Mathematical modeling of stock market states using the system of difference equation
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Abstract
The objective of this research is to present the mathematical model of stock market states using the system of a difference equation. Beginning with the study of the analysis model in the Markov chain and converting it into a system of difference equations, which can be considered analytical solution different from finding the solution in the form of a Markov chain that requires a numerical method to find the numerical solution. In the process of determining the solution of the system of a difference equation the Wolfram Alpha program is used to help for finding the characteristic equation, eigenvalues, and eigenvectors and the use of Microsoft Excel to find the numerical solution and show the solution graph. A mathematical model about the stock market states is considered bull markets, bear markets and stagnant markets. Analysis of long-term behavior in the case of stocks studied in this the initial state of 3 cases are considered, which are [1 0 0], [0 1 0] , and [0 0 1]. The results of the study show that the long-term behavior of stock states initial with all 3 cases yields results. Likewise, there is a probability of a bull market status of 0.6250, a bear market of 0.3125 , and a stagnant market of 0.0625, suggesting that over time the stock studied has a probability of an uptrend, which will be useful mathematical information to be considered together with other trading data.
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