1st Edition
Capital Account Liberation Methods and Applications
Along with the development of economic globalization, many countries have begun to relax their controls on their capital accounts. However, the recent financial crises in Latin American countries as well as the exchange rate crises in Southeast Asian countries have shown that there is major risk associated with capital account liberalization.
This book details the benefits and risks of capital account liberalization and explains how to take an open-door policy at the appropriate time in order to reduce the risk to the lowest possible level. Supplying a complete mathematical analysis framework for the study of the problem of capital account liberalization, it presents a few important models that have been developed for the study of capital account liberalization.
Next, the book examines the influence of capital account liberalization on the stability of financial markets by greatly expanding the scope of ordinary differential equation theory to the analysis of local stabilities. It conveys cutting-edge results while providing a general yet simple analysis framework, enriched with practical experiences from developing countries.
This book applies the theory of limit cycles to the study of problems related to capital account liberalization and discusses the contagion of financial crises among different countries. Many problems related to capital account liberalization are formulated as optimization models, showing the fact that much broader economic issues can be solved by employing optimization methods.
The book concludes by comparing the contagion effect of financial markets between nations with a relatively high degree of openness with those characterized by a moderate degree of openness. Explaining how to determine optimal capital inflows and outflows, this book provides you with the understanding required to accurately determine the characteristics, backgrounds, causes, and roles of capital account liberalization and relevant capital flows.
From Theory to Visualization: General Analysis Framework in Finance
Mathematical Applications in Finance
Synergetic Approach
Mathematical Models in Finance
Mathematical Principles in Finance
Financial Balances Equation
A Model in Canonical Form
Rationality of Behavior
Rational Expectations Principle
Model of the Russian Economy in the Crisis Period
Model of the Japanese Economy in the Crisis Period
Mathematical Estimations in Finance
Introduction
Estimation
Conclusions
Mathematical Approximations in Finance
Introduction
Main Results
Conclusions
Game Theory in Finance
Model Assumptions
Evolutionary Game Model
Stability Analysis
Model Summary
Visualization Technology in Finance
Introduction
Self-Organizing Maps
Clustering of the SOM
Identifying Systemic Financial Crises
From Micheal to Heckscher–Ohlin: ODE for Capital Account Liberation
General Theory of Ordinary Differential Equations
Basic Concepts of Ordinary Differential Equations
Systems with Constant Coefficients
Dynamic Path of Nonperforming Loans: First-Order ODE
Introduction
Hypothesis
The Model
Analysis
Conclusions
Stock Market’s Liquidity Risk: Second-Order ODE
Introduction
The Model
Exogenous Shocks
Numerical Example
Stability of Michael Model under Capital Control: Two-Dimensional Systems (I)
Introduction
The Model
Stability Analysis
Conclusions
Exchange Rate Fluctuations under Capital Control: Two-Dimensional Systems (II)
Introduction
Stability Analysis
Conclusions
Dynamic Optimization of Competitive Agents: Three-Dimensional Systems
Introduction
The Model
Analysis
Conclusions
Dynamic Heckscher–Ohlin Model: Four-Dimensional Systems
Introduction
The Model
Local Stability Analysis
Conclusions
Instability: Risk of Capital Flow
Introduction
Instability σ
Empirical Examples
Conclusion
From European to Asian Option: PDE for Capital Account Liberation
General Method of Parabolic Partial Differential Equations of Second Order
Pricing of Carbon Emission Cost: Linear Parabolic PDEs (I)
Introduction
The Model
The Calculation
Conclusions
Pricing of Foreign Currency Option: Linear Parabolic PDEs (II)
Introduction
The Model
The Solution
Pricing of Credit Default Swaps: Linear Parabolic PDEs (III)
Introduction
The Model
The Solution
Pricing of Forward Exchange Rate: Linear Parabolic PDEs (IV)
Pricing of Arithmetic Average Asian Option: Nonlinear Parabolic PDEs(I)
Introduction
The Lemma
Decomposition of the Solution
Estimation for Error
Estimation of the Error Term
Conclusions
Pricing of European Exchange Options: Nonlinear Parabolic PDEs (II)
Introduction
Foreign Exchange Option with Fractional Brownian Motion
Conclusions
From Financial Crises to Currency Substitution: Limit Cycle Theory for Capital Account Liberation
General Theory of Limit Cycles
Poincare Problem: Quadratic Polynomial Differential Systems (I)
Introduction
Foreign Assets and Foreign Liabilities: Quadratic Polynomial Differential Systems (II)
Introduction
Macroeconomic Model
Dynamics Analysis
Conclusion
Dynamics of Employment: Cubic Polynomial Differential Systems (I)
Introduction
Model
Calculation
Conclusions
Contagion of Financial Crisis: Cubic Polynomial Differential Systems (II)
Introduction
Model
Analysis
Conclusions
Contagion of Currency Crises: Fractional Differential Systems (I)
Introduction
Model and Analysis
Conclusions
Contagion of Currency Crises with Extra-Absorption: Fractional Differential Systems (II).
