.5 Models with Options.- 7.6 Qualitative Properties.- 7.7 Network Optimization Reformulation.- 7.8 Sources and Notes.- 8 Dynamic Single Country Models.- 8.1 Dynamic Perfect Market Financial Models.- 8.1.1 A Dynamic General Utility Function Model.- 8.1.2 A Dynamic Financial Model with Futures.- 8.1.3 A Dynamic Financial Model with Options.- 8.2 Stability Analysis.- 8.3 A Discrete Time Algorithm.- 8.3.1 Euler Method for the Section 8.1.1 Model.- 8.3.2 Euler Method for the Section 8.1.2 Model.- 8.3.3 Euler Method for the Section 8.1.3 Model.- 8.3.4 Numerical Examples.- 8.4 Sources and Notes.- 9 Static Imperfect Market Models.- 9.1 A General Imperfect Market Model.- 9.1.1 Quadratic Utility Functions.- 9.2 Qualitative Properties.- 9.3 Network Optimization in a Special Case.- 9.4 Computation of Imperfect Market Equilibria.- 9.4.1 The Modified Projection Method.- 9.4.2 Numerical Examples.- 9.4.3 The Primal-Dual Method.- 9.5 Sources and Notes.- 10 Dynamic Imperfect Market Models.- 10.1 The Dynamic Imperfect Financial Model.- 10.2 Stability Analysis.- 10.3 A Discrete Time Algorithm.- 10.3.1 Numerical Examples.- 10.4 Sources and Notes.- IV International Models.- 11 International Financial Models.- 11.1 Static International Financial Models.- 11.1.1 Quadratic Utility Functions.- 11.2 Qualitative Properties.- 11.2.1 Comparative Statics.- 11.3 International Financial Adjustment Process.- 11.4 Stability Analysis.- 11.5 Network Optimization Reformulation.- 11.6 Computation of International Equilibria.- 11.6.1 The Modified Projection Method.- 11.6.2 The Euler Method.- 11.6.3 Numerical Examples.- 11.7 Sources and Notes.- 12 International Models with Hedging.- 12.1 International Hedging Models.- 12.1.1 Special Cases and Variants of the International Hedging Model.- 12.2 Qualitative Analysis.- 12.3 International Financial Adjustment Process.- 12.4 Stability Analysis.- 12.5 Network Optimization Reformulation.- 12.6 Computational Methods.- 12.6.1 Modified Projection Method.- 12.6.2 Euler Method for the Adjustment Process of Section.- 12.3.- 12.7 Sources and Notes.- 13 Imperfect Market Models.- 13.1 International Financial Equilibrium Models.- 13.1.1 Quadratic Utility Functions.- 13.2 Qualitative Properties.- 13.3 International Financial Adjustment Process.- 13.4 Stability Analysis.- 13.5 Network Optimization in a Special Case.- 13.6 Computation of International Equilibria.- 13.6.1 The Modified Projection Method.- 13.6.2 The Euler Method.- 13.6.3 A Numerical Example.- 13.7 An Addendum.- 13.8 Sources and Notes.- V Flow of Funds and Estimation.- 14 Flow of Funds Models.- 14.1 Network Models.- 14.2 SEA for Financial Flow of Funds Estimation.- 14.2.1 An Elastic Exact Equilibration Algorithm.- 14.3 A Numerical Example.- 14.4 Sources and Notes.- VI Empirical Results.- 15 Empirical Analysis.- 15.1 Estimation of Inputs to Financial Processes.- 15.1.1 Collection of Data.- 15.2 Numerical Examples.- 15.3 Future Directions for Research.- 15.4 Conclusions and Summary.- 15.5 Sources and Notes.- A Linear Algebra and Analysis.- A.1 Linear Algebra.- A.1.1 Vectors.- A.1.2 Matrices.- A.2 Real Analysis.- A.2.1 Sets.- A.2.2 Functions.- A.3 Optimization.- A.3.1 Karush-Kuhn-Tucker Optimization Conditions.- B Probability.- B.1 Probability Theory.- B.1.1 Random Variables and Probability Distributions.- B.1.2 Expectations of a Random Variable.- B.1.2.1 Normal Distribution.- B.1.2.2 Joint Distributions.- C Black and Scholes Model.- List of Figures.- List of Tables.