Stochastic analysis of stock price changes as markov chain in finite states

In this work, stochastic analysis of Markov chain model used to examine stock price formation in finite states. The data was subjected to 5-step transition matrix for independent stocks where transition matrix replicated the use of 3-states transition probability matrix. This enables us proffer precise condition of obtaining expected mean rate of return of each stock. Out of the four stocks studied, stock (1), stock (2), stock (3) and stock (4), it  was also discovered that stock (1) has the highest mean rate of return:4.0548 and Stock (4) has the best probability of price increasing in the near future:21%. This informs the investor about the behavior of the stocks for the purpose of decision making. From the stochastic analysis, it is revealed that stock price changes are memory-less satisfying the properties of Markov chain. i.e., it converges to a point or becomes stationary at n=5 ie S1:0.1967-0.2354,S2:0.2053-0.1913,S3:0.1972-0.2051 and S4:0.2023-0.1835. Also all states of the transition communicate and are all time dependent.