Application of Ito’s Theorem on the Value of Economic Variables of Business Cycles

To effectively manage an investment depends mainly on the value of each economic variables. Stochastic Differential Equation (SDE) is prevailing mathematical equation used for such prediction. Four systems of SDE were re-formulated from Bouali's firm model to value economic variables of business cycles and solved using the Ito's lemma. The detailed and coincided conditions are effectively achieved which gave rise to the valuation of profits, reinvestments, flow of borrowing and value of profits as a result of quadratic function with periodic influences in time varying investment. From the stochastic analysis, the results showed as follows: (i) an increase in reinvestments and flow of borrowing increases the value of profits over time (ii) the value of profit over time in the economic structural circuit shows positive linear trend of the investment, (iii) increase in the variations of yearly reassessment rate of the business increases the value of reinvestments over time. (iv) the value of profits as a quadratic function with periodic influences grows exponentially over time. Notwithstanding, the effects of the value of the economic variables were analyzed and ic solutions of economic variables and other relevant parameters were discussed within the investment cycles. The results presented here will be beneficial to investors in taken vital decisions based on the levels of their investments.