Formulation of Stochastic Investment Model of a Stock Market

We formulated four compartments stochastic differential equations of a stock markets from schematic diagram of stock market interaction. In stock markets, return on investment is the most important single factor to investors. Stock investors desire to know the behaviour of return on investment and its volatility at a particular period (either short or long period).The four compartments include stock price, return on investment, return on investment volatility and stock price volatility. The formulation was a modification and extension of Heston’s model of two compartments (Stock price and its volatility). In this research work, the formulation follow geometric Brownian motion model. We showed the existence and uniqueness of the solution. We conclude that the formulated model can be use to show the real application of stock market in four compartment. © 2016, The Indian Society for Probability and Statistics (ISPS).