Stability and controllability analysis of stochastic model for stock market prices

Abstract

In this paper, a stochastic vector differential equation model that could consider environmental effects in decision making of investors in stock exchange market has been developed, stability and controllability theorems on stock market forces were developed and analyzed. New novel results were obtained by utilizing properties of the transition (or fundamental) matrix solution (a function of the drift) and by placing some boundedness condition on the stochastic part of the model (a function of the volatility). Furthermore, asymptotic null controllability results were obtained by the non-singularity of the controllability matrix (a function of the drift) by defining some control measure on the stochastic vector equation. Examples are given using data from Nigeria stock exchange to illustrate the effectiveness of the model and simulation output results presented using MATLAB.