System of Non-Linear Stochastic Differential Equations with Financial Market Quantities

Abstract

In this paper, two systems of modified stochastic differential equations were considered. The variable coefficient problem was solved using Ito’s theorem to obtain an analytical solutions which was used to generate various behaviors of asset values which shows as follows: (i) increase in when are fixed increases the value of asset returns. (ii) a little increase on time when return rates and stock volatility are fixed increases the value of assets.(iii) an increase in the volatility parameter increases the value of asset pricing and parameter shows the various levels of long term investment plans, (iv) increase in rate of mean-reversion parameter reduces the value of asset. (v) An increase in the volatility parameter decreases the value of asset pricing (vi) The goodness of fit probability QQplots are not statistically significant and besides do come from a common distribution which has a vital meaning in the assessment of asset values for capital market investments. Nevertheless, the Tables 1,2 and 3 are best in comparisons with Tables 4,5 and 6 in terms of predictions for capital investments. The governing investment equations are unique and therefore are found to be satisfactory.