Introduction
Dynamic Model between Two Countries
Stability Analysis
Conclusions
Thomas Constraint in Currency Substitutions
General Theory
Extended Thomas Model
Conclusions
Relative Risk Aversion Coefficient
Introduction
Analysis of Relative Risk Aversion Coefficients
Conclusions
From Normal to Abnormal Flow of Capital: Optimizations for Capital Account Liberation
Optimization Models in Finance
Hot Money and Serial Financial Crises: Objectives with Recursively Defined Variables
Dutch Disease and Optimal Taxation: Objectives with Linear Multivariable
Optimal Growth Rate of Consumable Resource: Objectives with Discrete Variables
Dynamics of Ecosystem Service Provision: Objectives with Bivariate Factors
Illiquid Markets with Discrete Order Flows: Objectives Double Integrals
Optimal Time of Removing Quarantine Bans: Objectives with Infinite Integrals
Risk Premium and Exchange Rates: Objectives with Utility Function
Endowment Risk and Monetary Policy: Objectives with Integrals of Utility Functions
Optimal Asset Allocation: Continuous Objective Functions
Verdier Equation: Differential Constraint Conditions
Introduction
Solution of Verdier Equation
Asset Pricing Based on Quadric Programming: Discrete Objective Function
Introduction
Modeling
Solutions of (P1)
Example
Conclusions
Abnormal Flows of Capital: Discrete Constraint Conditions
Introduction
Model
Visualization
Numerical Example
Conclusions
From Underground Economics to Financial Contagion: Regressions for Capital Account Liberation
General Methods of Regression Analysis
Sample Mean
Linear Regression Model
Mean of Least-Squares Estimator
Variance of Least-Squares Estimator
Gauss–Markov Theorem
Residuals
Estimation of Error Variance
Mean-Square Forecast Error
Covariance Matrix Estimation under Homoskedasticity
Covariance Matrix Estimation under Heteroskedasticity
Measures of Fit
Who Controls the Future? Presidential Election and Economic Policy in America
Background
Model
Data
Regression Results
Gone with the Wind: Cigarette Taxes in the State
Background
Data
Linear Regression Model
Conclusions
Undercurrents: The Underground Economy and Financial Development
Background
Linear Model
Data
Conclusions
Who Cares about My Health? The Baumol Model
Background
Nonlinear Model
Regression Results
Conclusions
Sail against the Current: Held Currencies in Own Hands
Background
Model
Data
Conclusions
Nowhere to Hide: Financial Contagion Effects
Background
SVAR Modeling
Regression
Financial Contagion Effect between Markets with High Capital Account Openness
Financial Contagion Effect between Markets with At Least Moderate Capital Account Liberation
References
Index
Biography
Ying Yirong is professor of finance and is associate chair of the Department of Finance, College of Economics, Shanghai University, Shanghai, China. He earned his BSc in mathematics in 1982 from the Mathematics Department of Northwest University (China) and his PhD in mathematics in 2000 from the Mathematics Department of Xidian University. In 2002, Dr. Yirong did one year of postdoctoral study at the Institute of Contemporary Finance, Shanghai Jiao-Tong University.
Professor Yirong has taught many different courses in the areas of economics and finance, such as econometrics, financial economics, financial physics, applied statistics, financial engineering, economic cybernetics, and low carbon economy. His research interests include financial engineering, financial mathematics, securities pricing, and risk management.
Jeffrey Yi-Lin Forrest holds all his educational degrees (BSc, MS, and PhD) in pure mathematics, respectively, from Northwest University (China), Auburn University (United States), and Carnegie Mellon University (United States), where he has one-year postdoctoral experience in statistics. Currently, he is a guest or specially appointed professor in economics, finance, systems science, and mathematics at several major universities in China, including Huazhong University of Science and Technology, the National University of Defense Technology, and Nanjing University of Aeronautics and Astronautics, and a tenured professor of mathematics at the Pennsylvania State System of Higher Education (Slippery Rock campus). Since 1993, Dr. Forrest has been serving as the president of the International Institute for General Systems Studies, Inc. Along with various professional endeavors he has organized, Dr. Forrest has had the honor to mobilize scholars from more than 80 countries representing more than 50 different scientific disciplines.