Application of E^p-Stability to Impulsive Financial Model

In this paper, we consider an impulsive stochastic model for an investment with production and saving profiles. The conditions for financial growth for the investment are investigated under impulsive action and results are obtained using the quantitative and Ep stability methods. The impulsive stochastic differential equation considered is assumed to be driven by a process with jump and non-linear gestation properties. One of the results established shows that, in the long run, it is impossible for a financial investment to grow or dominates the prescribed average financial investment but has a threshold value for which the investment cannot grow beyond. It is also established that an $E^{p}-$ stable investment vector can be found which allows financial growth but this vector must be constrained to be in a given invariant set:It is advisable for the saving and depreciation to satisfy certain growth rates for proper income and investment growths.