Markov Chain Models with Vector Valued Nonhomogeneous Stochastic Differential Equation in Predicting and Assessing Stock Market Returns

Abstract

The stock market performance and operation has been widely recognized as a significantly viable investment field in financial markets. In this paper, a two-model approach of Markov Chain and vector valued non-homogenous Stochastic Differential Equation (SDE) were considered for stock price movements and rate of returns respectively. Firstly, the stock prices were transformed into 3-steps transition probability matrices of each independent year. The probabilities of future stock price movements were known accordingly. The iterations of weekly predictions of price changes were considered on different days which after one iterations converged in the two years data. More so, theorems of steady-state were applied on the stochastic matrix results of Dangote Cement stock price movements. The theorems were proved to show stochastic formation of memory- less property. From the solution matrix of stochastic analysis showed that Dangote stock price data of 2023, has the best probability of price been bullish in the near future: 32%, which is a tool for proper decision making in the day-to-day management of the company; which shows it is profit making organization and are hopeful for future investment plans both short or long term respectively. Also, another form of results were obtained by developing vector valued non-homogenous stochastic differential equation which were later reduced to non-homogenous differential equation by adopting the method of variation of parameters closed form analytical solution were obtained. Example is given to illustrate the effectiveness of the system for return rates of the investments.