Applications of linear and nonlinear ordinary differential equations in economics and finance --- examples of Taiwan stock index TAIEX and German stock index DAX

• Main Authors: TSUNG-JUI,CHIANG LIN, 姜林宗叡
• Other Authors: Daniel Wei-Chung Miao
• Format: Others
• Language: en_US
• Published: 2019
• Online Access: http://ndltd.ncl.edu.tw/handle/sn435w

博士 === 國立臺灣科技大學 === 財務金融研究所 === 107 === ABSTRACT Among all kinds of macroeconomic indicators, the stock market prices are an important leading indicator used to reflect investors’ expectations for the future economy. In the past, the stock prices are mostly analyzed by statistical models in finance. Often used models include financial time series models and stochastic process. Different from statistical methods, the approach of the dynamic system and differential equations is applied in this study to model the stock index. This mathematical instrument originates from physics and is widely applied in many research field such as Biology, Control Theory, Economics. However, if the movement of the studied subject is too dynamic, modelling the movement will be difficult. Therefore, “parabola approximation” and “dynamic integration” are specifically used to solve nonlinear differential equations in this study. Several models are built step by step from one-coefficient ordinary differential equations, two-coefficient nonlinear ordinary differential equations to generalized parabola differential equations. Examples of two stock indices, Taiwan TAIEX and German DAX are performed. The best choice of characterizing the stock index prices from the models of the same type is recommended for different series of the stock index prices from the empirical study results. In this way, we can provide a new viewpoint for explaining the trends of the stock indices and in the future we may evaluate the derivatives underlying the stock indices.