Effect of Different Trend Functions with Stochastic Terms and Measurable Spaces for Capital Markets

Matrix calculus provides analytical tools for manipulating and optimising financial models based on stochastic variables, which capture market randomness, all within the theoretically rigorous framework of measurable spaces. In particular, this paper considered the problem of matrix differential calculus with stochastic term and measurable spaces for investment plans. Therefore, the uses of stochastic matrix calculus to Dangote Cement stock market prices were considered. The mathematical formulations of the problem were developed through illustrative cases namely: to established the rate of change of the stochastic matrix understudy for different trend functions such as: stochastic linear, stochastic quadratic, stochastic cubic, stochastic seasonal and stochastic exponential trends which are informative to any corporate investors. From the stochastic analysis of the problem, inflation parameters were used to examine the rate of change of relative amount of independent cement according to sales, the total cost of cement to four significant marketers to diverse localities with respect to different trend functions and their associative random fluctuations. Therefore, understanding the characteristics of each trend functions; investors can develop strategies to navigate the complexities of Dangote Cement's stock price dynamics. Finally, we related the stock price matrix elements to the measurable spaces by defining events and measurable functions which different examples were given accordingly.