1st Edition

# Capital Account Liberation Methods and Applications

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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 (

*P*1)

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

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.